document_title: Factor analysis

question_text: who is credited with promoting the use of factor analysis and why

question_tokens: who is credited with promoting the use of factor analysis and why

text: Factor analysis

text: Statistical model[edit]

text: Definition[edit]

text:
Suppose we have a set of

p

{\displaystyle p}

 observable random variables,

x

1

,
…
,

x

p

{\displaystyle x_{1},\dots ,x_{p}}

 with means

μ

1

,
…
,

μ

p

{\displaystyle \mu _{1},\dots ,\mu _{p}}

.

text:
Suppose for some unknown constants

l

i
j

{\displaystyle l_{ij}}

 and

k

{\displaystyle k}

 unobserved random variables

F

j

{\displaystyle F_{j}}

 (called "common factors," because they influence all the observed random variables), where

i
∈

1
,
…
,
p

{\displaystyle i\in {1,\dots ,p}}

 and

j
∈

1
,
…
,
k

,

{\displaystyle j\in {1,\dots ,k},}

 where

k
<
p

{\displaystyle k<p}

, we have

text:
Here, the

ε

i

{\displaystyle \varepsilon _{i}}

 are unobserved stochastic error terms with zero mean and finite variance, which may not be the same for all

i

{\displaystyle i}

.

text: In matrix terms, we have

text:
If we have

n

{\displaystyle n}

 observations, then we will have the dimensions

x

p
×
n

{\displaystyle x_{p\times n}}

,

L

p
×
k

{\displaystyle L_{p\times k}}

, and

F

k
×
n

{\displaystyle F_{k\times n}}

. Each column of

x

{\displaystyle x}

 and

F

{\displaystyle F}

 denotes values for one particular observation, and matrix

L

{\displaystyle L}

 does not vary across observations.

text:
Also we will impose the following assumptions on

F

{\displaystyle F}

:

text:
F

{\displaystyle F}

 and

ε

{\displaystyle \varepsilon }

 are independent.

E

(
F
)
=
0.

{\displaystyle \mathrm {E} (F)=0.}

C
o
v

(
F
)
=
I

{\displaystyle \mathrm {Cov} (F)=I}

 (to make sure that the factors are uncorrelated).

text:
Any solution of the above set of equations following the constraints for

F

{\displaystyle F}

 is defined as the factors, and

L

{\displaystyle L}

 as the loading matrix.

text:
Suppose

C
o
v

(
x
−
μ
)
=
Σ

{\displaystyle \mathrm {Cov} (x-\mu )=\Sigma }

. Then note that from the conditions just imposed on

F

{\displaystyle F}

, we have

text: or

text: or

text:
Note that for any orthogonal matrix

Q

{\displaystyle Q}

, if we set

L
=
L
Q

{\displaystyle L=LQ}

 and

F
=

Q

T

F

{\displaystyle F=Q^{T}F}

, the criteria for being factors and factor loadings still hold. Hence a set of factors and factor loadings is unique only up to an orthogonal transformation.

text: Example[edit]

text: Suppose a psychologist has the hypothesis that there are two kinds of intelligence, "verbal intelligence" and "mathematical intelligence", neither of which is directly observed. Evidence for the hypothesis is sought in the examination scores from each of 10 different academic fields of 1000 students. If each student is chosen randomly from a large population, then each student's 10 scores are random variables. The psychologist's hypothesis may say that for each of the 10 academic fields, the score averaged over the group of all students who share some common pair of values for verbal and mathematical "intelligences" is some constant times their level of verbal intelligence plus another constant times their level of mathematical intelligence, i.e., it is a combination of those two "factors". The numbers for a particular subject, by which the two kinds of intelligence are multiplied to obtain the expected score, are posited by the hypothesis to be the same for all intelligence level pairs, and are called "factor loading" for this subject. For example, the hypothesis may hold that the average student's aptitude in the field of astronomy is

text: The numbers 10 and 6 are the factor loadings associated with astronomy. Other academic subjects may have different factor loadings.

text: Two students having identical degrees of verbal intelligence and identical degrees of mathematical intelligence may have different aptitudes in astronomy because individual aptitudes differ from average aptitudes. That difference is called the "error" — a statistical term that means the amount by which an individual differs from what is average for his or her levels of intelligence (see errors and residuals in statistics).

text: The observable data that go into factor analysis would be 10 scores of each of the 1000 students, a total of 10,000 numbers. The factor loadings and levels of the two kinds of intelligence of each student must be inferred from the data.

text: Mathematical model of the same example[edit]

text:
In the following, matrices will be indicated by indexed variables. "Subject" indices will be indicated using letters a,b and c, with values running from 1 to

N

a

{\displaystyle N_{a}}

 which is equal to 10 in the above example.  "Factor" indices will be indicated using letters p, q and r, with values running from 1 to

N

p

{\displaystyle N_{p}}

 which is equal to 2 in the above example. "Instance" or "sample" indices will be indicated using letters i,j and k, with values running from 1 to

N

i

{\displaystyle N_{i}}

. In the example above, if a sample of

N

i

=
1000

{\displaystyle N_{i}=1000}

 students responded to the

N

a

=
10

{\displaystyle N_{a}=10}

 questions, the ith student's score for the ath question are given by

x

a
i

{\displaystyle x_{ai}}

. The purpose of factor analysis is to characterize the correlations between the variables

x

a

{\displaystyle x_{a}}

 of which the

x

a
i

{\displaystyle x_{ai}}

 are a particular instance, or set of observations. In order for the variables to be on equal footing, they are normalized:

text: where the sample mean is:

text: and the sample variance is given by:

text: The factor analysis model for this particular sample is then:

text: or, more succinctly:

text: where

text:
F

1
,
i

{\displaystyle F_{1,i}}

 is the ith student's "verbal intelligence",

F

2
,
i

{\displaystyle F_{2,i}}

 is the ith student's "mathematical intelligence",

ℓ

a
p

{\displaystyle \ell _{ap}}

 are the factor loadings for the ath subject, for p = 1, 2.

text: In matrix notation, we have

text: Observe that by doubling the scale on which "verbal intelligence"—the first component in each column of F—is measured, and simultaneously halving the factor loadings for verbal intelligence makes no difference to the model. Thus, no generality is lost by assuming that the standard deviation of the factors for verbal intelligence is 1. Likewise for mathematical intelligence. Moreover, for similar reasons, no generality is lost by assuming the two factors are uncorrelated with each other. In other words:

text:
where

δ

p
q

{\displaystyle \delta _{pq}}

 is the Kronecker delta (0 when

p
≠
q

{\displaystyle p\neq q}

 and 1 when

p
=
q

{\displaystyle p=q}

).The errors are assumed to be independent of the factors:

text: Note that, since any rotation of a solution is also a solution, this makes interpreting the factors difficult. See disadvantages below. In this particular example, if we do not know beforehand that the two types of intelligence are uncorrelated, then we cannot interpret the two factors as the two different types of intelligence. Even if they are uncorrelated, we cannot tell which factor corresponds to verbal intelligence and which corresponds to mathematical intelligence without an outside argument.

text:
The values of the loadings L, the averages μ, and the variances of the "errors" ε must be estimated given the observed data X and F (the assumption about the levels of the factors is fixed for a given F).
The "fundamental theorem" may be derived from the above conditions:

text:
The term on the left is the (a,b) term of the correlation matrix (an

N

a

×

N

a

{\displaystyle N_{a}\times N_{a}}

 matrix) of the observed data, and its

N

a

{\displaystyle N_{a}}

 diagonal elements will be 1's. The last term on the right will be a diagonal matrix with terms less than unity. The first term on the right is the "reduced correlation matrix" and will be equal to the correlation matrix except for its diagonal values which will be less than unity. These diagonal elements of the reduced correlation matrix are called "communalities" (which represent the fraction of the variance in the observed variable that is accounted for by the factors):

text:
The sample data

z

a
i

{\displaystyle z_{ai}}

 will not, of course, exactly obey the fundamental equation given above due to sampling errors, inadequacy of the model, etc. The goal of any analysis of the above model is to find the factors

F

p
i

{\displaystyle F_{pi}}

 and loadings

ℓ

a
p

{\displaystyle \ell _{ap}}

 which, in some sense, give a "best fit" to the data. In factor analysis, the best fit is defined as the minimum of the mean square error in the off-diagonal residuals of the correlation matrix:[9]

text: This is equivalent to minimizing the off-diagonal components of the error covariance which, in the model equations have expected values of zero. This is to be contrasted with principal component analysis which seeks to minimize the mean square error of all residuals.[9] Before the advent of high speed computers, considerable effort was devoted to finding approximate solutions to the problem, particularly in estimating the communalities by other means, which then simplifies the problem considerably by yielding a known reduced correlation matrix. This was then used to estimate the factors and the loadings. With the advent of high-speed computers, the minimization problem can be solved iteratively with adequate speed, and the communalities are calculated in the process, rather than being needed beforehand. The MinRes algorithm is particularly suited to this problem, but is hardly the only iterative means of finding a solution.

text: If the solution factors are allowed to be correlated (as in oblimin rotation, for example), then the corresponding mathematical model uses skew coordinates rather than orthogonal coordinates.

text: Geometric interpretation[edit]

text:
The parameters and variables of factor analysis can be given a geometrical interpretation. The data (

z

a
i

{\displaystyle z_{ai}}

), the factors (

F

p
i

{\displaystyle F_{pi}}

) and the errors (

ε

a
i

{\displaystyle \varepsilon _{ai}}

) can be viewed as vectors in an

N

i

{\displaystyle N_{i}}

-dimensional Euclidean space (sample space), represented as

z

a

{\displaystyle \mathbf {z} _{a}}

,

F

p

{\displaystyle \mathbf {F} _{p}}

 and

ε

a

{\displaystyle {\boldsymbol {\varepsilon }}_{a}}

 respectively. Since the data are standardized, the data vectors are of unit length (

z

a

⋅

z

a

=
1

{\displaystyle \mathbf {z} _{a}\cdot \mathbf {z} _{a}=1}

). The factor vectors define an

N

p

{\displaystyle N_{p}}

-dimensional linear subspace (i.e. a hyperplane) in this space, upon which the data vectors are projected orthogonally. This follows from the model equation

text:
and the independence of the factors and the errors:

F

p

⋅

ε

a

=
0

{\displaystyle \mathbf {F} _{p}\cdot {\boldsymbol {\varepsilon }}_{a}=0}

. In the above example, the hyperplane is just a 2-dimensional plane defined by the two factor vectors. The projection of the data vectors onto the hyperplane is given by

text:
and the errors are vectors from that projected point to the data point and are perpendicular to the hyperplane. The goal of factor analysis is to find a hyperplane which is a "best fit" to the data in some sense, so it doesn't matter how the factor vectors which define this hyperplane are chosen, as long as they are independent and lie in the hyperplane. We are free to specify them as both orthogonal and normal (

F

p

⋅

F

q

=

δ

p
q

{\displaystyle \mathbf {F} _{p}\cdot \mathbf {F} _{q}=\delta _{pq}}

) with no loss of generality. After a suitable set of factors are found, they may also be arbitrarily rotated within the hyperplane, so that any rotation of the factor vectors will define the same hyperplane, and also be a solution. As a result, in the above example, in which the fitting hyperplane is two dimensional, if we do not know beforehand that the two types of intelligence are uncorrelated, then we cannot interpret the two factors as the two different types of intelligence. Even if they are uncorrelated, we cannot tell which factor corresponds to verbal intelligence and which corresponds to mathematical intelligence, or whether the factors are linear combinations of both, without an outside argument.

text:
The data vectors

z

a

{\displaystyle \mathbf {z} _{a}}

 have unit length. The correlation matrix for the data is given by

r

a
b

=

z

a

⋅

z

b

{\displaystyle r_{ab}=\mathbf {z} _{a}\cdot \mathbf {z} _{b}}

. The correlation matrix can be geometrically interpreted as the cosine of the angle between the two data vectors

z

a

{\displaystyle \mathbf {z} _{a}}

 and

z

b

{\displaystyle \mathbf {z} _{b}}

. The diagonal elements will clearly be 1's and the off diagonal elements will have absolute values less than or equal to unity. The "reduced correlation matrix" is defined as

text: The goal of factor analysis is to choose the fitting hyperplane such that the reduced correlation matrix reproduces the correlation matrix as nearly as possible, except for the diagonal elements of the correlation matrix which are known to have unit value.  In other words, the goal is to reproduce as accurately as possible the cross-correlations in the data. Specifically, for the fitting hyperplane, the mean square error in the off-diagonal components

text: is to be minimized, and this is accomplished by minimizing it with respect to a set of orthonormal factor vectors. It can be seen that

text:
The term on the right is just the covariance of the errors. In the model, the error covariance is stated to be a diagonal matrix and so the above minimization problem will in fact yield a "best fit" to the model: It will yield a sample estimate of the error covariance which has its off-diagonal components minimized in the mean square sense. It can be seen that since the

z
^

a

{\displaystyle {\hat {z}}_{a}}

 are orthogonal projections of the data vectors, their length will be less than or equal to the length of the projected data vector, which is unity. The square of these lengths are just the diagonal elements of the reduced correlation matrix. These diagonal elements of the reduced correlation matrix are known as "communalities":

text: Large values of the communalities will indicate that the fitting hyperplane is rather accurately reproducing the correlation matrix. It should be noted that the mean values of the factors must also be constrained to be zero, from which it follows that the mean values of the errors will also be zero.

text: Practical implementation[edit]

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text: Types of factor analysis[edit]

text: Exploratory factor analysis (EFA) is used to identify complex interrelationships among items and group items that are part of unified concepts.[10]  The researcher makes no a priori assumptions about relationships among factors.[10]

text: Confirmatory factor analysis (CFA) is a more complex approach that tests the hypothesis that the items are associated with specific factors.[10] CFA uses structural equation modeling to test a measurement model whereby loading on the factors allows for evaluation of relationships between observed variables and unobserved variables.[10]  Structural equation modeling approaches can accommodate measurement error, and are less restrictive than least-squares estimation.[10]  Hypothesized models are tested against actual data, and the analysis would demonstrate loadings of observed variables on the latent variables (factors), as well as the correlation between the latent variables.[10]

text: Types of factoring[edit]

text: Principal component analysis (PCA) is a widely used method for factor extraction, which is the first phase of EFA.[10] Factor weights are computed to extract the maximum possible variance, with successive factoring continuing until there is no further meaningful variance left.[10] The factor model must then be rotated for analysis.[10]

text: Canonical factor analysis, also called Rao's canonical factoring, is a different method of computing the same model as PCA, which uses the principal axis method. Canonical factor analysis seeks factors which have the highest canonical correlation with the observed variables. Canonical factor analysis is unaffected by arbitrary rescaling of the data.

text: Common factor analysis, also called principal factor analysis (PFA) or principal axis factoring (PAF), seeks the least number of factors which can account for the common variance (correlation) of a set of variables.

text: Image factoring is based on the correlation matrix of predicted variables rather than actual variables, where each variable is predicted from the others using multiple regression.

text: Alpha factoring is based on maximizing the reliability of factors, assuming variables are randomly sampled from a universe of variables. All other methods assume cases to be sampled and variables fixed.

text: Factor regression model is a combinatorial model of factor model and regression model; or alternatively, it can be viewed as the hybrid factor model,[11] whose factors are partially known.

text: Terminology[edit]

text: Factor loadings: Commonality is the square of standardized outer loading of an item. Analogous to Pearson's r, the squared factor loading is the percent of variance in that indicator variable explained by the factor. To get the percent of variance in all the variables accounted for by each factor, add the sum of the squared factor loadings for that factor (column) and divide by the number of variables. (Note the number of variables equals the sum of their variances as the variance of a standardized variable is 1.) This is the same as dividing the factor's eigenvalue by the number of variables.

text: Interpreting factor loadings: By one rule of thumb in confirmatory factor analysis, loadings should be .7 or higher to confirm that independent variables identified a priori are represented by a particular factor, on the rationale that the .7 level corresponds to about half of the variance in the indicator being explained by the factor. However, the .7 standard is a high one and real-life data may well not meet this criterion, which is why some researchers, particularly for exploratory purposes, will use a lower level such as .4 for the central factor and .25 for other factors. In any event, factor loadings must be interpreted in the light of theory, not by arbitrary cutoff levels.

text: In oblique rotation, one gets both a pattern matrix and a structure matrix. The structure matrix is simply the factor loading matrix as in orthogonal rotation, representing the variance in a measured variable explained by a factor on both a unique and common contributions basis. The pattern matrix, in contrast, contains coefficients which just represent unique contributions. The more factors, the lower the pattern coefficients as a rule since there will be more common contributions to variance explained. For oblique rotation, the researcher looks at both the structure and pattern coefficients when attributing a label to a factor. Principles of oblique rotation can be derived from both cross entropy and its dual entropy.[12]

text: Communality: The sum of the squared factor loadings for all factors for a given variable (row) is the variance in that variable accounted for by all the factors, and this is called the communality. The communality measures the percent of variance in a given variable explained by all the factors jointly and may be interpreted as the reliability of the indicator.

text: Spurious solutions: If the communality exceeds 1.0, there is a spurious solution, which may reflect too small a sample or the researcher has too many or too few factors.

text: Uniqueness of a variable: That is, uniqueness is the variability of a variable minus its communality.

text: Eigenvalues/characteristic roots: The eigenvalue for a given factor measures the variance in all the variables which is accounted for by that factor. The ratio of eigenvalues is the ratio of explanatory importance of the factors with respect to the variables. If a factor has a low eigenvalue, then it is contributing little to the explanation of variances in the variables and may be ignored as redundant with more important factors. Eigenvalues measure the amount of variation in the total sample accounted for by each factor.

text: Extraction sums of squared loadings: Initial eigenvalues and eigenvalues after extraction (listed by SPSS as "Extraction Sums of Squared Loadings") are the same for PCA extraction, but for other extraction methods, eigenvalues after extraction will be lower than their initial counterparts. SPSS also prints "Rotation Sums of Squared Loadings" and even for PCA, these eigenvalues will differ from initial and extraction eigenvalues, though their total will be the same.

text: Factor scores (also called component scores in PCA): are the scores of each case (row) on each factor (column). To compute the factor score for a given case for a given factor, one takes the case's standardized score on each variable, multiplies by the corresponding loadings of the variable for the given factor, and sums these products. Computing factor scores allows one to look for factor outliers. Also, factor scores may be used as variables in subsequent modeling. (Explained from PCA not from Factor Analysis perspective).

text: Criteria for determining the number of factors[edit]

text: Researchers wish to avoid such subjective or arbitrary criteria for factor retention as "it made sense to me". A number of objective methods have been developed to solve this problem, allowing users to determine an appropriate range of solutions to investigate. Methods may not agree. For instance, the parallel analysis may suggest 5 factors while Velicer's MAP suggests 6, so the researcher may request both 5 and 6-factor solutions and discuss each in terms of their relation to external data and theory.

text: Modern criteria[edit]

text: Horn's parallel analysis (PA): A Monte-Carlo based simulation method that compares the observed eigenvalues with those obtained from uncorrelated normal variables. A factor or component is retained if the associated eigenvalue is bigger than the 95th percentile of the distribution of eigenvalues derived from the random data. PA is one of the most recommended rules for determining the number of components to retain,[citation needed] but many programs fail to include this option (a notable exception being R ).[13] However, Formann provided both theoretical and empirical evidence that its application might not be appropriate in many cases since its performance is considerably influenced by sample size, item discrimination, and type of correlation coefficient.[14]

text: Velicer’s (1976) MAP test[15] “involves a complete principal components analysis followed by the examination of a series of matrices of partial correlations” (p. 397). The squared correlation for Step “0” (see Figure 4) is the average squared off-diagonal correlation for the unpartialed correlation matrix. On Step 1, the first principal component and its associated items are partialed out. Thereafter, the average squared off-diagonal correlation for the subsequent correlation matrix is then computed for Step 1. On Step 2, the first two principal components are partialed out and the resultant average squared off-diagonal correlation is again computed. The computations are carried out for k minus one step (k representing the total number of variables in the matrix). Thereafter, all of the average squared correlations for each step are lined up and the step number in the analyses that resulted in the lowest average squared partial correlation determines the number of components or factors to retain.[15] By this method, components are maintained as long as the variance in the correlation matrix represents systematic variance, as opposed to residual or error variance. Although methodologically akin to principal components analysis, the MAP technique has been shown to perform quite well in determining the number of factors to retain in multiple simulation studies.[16][17][18] This procedure is made available through SPSS's user interface. See Courtney (2013)[19] for guidance.

text: Older methods[edit]

text: Kaiser criterion: The Kaiser rule is to drop all components with eigenvalues under 1.0 – this being the eigenvalue equal to the information accounted for by an average single  item. The Kaiser criterion is the default in SPSS and most statistical software but is not recommended when used as the sole cut-off criterion for estimating the number of factors as it tends to over-extract factors.[20] A variation of this method has been created where a researcher calculates confidence intervals for each eigenvalue and retains only factors which have the entire confidence interval greater than 1.0.[16][21]

text:
Scree plot[22]:
The Cattell scree test plots the components as the X axis and the corresponding eigenvalues as the Y-axis.  As one moves to the right, toward later components, the eigenvalues drop. When the drop ceases and the curve makes an elbow toward less steep decline, Cattell's scree test says to drop all further components after the one starting the elbow.  This rule is sometimes criticised for being amenable to researcher-controlled "fudging".  That is, as picking the "elbow" can be subjective because the curve has multiple elbows or is a smooth curve, the researcher may be tempted to set the cut-off at the number of factors desired by their research agenda.[citation needed]

text: Variance explained criteria: Some researchers simply use the rule of keeping enough factors to account for 90% (sometimes 80%) of the variation.  Where the researcher's goal emphasizes parsimony (explaining variance with as few factors as possible), the criterion could be as low as 50%.

text: Rotation methods[edit]

text: The unrotated output maximizes variance accounted for by the first and subsequent factors, and forces the factors to be orthogonal. This data-compression comes at the cost of having most items load on the early factors, and usually, of having many items load substantially on more than one factor. Rotation serves to make the output more understandable, by seeking so-called "Simple Structure": A pattern of loadings where each item loads strongly on only one of the factors, and much more weakly on the other factors. Rotations can be orthogonal or oblique (allowing the factors to correlate).

text: Varimax rotation is an orthogonal rotation of the factor axes to maximize the variance of the squared loadings of a factor (column) on all the variables (rows) in a factor matrix, which has the effect of differentiating the original variables by extracted factor. Each factor will tend to have either large or small loadings of any particular variable. A varimax solution yields results which make it as easy as possible to identify each variable with a single factor. This is the most common rotation option. However, the orthogonality (i.e., independence) of factors is often an unrealistic assumption. Oblique rotations are inclusive of orthogonal rotation, and for that reason, oblique rotations are a preferred method.[23]

text: Quartimax rotation is an orthogonal alternative which minimizes the number of factors needed to explain each variable. This type of rotation often generates a general factor on which most variables are loaded to a high or medium degree. Such a factor structure is usually not helpful to the research purpose.

text: Equimax rotation is a compromise between varimax and quartimax criteria.

text: Direct oblimin rotation is the standard method when one wishes a non-orthogonal (oblique) solution – that is, one in which the factors are allowed to be correlated. This will result in higher eigenvalues but diminished interpretability of the factors. See below.[clarification needed]

text: Promax rotation is an alternative non-orthogonal (oblique) rotation method which is computationally faster than the direct oblimin method and therefore is sometimes used for very large datasets.

text: In psychometrics[edit]

text: History[edit]

text: Charles Spearman pioneered the use of factor analysis in the field of psychology and is sometimes credited with the invention of factor analysis. He discovered that school children's scores on a wide variety of seemingly unrelated subjects were positively correlated, which led him to postulate that a general mental ability, or g, underlies and shapes human cognitive performance. His postulate now enjoys broad support in the field of intelligence research, where it is known as the g theory.

text: Raymond Cattell expanded on Spearman's idea of a two-factor theory of intelligence after performing his own tests and factor analysis. He used a multi-factor theory to explain intelligence. Cattell's theory addressed alternate factors in intellectual development, including motivation and psychology. Cattell also developed several mathematical methods for adjusting psychometric graphs, such as his "scree" test and similarity coefficients. His research led to the development of his theory of fluid and crystallized intelligence, as well as his 16 Personality Factors theory of personality. Cattell was a strong advocate of factor analysis and psychometrics. He believed that all theory should be derived from research, which supports the continued use of empirical observation and objective testing to study human intelligence.

text: Applications in psychology[edit]

text: Factor analysis is used to identify "factors" that explain a variety of results on different tests. For example, intelligence research found that people who get a high score on a test of verbal ability are also good on other tests that require verbal abilities. Researchers explained this by using factor analysis to isolate one factor, often called crystallized intelligence or verbal intelligence, which represents the degree to which someone is able to solve problems involving verbal skills.

text: Factor analysis in psychology is most often associated with intelligence research. However, it also has been used to find factors in a broad range of domains such as personality, attitudes, beliefs, etc. It is linked to psychometrics, as it can assess the validity of an instrument by finding if the instrument indeed measures the postulated factors.

text: Advantages[edit]

text:
Reduction of number of variables, by combining two or more variables into a single factor. For example, performance at running, ball throwing, batting, jumping and weight lifting could be combined into a single factor such as general athletic ability. Usually, in an item by people matrix, factors are selected by grouping related items. In the Q factor analysis technique, the matrix is transposed and factors are created by grouping related people: For example, liberals, libertarians, conservatives and socialists, could form separate groups.
Identification of groups of inter-related variables, to see how they are related to each other. For example, Carroll used factor analysis to build his Three Stratum Theory. He found that a factor called "broad visual perception" relates to how good an individual is at visual tasks. He also found a "broad auditory perception" factor, relating to auditory task capability. Furthermore, he found a global factor, called "g" or general intelligence, that relates to both "broad visual perception" and "broad auditory perception". This means someone with a high "g" is likely to have both a high "visual perception" capability and a high "auditory perception" capability, and that "g" therefore explains a good part of why someone is good or bad in both of those domains.

text: Disadvantages[edit]

text:
"...each orientation is equally acceptable mathematically. But different factorial theories proved to differ as much in terms of the orientations of factorial axes for a given solution as in terms of anything else, so that model fitting did not prove to be useful in distinguishing among theories." (Sternberg, 1977[24]). This means all rotations represent different underlying processes, but all rotations are equally valid outcomes of standard factor analysis optimization. Therefore, it is impossible to pick the proper rotation using factor analysis alone.
Factor analysis can be only as good as the data allows. In psychology, where researchers often have to rely on less valid and reliable measures such as self-reports, this can be problematic.
Interpreting factor analysis is based on using a "heuristic", which is a solution that is "convenient even if not absolutely true".[25] More than one interpretation can be made of the same data factored the same way, and factor analysis cannot identify causality.

text: Exploratory factor analysis versus principal components analysis[edit]

text: While exploratory factor analysis and principal component analysis are treated as synonymous techniques in some fields of statistics, this has been criticised (e.g. Fabrigar et al., 1999;[26] Suhr, 2009[27]). In factor analysis, the researcher makes the assumption that an underlying causal model exists, whereas PCA is simply a variable reduction technique.[28] Researchers have argued that the distinctions between the two techniques may mean that there are objective benefits for preferring one over the other based on the analytic goal.  If the factor model is incorrectly formulated or the assumptions are not met, then factor analysis will give erroneous results. Factor analysis has been used successfully where adequate understanding of the system permits good initial model formulations. Principal component analysis employs a mathematical transformation to the original data with no assumptions about the form of the covariance matrix. The aim of PCA is to determine a few linear combinations of the original variables that can be used to summarize the data set without losing much information.[29]

text: Arguments contrasting PCA and EFA[edit]

text: Fabrigar et al. (1999)[26] address a number of reasons used to suggest that principal components analysis is not equivalent to factor analysis:

text:
It is sometimes suggested that principal components analysis is computationally quicker and requires fewer resources than factor analysis. Fabrigar et al. suggest that the ready availability of computer resources have rendered this practical concern irrelevant.
PCA and factor analysis can produce similar results. This point is also addressed by Fabrigar et al.; in certain cases, whereby the communalities are low (e.g., .40), the two techniques produce divergent results. In fact, Fabrigar et al. argue that in cases where the data correspond to assumptions of the common factor model, the results of PCA are inaccurate results.
There are certain cases where factor analysis leads to 'Heywood cases'. These encompass situations whereby 100% or more of the variance in a measured variable is estimated to be accounted for by the model. Fabrigar et al. suggest that these cases are actually informative to the researcher, indicating a misspecified model or a violation of the common factor model. The lack of Heywood cases in the PCA approach may mean that such issues pass unnoticed.
Researchers gain extra information from a PCA approach, such as an individual’s score on a certain component – such information is not yielded from factor analysis. However, as Fabrigar et al. contend, the typical aim of factor analysis – i.e. to determine the factors accounting for the structure of the correlations between measured variables – does not require knowledge of factor scores and thus this advantage is negated. It is also possible to compute factor scores from a factor analysis.

text: Variance versus covariance[edit]

text: Factor analysis takes into account the random error that is inherent in measurement, whereas PCA fails to do so. This point is exemplified by Brown (2009),[30] who indicated that, in respect to the correlation matrices involved in the calculations:

text: "In PCA, 1.00s are put in the diagonal meaning that all of the variance in the matrix is to be accounted for (including variance unique to each variable, variance common among variables, and error variance). That would, therefore, by definition, include all of the variance in the variables. In contrast, in EFA, the communalities are put in the diagonal meaning that only the variance shared with other variables is to be accounted for (excluding variance unique to each variable and error variance). That would, therefore, by definition, include only variance that is common among the variables."

text: For this reason, Brown (2009) recommends using factor analysis when theoretical ideas about relationships between variables exist, whereas PCA should be used if the goal of the researcher is to explore patterns in their data.

text: Differences in procedure and results[edit]

text: The differences between principal components analysis and factor analysis are further illustrated by Suhr (2009):[27]

text:
PCA results in principal components that account for a maximal amount of variance for observed variables; FA account for common variance in the data.
PCA inserts ones on the diagonals of the correlation matrix; FA adjusts the diagonals of the correlation matrix with the unique factors.
PCA minimizes the sum of squared perpendicular distance to the component axis; FA estimates factors which influence responses on observed variables.
The component scores in PCA represent a linear combination of the observed variables weighted by eigenvectors; the observed variables in FA are linear combinations of the underlying and unique factors.
In PCA, the components yielded are uninterpretable, i.e. they do not represent underlying ‘constructs’; in FA, the underlying constructs can be labeled and readily interpreted, given an accurate model specification.

text: In marketing[edit]

text: The basic steps are:

text:
Identify the salient attributes consumers use to evaluate products in this category.
Use quantitative marketing research techniques (such as surveys) to collect data from a sample of potential customers concerning their ratings of all the product attributes.
Input the data into a statistical program and run the factor analysis procedure. The computer will yield a set of underlying attributes (or factors).
Use these factors to construct perceptual maps and other product positioning devices.

text: Information collection[edit]

text: The data collection stage is usually done by marketing research professionals. Survey questions ask the respondent to rate a product sample or descriptions of product concepts on a range of attributes. Anywhere from five to twenty attributes are chosen. They could include things like: ease of use, weight, accuracy, durability, colourfulness, price, or size. The attributes chosen will vary depending on the product being studied. The same question is asked about all the products in the study. The data for multiple products is coded and input into a statistical program such as R, SPSS, SAS, Stata, STATISTICA, JMP, and SYSTAT.

text: Analysis[edit]

text: The analysis will isolate the underlying factors that explain the data using a matrix of associations.[31] Factor analysis is an interdependence technique. The complete set of interdependent relationships is examined. There is no specification of dependent variables, independent variables, or causality. Factor analysis assumes that all the rating data on different attributes can be reduced down to a few important dimensions. This reduction is possible because some attributes may be related to each other. The rating given to any one attribute is partially the result of the influence of other attributes. The statistical algorithm deconstructs the rating (called a raw score) into its various components, and reconstructs the partial scores into underlying factor scores. The degree of correlation between the initial raw score and the final factor score is called a factor loading.

text: Advantages[edit]

text:
Both objective and subjective attributes can be used provided the subjective attributes can be converted into scores.
Factor analysis can identify latent dimensions or constructs that direct analysis may not.
It is easy and inexpensive.

text: Disadvantages[edit]

text:
Usefulness depends on the researchers' ability to collect a sufficient set of product attributes.  If important attributes are excluded or neglected, the value of the procedure is reduced.
If sets of observed variables are highly similar to each other and distinct from other items, factor analysis will assign a single factor to them.  This may obscure factors that represent more interesting relationships.[clarification needed]
Naming factors may require knowledge of theory because seemingly dissimilar attributes can correlate strongly for unknown reasons.

text: In physical and biological sciences[edit]

text: Factor analysis has also been widely used in physical sciences such as geochemistry,  hydrochemistry,[32] astrophysics and cosmology, as well as biological sciences, such as ecology, molecular biology and biochemistry.

text:
In groundwater quality management, it is important to relate the spatial distribution of different chemical
parameters to different possible sources, which have different chemical signatures. For example, a sulfide mine is likely to be associated with high levels of acidity, dissolved sulfates and transition metals. These signatures can be identified as factors through R-mode factor analysis, and the location of possible sources can be suggested by contouring the factor scores.[33]

text: In geochemistry, different factors can correspond to different mineral associations, and thus to mineralisation.[34]

text: In microarray analysis[edit]

text: Factor analysis can be used for summarizing high-density oligonucleotide DNA microarrays data at probe level for Affymetrix GeneChips. In this case, the latent variable corresponds to the RNA concentration in a sample.[35]

text: Implementation[edit]

text: Factor analysis has been implemented in several statistical analysis programs since the 1980s:

text:
BMDP
JMP (statistical software)
Python: module Scikit-learn[36]
R (with the base function factanal or fa function in package psych). Rotations are implemented in the GPArotation R package.
SAS (using PROC FACTOR or PROC CALIS)
SPSS[37]
Stata


document_title: List of towns and cities with 100,000 or more inhabitants/cityname: E

question_text: name of places starting with e in india

question_tokens: name of places starting with e in india

root

text: List of cities beginning with letter E[edit]

text:
City
Country

Eastbourne
 United Kingdom

Ebetsu
 Japan

Ebina
 Japan

Ecatepec
 Mexico

Ede
 Netherlands

Ede
 Nigeria

Edéa
 Cameroon

Edinburgh
 United Kingdom

Edirne
 Turkey

Edmonton
 Canada

Eilat
 Israel

Eindhoven
 Netherlands

Ekibastuz
 Kazakhstan

El Aaiún
 Western Sahara

El Alto
 Bolivia

El Eulma
 Algeria

El Jadida
 Morocco

El Khroub
 Algeria

El Monte
 United States

El Oued
 Algeria

El Paso
 United States

El Progreso
 Honduras

Elazığ
 Turkey

Elbląg
 Poland

Elche
 Spain

Eldoret
 Kenya

Elektrostal
 Russia

Elista
 Russia

Elizabeth
 United States

Elk Grove
 United States

El-Mahalla El-Kubra
 Egypt

Eluru
 India

English Bazar
 India

Enschede
 Netherlands

Ensenada
 Mexico

Enshi
 China

Enugu
 Nigeria

Envigado
 Colombia

Erbil
 Iraq

Erfurt
 Germany

Erie
 United States

Erlangen
 Germany

Erode
 India

Erzincan
 Turkey

Erzurum
 Turkey

Escondido
 United States

Esenler
 Turkey

Esfahan
 Iran

Eskişehir
 Turkey

Esmeraldas
 Ecuador

Espoo
 Finland

Essen
 Germany

Etawah
 India

Eugene
 United States

Eujeongbu
 South Korea

Evansville
 United States

Exeter
 United Kingdom

Ezhou
 China

tag: table


document_title: The Limehouse Golem

question_text: who is the golem in the limehouse golem

question_tokens: who is the golem in the limehouse golem

text: The Limehouse Golem

text: Plot[edit]

text: A series of murders has shaken the community of Limehouse in Victorian London to the point where people believe that only a legendary creature from dark times – the mythical so-called Golem – must be responsible. When music-hall star Elizabeth Cree is accused of poisoning her husband John on the same night as the last Golem murders, assigned Inspector John Kildare discovers evidence linking John Cree to the Golem murders, and finds himself determined to crack both cases before Elizabeth is hanged for her accused crime.

tag: p

text: Having found a diary of the Golem's crimes, written by the Golem himself in a book on the art of murder, kept in the reading room of the library, Kildare determines that the Golem must be one of the four men in the library on the date of the last entry; Dan Leno, Karl Marx, George Gissing and John Cree. Kildare acquires handwriting samples of the other three men while listening to Elizabeth's story about how she was the daughter of an unmarried mother and went from sewing sail-cloths at the docks to becoming a music-hall star.

text: When Elizabeth’s abusive mother died, she befriended Dan Leno and fell in with his music-hall troupe, performing bawdy comic songs while dressed as a man. Her act quickly becomes second in popularity only to Leno himself, but she aspires to also become a dramatic actor. John Cree, a struggling playwright, begins trying to woo her, offering her a leading part in his new play. She does not respond to his advances but her fellow performer, Aveline Ortega (María Valverde), becomes jealous and sabotages her first dramatic role.

text: Elizabeth is entrapped by the theatre’s owner, a man known as ‘Uncle’(Eddie Marsan), and is forced to pose nude for photographs and to beat him for his sexual gratification. She tells John, who offers to marry her and keep her safe. Elizabeth accepts, and Kildare notes that Uncle died suddenly only days later, leaving the theatre to Dan Leno. John’s career stalls, and he grows bitter towards Elizabeth, who supports him financially, eventually beginning an affair with Aveline and suspending work on ‘’Misery Junction’’ to spite Elizabeth. The two remained estranged until John Cree’s poisoning.

text: Kildare finally finds a handwritten copy of the play written by Cree before his death on the day that Elizabeth is to be hanged.  He gets an hour's postponement to her sentence, hoping that revealing John Cree's crimes will cause her sentence to be commuted. However, after speaking with Elizabeth, Kildare realizes that she is the true Golem rather than her husband. She killed 'Uncle', and then began committing murders as the Golem to make a lasting name for herself, poisoning her husband when he found evidence of her crimes.

text: Broken at this revelation, Kildare delays announcing the revelation that Cree was the Golem to the press until after Elizabeth is hanged, granting her the 'fame' of eliminating the Golem rather than the greater fame of being a killer. In the final scene, Dan Leno's troupe perform John's play, rewritten to tell Elizabeth's life story, but Aveline Ortega, playing the part of Elizabeth, dies accidentally during the hanging scene. Leno covers up the death and takes the curtain call dressed as Elizabeth, and we see Elizabeth take a bow on stage with him, using Leno's catchphrase: "Here we are again!"

text: Cast[edit]

text:
Bill Nighy as Inspector John Kildare
Olivia Cooke as Elizabeth Cree
Amelia Crouch as Young Elizabeth
Douglas Booth as Dan Leno
Daniel Mays as Constable George Flood
Sam Reid as John Cree
María Valverde as Aveline Ortega
Eddie Marsan as Uncle
Henry Goodman as Karl Marx
Paul Ritter as Augustus Rowley
Morgan Watkins as George Gissing
Peter Sullivan as Inspector Roberts
Adam Brown as Mr Gerrard
Clive Brunt as Charlie

tag: ul

text: Production[edit]

text: Screenwriter Jane Goldman read the book years before she was a professional screenwriter and kept it in mind as a potential project. She explains, "What’s funny is that I read the book long before I was screenwriting. I think it was the only time that I can remember when I read a book and thought, 'Gosh, I hope somebody makes a movie of this!' ... Weirdly, years later I was on a film jury together with the producer whom I had read had the rights and I asked him whatever happened to the adaptation and said that I loved the book. That is how this came about, because he said the rights were free again and asked, 'Do you want to do it?'"[3]

text: It was announced on 17 April 2015 that Alan Rickman, Olivia Cooke, and Douglas Booth had been cast in leading roles for the film, to be directed by Juan Carlos Medina.[4] Rickman later left the project due to declining health after he was diagnosed with pancreatic cancer.[5] Principal photography for The Limehouse Golem began in October 2015 in West Yorkshire, with filming taking place in locations such as Leeds and Keighley.[6] Production also took place in Manchester, with cast members Bill Nighy and Daniel Mays being spotted on set in Deansgate.[7] Principal photography concluded on 26 November 2015. Johan Söderqvist composed the film's score.[8] The film is dedicated to Rickman, who died in January 2016.[9]

text: Release[edit]

text: The film had its world premiere at the Toronto International Film Festival on 10 September 2016.[10][11] It was released in the United Kingdom on 1 September 2017[12] and in the United States on 8 September 2017, in a limited release and through video on demand by RLJ Entertainment.[13]

text: Critical reception[edit]

text: The Limehouse Golem received positive reviews from film critics. It holds a 74% approval rating on review aggregator website Rotten Tomatoes, based on 72 reviews, with a weighted average of 7.4/10.[14] Ikon London Magazine commented that "the film was exquisitely shot, with fantastic period sets, locations, and wardrobe".[15]


document_title: The Legend of Bagger Vance

question_text: where is the legend of bagger vance filmed

text: The Legend of Bagger Vance

text: Plot[edit]

text: As an old man having his sixth heart attack while playing golf, Hardy Greaves (Jack Lemmon) contemplates how his wife used to ask him (before her passing) why he insisted on playing "a game that seems destined to kill[4]" him. Explaining his love for the game, he begins the story of his childhood idol: Rannulph Junuh (Matt Damon).

text: Junuh is the favorite son of Savannah, Georgia: a noteworthy golfer from a wealthy family, he and his beautiful girlfriend named Adele Invergordon (Charlize Theron) seem to have it all. While serving as a captain in the US Army during World War I, Junuh is traumatized when his entire company is wiped out in battle. Though he earns the Medal of Honor, he disappears after the war, returning to Georgia years later as a broken-down alcoholic.

text: At the start of the Great Depression (circa 1930[5]), Adele is trying to recover her family's lost fortune by holding a four-round, two-day exhibition match between  Bobby Jones (Joel Gretsch) and Walter Hagen (Bruce McGill), the best golfers of the era, with a grand prize of $10,000, at a golf resort her father opened as the Depression struck. However, she needs a local participant to generate local interest. The young Greaves (J. Michael Moncrief) speaks up for his hero, Junuh, prompting Adele to ask her estranged lover to play.

text: Junuh is approached by a mysterious traveler carrying a suitcase, who appears while Junuh is trying to hit golf balls into the dark void of night. The man identifies himself as Bagger Vance (Will Smith) and says he will be Junuh's caddie. With Greaves as assistant caddie, Bagger helps Junuh come to grips with his personal demons and play golf again.

text: When the match starts, Jones and Hagen each play well in their distinctive ways, but the disengaged Junuh plays poorly and is far behind after the first round. With Bagger caddying for him and giving advice, Junuh rediscovers his "authentic swing" in the second round and makes up some ground. In the third round, he closes the gap even more, hitting a hole in one in the process. Meanwhile, Junuh and Adele rekindle their romance.

text: Late in the final round, Junuh disregards Bagger's advice at a crucial point and after that plays poorly. He hits a ball into a forest, where he has a traumatic World War I flashback, but Bagger's words help him to focus on the game. Junuh pulls back to a tie with Jones and Hagen, then has a chance to win on the final hole, but has the integrity to call a penalty on himself when his ball moves after he tries to remove a loose impediment.

text: Seeing Junuh has grown and matured, Bagger decides his golfer doesn't need him any more. With the 18th hole left unfinished, Bagger gives the position of caddie to Greaves, and leaves Junuh as mysteriously as he came.

text: Though losing a chance to win because of the penalty, Junuh sinks an improbable putt and the match ends in a gentlemanly three-way tie. The three golfers shake hands with all of Savannah cheering. Junuh and Adele get back together.

text: The old Greaves wakes up and sees an unaged Bagger Vance beckoning him from a distance. Hardy follows, presumably to the afterlife.

text: Cast[edit]

text:
Will Smith as Bagger Vance
Matt Damon as Rannulph Junuh
Charlize Theron as Adele Invergordon
Bruce McGill as Walter Hagen
Joel Gretsch as Bobby Jones
J. Michael Moncrief as Hardy Greaves
Lane Smith as Grantland Rice
Peter Gerety as Neskaloosa
Wilbur Fitzgerald as Roy
Jack Lemmon (uncredited) as Narrator / Old Hardy Greaves

text: Production notes [edit]

text: Similarities to the Hindu epic Mahabharata[edit]

text: The plot is loosely based on the Hindu sacred text the Bhagavad Gita, where the Warrior/Hero Arjuna (R. Junuh) refuses to fight.  The god Krishna appears as Bhagavan (Bagger Vance) to help him to follow his path as the warrior and hero that he was meant to be. This relationship was fully explained by Steven J. Rosen in his book Gita on the Green, for which Steven Pressfield wrote the foreword.[6]

text: Filming[edit]

text: Portions of the exhibition match were set at the Kiawah Island Golf Resort in South Carolina, United States, considered one of the toughest in the country. The scene in which Greaves has a heart attack was shot on No. 11 of the resort's Cougar Point golf course.  The final hole in the film was temporary, so the filming did not interfere with the club activities, and cost US $200,000 to build.  However, most of the golf scenes were filmed at Colleton River Plantation,[7] just off Hilton Head Island.[8] Certain segments of this film were also filmed in Savannah and Jekyll Island, Georgia.[9]

text: Reception[edit]

text: Critical response  [edit]

text: Reaction from the movie critics was mixed. Rotten Tomatoes gives the film a score of 43% based on 129 reviews, with an average rating of 5.2/10. The website's critical consensus reads, "Despite the talent involved in The Legend of Bagger Vance, performances are hindered by an inadequate screenplay full of flat characters and bad dialogue. Also, not much happens, and some critics are offended by how the film glosses over issues of racism."[10] On Metacritic, the film has a weighted average score of 47 out of 100, based on 35 critics, indicating "mixed or average reviews".[11]

text: Film critic Roger Ebert, who gave it 3½ stars, said,  "It handles a sports movie the way Billie Holiday handled a trashy song, by finding the love and pain beneath the story. Redford and his writer, Jeremy Leven, starting from a novel by Steven Pressfield, are very clear in their minds about what they want to do. They want to explain why it is possible to devote your life to the love of golf, and they want to hint that golf and life may have a lot in common".[12] The BBC's George Perry called it a  "sumptuously photographed film" but added that "in spite of being lovely to look at, it is pretentious piffle, although Will Smith shows skill and subtlety in his ludicrous role".[13]

text: Time called it one of the most "embarrassing" films of recent years for its treatment of African Americans and the use of a "Magical African-American Friend".[3]

text: Box office[edit]

text: The Legend of Bagger Vance opened at #3 at the U.S. box office, grossing $11,516,712 from 2,061 theaters.[14] According to the Internet Movie Database, the film's total gross came to $30,695,227, far short of its estimated $80 million budget.[15]

text: Soundtrack [edit]

text: The now out-of-print soundtrack to The Legend of Bagger Vance was released on November 7, 2000. It was mostly written by Rachel Portman, except for tracks one ("My Best Wishes"), thirteen ("Bluin’ the Blues") and fourteen ("Mood Indigo"), which were written by Fats Waller, Muggsy Spanier and Duke Ellington, respectively.

text:
My Best Wishes (2:27)
The Legend of Bagger Vance (2:11)
Savannah Needs a Hero (4:53)
Bagger Offers to Caddy for Junuh (4:07)
Bagger & Hardy Measure the Course at Night (2:32)
The Day of the Match Dawns (3:07)
Birdie (1:46)
Junuh Sees the Field (5:11)
Hole in One (2:30)
Junuh Comes Out of the Woods (3:55)
Bagger Leaves (3:12)
Old Hardy Joins Bagger by the Sea (5:50)
Bluin' the Blues (2:27)
Mood Indigo (3:07)

tag: ol

text: Total soundtrack time: 47:15


document_title: Grand Theft Auto V

question_text: when did gta 5 come out on pc

question_tokens: when did gta 5 come out on pc

text: Grand Theft Auto V

text: Gameplay

text: Grand Theft Auto V is an action-adventure game[2] played from either a first-person[3][b] or third-person perspective.[4] Players complete missions—linear scenarios with set objectives—to progress through the story.[5] Outside of the missions, players may freely roam the open world. Composed of the San Andreas open countryside area, including the fictional Blaine County, and the fictional city of Los Santos, the world is much larger in area than earlier entries in the series.[6][c] It may be fully explored after the game's beginning without restriction, although story progress unlocks more gameplay content.[8]

text: Players use melee attacks, firearms and explosives to fight enemies,[d] and may run, jump, swim or use vehicles to navigate the world.[e] To accommodate the map's size, the game introduces vehicle types absent in its predecessor Grand Theft Auto IV, such as fixed-wing aircraft.[11] In combat, auto-aim and a cover system may be used as assistance against enemies.[12] Should players take damage, their health meter will gradually regenerate to its halfway point.[f] Players respawn at hospitals when their health depletes.[10] If players commit crimes, law enforcement agencies may respond as indicated by a "wanted" meter in the head-up display (HUD).[13] Stars displayed on the meter indicate the current wanted level (for example, at the maximum five-star level, police helicopters and SWAT teams swarm to lethally dispatch players).[14][g] Law enforcement officers will search for players who leave the wanted vicinity. The meter enters a cool-down mode and eventually recedes when players are hidden from the officers' line of sight that displays on the mini-map.[16][h]

text: The single-player mode lets players control three characters: Michael De Santa, Trevor Philips and Franklin Clinton—criminals whose stories interconnect as they complete missions. Some missions are completed with only one character and others feature two or three.[18] Outside the missions, players may switch between characters at will by a directional compass on the HUD. The game may switch characters automatically during missions to complete certain objectives. A character's compass avatar will flash red if he is in danger and needs help, and flash white if he has a strategic advantage.[19] Though players completes missions as any of the three protagonists, the more difficult heist missions require aid from AI-controlled accomplices with unique skill sets like computer hacking and driving. If an accomplice survives a successful heist, they take a cut from the cash reward[20] and may be available for later missions with improvements to their unique skills.[21] Some heists afford multiple strategies; in a holdup mission, players may either stealthily subdue civilians with an incapacitating agent or conspicuously storm the venue with guns drawn.[22]

text: Each character has a set of eight skills that represent their ability in certain areas such as shooting and driving. Though skills improve through play, each character has a skill with expertise by default (i.e. Trevor's flying skill).[23] The eighth "special" skill determines the effectiveness in performing an ability that is unique to each respective character. Michael enters bullet time in combat, Franklin slows down time while driving, and Trevor deals twice as much damage to enemies while taking half as much in combat.[24] A meter on each character's HUD depletes when an ability is being used and regenerates when players perform skilful actions (for example, drifting in vehicles as Franklin or performing headshots as Michael).[25]

text: While free roaming the game world, players may engage in context-specific activities such as scuba diving underwater or BASE jumping via parachute. Each character has a smartphone for contacting friends, starting activities and accessing an in-game Internet.[26] The Internet lets players trade in stocks via a stock market.[27] Players may purchase properties such as garages and businesses, upgrade the weapons and vehicles in each character's arsenal, and customise their appearance by purchasing outfits, haircuts and tattoos.[28]

text: Plot

text: Michael Townley, Trevor Philips, and Brad Snider partake in a botched robbery in Ludendorff, North Yankton. Nine years later, Michael is living under witness protection with his family in Los Santos, under the alias Michael De Santa. Across town, gangbanger Franklin Clinton is working for a corrupt Armenian car salesman and meets Michael while attempting to fraudulently repossess his son's car; the two later become friends. When Michael finds his wife Amanda sleeping with her tennis coach, he and Franklin chase the coach to a mansion, which Michael destroys in anger. The owner turns out to be the girlfriend of Martin Madrazo, a Mexican drug lord who demands compensation to avoid further violence. Michael returns to a life of crime to obtain the money, enlisting Franklin as an accomplice. With the help of Michael's old friend Lester, a crippled hacker, they perform a jewellery shop heist to pay off the debt. Trevor, who now lives in a trailer park on the outskirts of Los Santos and believes Michael was killed in their failed robbery, hears of the heist and realises that it was Michael's handiwork; Trevor surprises Michael and reunites with him after tracking down his home.

text: The personal lives of the protagonists begin to spiral out of control. Michael's increasingly erratic behaviour prompts his family to leave him, and when he becomes a movie producer at film studio Richards Majestic, he comes into conflict with Devin Weston, a self-made billionaire venture capitalist and corporate raider who vows revenge after his attempts to shut down the studio are thwarted by Michael and his lawyer dies in an accident. Franklin rescues his friend Lamar Davis from gangster and former friend Harold "Stretch" Joseph, who repeatedly attempts to kill Lamar to prove himself to his new brethren. Trevor's reckless efforts to consolidate his control over various black markets in Blaine County see him waging war against The Lost outlaw motorcycle club, several Latin American street gangs, rival meth dealers, hillbillies, private security firm Merryweather, and Triad kingpin Wei Cheng.

text: Federal Investigation Bureau (FIB) agents Dave Norton and Steve Haines contact Michael and demand that he perform a series of operations to undermine a rival agency, the International Affairs Agency (IAA).[i] Under Steve's direction and with Lester's help, they attack an armoured convoy carrying funds intended for the IAA and steal an experimental chemical weapon from an IAA-controlled lab. As Steve comes under increasing scrutiny, he forces Michael and Franklin to erase any evidence being used against him from the FIB servers. Michael takes the opportunity to wipe the data on his own activities, destroying Steve's leverage over him. Michael, Trevor, Franklin, and Lester start planning their most daring feat ever: raiding the Union Depository's gold bullion reserve.

text: Michael reconciles with his family. However, Trevor discovers that Brad was not imprisoned as led to believe, but killed during the heist and buried in the grave marked for Michael. Trevor's feelings of betrayal cause friction within the group and threaten to undermine their Union Depository plans. When Michael and Dave are betrayed by Steve and become caught in a Mexican standoff between the FIB, IAA, and Merryweather, Trevor, feeling that he is the only one that has the right to kill Michael, comes to their aid. Despite not forgiving Michael, Trevor agrees to perform the Union Depository heist and part ways with him afterwards.

text: The heist is completed successfully, but Franklin is then approached separately by Steve and Dave, who contend that Trevor is a liability, and Devin, who wants retribution for Michael's betrayal. Franklin has three choices: kill Trevor, kill Michael, or attempt to save both in a suicide mission. Should Franklin choose to kill either Michael or Trevor, he ceases contact with the man he spares and returns to his old life.[30][31] Otherwise, the trio withstand an onslaught from the FIB and Merryweather before going on to kill Steve, Stretch, Wei, and Devin. Michael and Trevor reconcile, and the three cease working together but remain friends.[32]

text: Development

text: Rockstar North began to develop Grand Theft Auto V in 2009, following Grand Theft Auto IV's release.[33] Development was conducted by a team of more than 1,000 people, including Rockstar North's core team and staff from parent company Rockstar Games' studios around the world.[34] The proprietary Rockstar Advanced Game Engine (RAGE) was overhauled for the game to improve its draw distance rendering capabilities.[35] The Euphoria and Bullet software handle additional animation and rendering tasks.[36] Having become familiar with the PlayStation 3 and Xbox 360 hardware over time, Rockstar found they were able to push the consoles' graphical capabilities further than in previous games.[37] Analyst estimations place the game's combined development and marketing budget at more than GB£170 million (US$265 million), which would make it the most expensive game ever made at that time.[38][j]

text: The open world was modelled on Southern California and Los Angeles,[40] and its design and in-game render constituted much of the game's early work.[41] Key members of the game world production team took field research trips throughout the region and documented their research with photo and video footage.[37] Google Maps projections of Los Angeles were used by the team to help design Los Santos' road networks.[42][43] To reflect and reproduce Los Angeles' demographic spread, the developers studied census data and watched documentaries about the city.[35] The team considered creating the open world the most technically demanding aspect of the game's production.[33]

text: A fundamental design goal from the outset was to innovate on the series core structure by giving players control of three lead protagonists instead of one.[41] The idea was first raised during Grand Theft Auto: San Andreas' development, but contemporaneous hardware restrictions made it infeasible.[44] Having developed two Grand Theft Auto IV episodic expansion packs featuring new protagonists in 2009, the team wanted to base Grand Theft Auto V around three simultaneously controlled protagonists.[11] The team viewed it as a spiritual successor to many of their previous games (such as Grand Theft Auto IV, Red Dead Redemption and Max Payne 3), and designed it to improve upon their gameplay mechanics.[19][45] They sought to improve the action gameplay by refining the shooting mechanics and cover system,[46] and reworked the driving mechanics to correct Grand Theft Auto IV's difficult vehicle controls.[47]

text: After an audition process, Ned Luke, Shawn Fonteno and Steven Ogg were selected to portray Michael, Franklin and Trevor, respectively.[48] Their performances were mostly recorded using motion capture technology,[49] but dialogue for scenes with characters seated in vehicles was recorded in studios instead.[50] The game is the first in its series to feature an original score, composed by a team of producers collaborating with each other over several years.[51] Licensed music provided by an in-game radio is also used.[52] The team licensed more than 241 tracks shared between fifteen radio stations, with an additional two stations providing talk radio.[k] Some of the tracks were written specifically for the game, such as rapper and producer Flying Lotus' original work composed for the FlyLo FM radio station he hosts.[54]

text: The game was first announced by Rockstar Games on 25 October 2011.[55] They released its debut trailer one week later,[56] with an official press release acknowledging its setting.[57] Journalists noted that the announcement ignited widespread anticipation within the gaming industry, which they owed to the cultural significance of the series.[58][59][60] The game missed its original projected Q2 2013 release date, pushed back to 17 September to allow for further polishing.[61] To spur pre-order game sales, Rockstar collaborated with several retail outlets to make a special edition with extra in-game features.[62] They ran a viral marketing strategy with a website for a fictional religious cult, "The Epsilon Program", that offered users the chance to feature in the game as members of the cult.[63]

text: A re-release of the game was announced for Microsoft Windows (PC), PlayStation 4 and Xbox One at E3 2014. This enhanced version features an increased draw distance, finer texture details, denser traffic, upgraded weather effects, and new wildlife and vegetation.[64] It includes a new on-foot first-person view option, which required the development team to overhaul the animation system to accommodate first-person gameplay.[3] The PlayStation 4 and Xbox One versions were released on 18 November 2014.[65] The PC version, initially scheduled for simultaneous release with the console versions,[64] was delayed until 14 April 2015.[66] According to Rockstar, it required extra development time for "polish".[67] The PC version is capable of 60 frames per second gameplay at 4K resolution, and the Rockstar Editor lets players capture and edit gameplay videos.[68] Design director Imran Sarwar announced in October 2017 that the game would not receive single-player downloadable content, despite Rockstar's original plan for a 2014 release, citing the continued growth of Grand Theft Auto Online and the upcoming Red Dead Redemption 2 as reasons for the cancellation.[69]

text: Reception

text: Initial release

text:
Reception

Aggregate score

Aggregator
Score

Metacritic
97/100[70][71]

Review scores

Publication
Score

Edge
10/10[72]

Eurogamer
9/10[73]

Famitsu
40/40[75]

Game Informer
9.75/10[74]

GameSpot
9/10[76]

GamesRadar+
[77]

IGN
10/10[78]

Joystiq
[79]

Play
97/100[80]

The Escapist
[81]

text: Grand Theft Auto V was released to critical acclaim.[82] Metacritic, which assigns a normalised rating in the 0–100 range, calculated an average score of 97 out of 100 based on 50 reviews for the PlayStation 3 version[70] and 58 reviews for the Xbox 360 version.[71] The game is Metacritic's fifth-highest rated, tied with a number of others.[l] Reviewers liked the multiple lead character formula,[84][74][78] heist mission design[85][86][87] and presentation,[16][80][88] but some did not agree on the quality of the story and characters.[73][79][81][89] IGN's Keza MacDonald called Grand Theft Auto V "one of the very best video games ever made",[78] and Play considered it "generation-defining" and "exceptional".[80] Edge wrote that it is a "remarkable achievement" in open world design and storytelling,[90] while The Daily Telegraph's Tom Hoggins declared it a "colossal feat of technical engineering".[91] It became only the second ever western developed game to be awarded a perfect score from the Japanese video game magazine Famitsu.[92]

text: CNET's Jeff Bakalar felt that the game encouraged players to engage with all three characters.[93] Edge found that switching players was helpful for avoiding long travel times to mission start points.[84] Because of the switching mechanic, Game Informer's Matt Bertz noted that players are kept "in the thick of the action" during shootouts.[74] Eurogamer's Tom Bramwell wrote that switching added a tactical element to shootouts as characters set up in strategic outposts would cause fewer "shooting gallery" situations than previous instalments.[73] IGN's MacDonald felt the switching feature gave players more choice in their approach and made missions less predictable.[78]

text: Giant Bomb's Jeff Gerstmann considered the heist missions a welcome deviation from series typical mission structure.[85] Eurogamer's Bramwell likened them to "blockbuster set-pieces"[73] and GameSpot's Carolyn Petit cited the 1995 film Heat as a stylistic influence on their design.[76] Joystiq's Xav de Matos felt creativity and methodical approaches were encouraged.[79] Polygon's Chris Plante likened rapid character switching during heist missions to "film editing, with the player serving as editor, switching rapidly to the most interesting perspective for any moment".[86] Computer and Video Games' Andy Kelly felt that overall mission design was more diverse than and lacked the escort errands of its predecessors.[87]

text: Edge praised the game's graphical fidelity and absence of load screens.[84] Play complimented the draw distances and weather and lighting systems.[80] Eurogamer's Bramwell considered the lighting system to be the game's biggest advancement.[73] Official Xbox Magazine (OXM)'s Mikel Reparaz thought that the game was "probably the Xbox 360's greatest technical achievement", and was surprised that the open world could render on the console.[89] Reviewers lauded the open world's design, some further complimenting the game for streamlining Los Angeles' geography into a well-designed city space.[16][73] GameTrailers' Brandon Jones considered the Los Angeles emulation authentic and the open world "full of voice and personality".[94] IGN and PlayStation Official Magazine (OPM) made favourable comparisons between Los Santos and Grand Theft Auto IV's Liberty City.[78][88] OXM's Reparez felt Los Santos surpassed the "grey and gritty" Liberty City.[89] Reviewers praised the world's satire of contemporary American culture[16][73][78][79][87]—OPM's Joel Gregory opined that "the scathing social commentary is, of course, present and correct".[88]

text: Destructoid's Jim Sterling called the sound design "impeccable" and praised the actors' performances, original soundtrack and licensed music use.[16] IGN and Giant Bomb commended the music selection and felt that the original score enhanced dramatic tension during missions.[78][85] GameSpot's Petit wrote that the score "lends missions more cinematic flavour".[76] Edge said that the licensed music enhanced the city's "already remarkable sense of space" and that the original score improved the atmosphere of the gameplay. They summarised the game as "a compendium of everything Rockstar has learnt about the power of game music in the past decade".[95]

text: Many reviewers found the land-based vehicles more responsive and easier to control than in previous games.[90][76][80][88][89] Game Informer's Bertz explained that "cars have a proper sense of weight, while retaining the agility necessary for navigating through traffic at high speeds".[74] In addition to the vehicle handling, most reviewers noted the shooting mechanics were tighter than they had been in previous games,[74][76][78] but Destructoid's Sterling felt that in spite of the improvements, auto-aim was "twitchy and unreliable" and cover mechanics "still come off as dated and unwieldy".[16] Some reviewers felt the game solved a continual problem by adding mid-mission checkpoints.[73][78][91]

text: The story and characters—particularly Trevor—polarised reviewers. Some felt that the narrative was not as well written as previous Rockstar games and cited Grand Theft Auto IV and Red Dead Redemption's plot strengths.[73][74][79][89] Others felt that the protagonists' contrasting personalities gave the narrative tighter pacing.[16][84][78][86] GamesRadar's Hollander Cooper thought the game negated inconsistencies in the story of previous entries, whose single lead protagonists had muddled morality.[77] GameSpot's Petit considered Trevor in particular a "truly horrible, terrifying, psychotic human being—and a terrific character".[76] Eurogamer's Bramwell found Trevor "shallow and unconvincing", and felt that his eccentricities hurt the narrative and overshadowed Michael and Franklin's character development.[73] Joystiq's de Matos faulted the protagonists' lack of likability for him, and found the ambivalence between Michael and Trevor a tired plot device as their conflict grew into a "seemingly endless cycle".[79] The Escapist's Greg Tito had difficulty connecting with the characters' emotions since they acted out of greed with no sense of morality and thus gave players little reason to support them.[81]

text: Re-release

text:
Re-release

Aggregate score

Aggregator
Score

Metacritic
(PC) 96/100[96]
(PS4) 97/100[97]
(XONE) 97/100[98]

Review scores

Publication
Score

Game Informer
9.75/10[100]

GameSpot
9/10[99]

IGN
10/10[101][102]

PC Gamer (US)
92%[103]

VideoGamer.com
10/10[104][105]

text: Grand Theft Auto V's re-release, similarly, received critical acclaim. Metacritic calculated an average score of 97 out of 100 based on 66 reviews for the PlayStation 4 version[97] and 14 reviews for the Xbox One version,[98] and 96 out of 100 based on 48 reviews for the PC version.[96] Game Informer's Andrew Reiner considered the addition of first-person "another significant breakthrough for the series" in the vein of Grand Theft Auto III's shift to third-person from Grand Theft Auto's bird's-eye view.[100] GameSpot's Mark Walton found that playing in first-person heightened the impact of Grand Theft Auto V's violence, which made him reflect on morality and character motivation more than before.[99] VideoGamer.com opined that players feel like inhabitants of the world, rather than "guns attached to a floating camera".[104] IGN's Dan Stapleton found the game more immersive in first-person, creating a "surprisingly different experience".[101] VideoGamer.com praised the "finer details" in first-person animations like camera lean when players take corners on motorcycles, or the navigational instruments in plane cockpits.[104] Reviewers found playing the game more difficult in first-person,[99][101] but Game Informer's Reiner preferred the challenge.[100]

text: GameSpot's Walton thought the graphics improvements made the open world "even more spectacular", especially because of improved spatial anti-aliasing. Of the first-person view, he said that "at ground level everything looks bigger and more imposing" because of the improved graphics.[99] IGN's Stapleton favoured the PlayStation 4 version's graphics over the Xbox One, but thought both consoles rendered the game well and maintained mostly consistent frame rates.[101] He praised the increased frame rate and graphics options offered in the PC version.[106] VideoGamer.com called the console version's frame rate so consistent it was "scarcely believable",[104] although GameSpot's Walton cited occasional frame rate dips.[99] GameSpot's Peter Brown opined that the PC version let players "witness the full extent of Rockstar's admirable handiwork", but noted that it "retains evidence of its last-gen roots ... with simple geometry".[99] VideoGamer.com praised the Rockstar Editor's accessibility on PC but criticised some of its limitations, such as camera angle restrictions.[105] IGN's Stapleton appreciated the PC version's customisable controls,[106] and GameSpot's Brown felt that constant switching between the mouse and keyboard and a gamepad was necessary for "the best experience".[99] PC Gamer's Chris Thursten called the game "the most beautiful, expansive and generous" of the series.[103]

text: On the game's multiplayer, IGN's Stapleton reported low player counts in matches, long wait times in lobbies, server disconnection and occasional crashes. "Because of that," he wrote, "I can't strongly recommend ... the multiplayer experience alone".[101] VideoGamer.com found online character progression streamlined by comparison with the original version. According to them, the "grind of just doing PvP until co-op Jobs arrive with regularity"[104] was lost, and newcomers would likely find multiplayer enjoyable and balanced. However, they wrote of frequent server disconnection, especially during load screens.[104] GameSpot's Walton thought that Grand Theft Auto Online "still suffers from a lack of direction" for its open-ended and frenetic gameplay, but still is fun.[99] Game Informer's Reiner reported "minimal lag or issues in the expanded firefights and races".[100]

text: Accolades

text: Grand Theft Auto V received multiple nominations and awards from gaming publications. Prior to its release, it received Most Anticipated Game at the 2012 Spike Video Game Awards.[58] The game was review aggregators Metacritic and GameRankings' highest rated for the year 2013.[107][108] The game appeared on several year-end lists of 2013's best games, receiving wins from independent journalist Tom Chick,[109] CNET,[110] Edge,[111] the 31st Golden Joystick Awards,[112] the 5th Annual Inside Gaming Awards[113] the Spike VGX 2013 Awards,[114] Slant Magazine[115] and Time.[116] It was named the Best Xbox Game by Canada.com,[117] GameSpot,[118] and IGN,[119] and the Best Multiplatform Game by Destructoid.[120] Rockstar Games and Rockstar North won Best Studio and Best Developer from Edge,[121] and the BAFTA Academy Fellowship Award at the 10th British Academy Video Games Awards.[122]

text: Various in-game elements were recognised with awards. Two characters, Trevor Philips and Lamar Davis, received numerous nominations for Best Character, and Lamar won the award from Giant Bomb.[123] The music received awards from Spike VGX,[114] Hardcore Gamer[124] and The Daily Telegraph.[125] Grand Theft Auto Online won Best Multiplayer from GameTrailers[126] and BAFTA,[122] and Best Xbox 360 Multiplayer from IGN.[127] Online was also nominated for Biggest Disappointment by Game Revolution[128] and Hardcore Gamer.[129] Grand Theft Auto V won Best Technical Achievement in the Telegraph Video Game Awards,[125] and Best Technology at the 14th Annual Game Developers Choice Awards.[130] The graphical and artistic design received awards from IGN,[131] The Daily Telegraph[125] and BAFTA,[122] and a nomination at the Game Developers Choice Awards.[130]

text: The game received numerous other awards. It was awarded the title of Most Immersive Game at the Inside Gaming Awards.[113] The general public voted for the game to receive the User Choice Award at the PlayStation Awards 2013[132] and the Community Choice award from Destructoid.[133] The game received the Platinum Award at the PlayStation Awards,[132] and was named the Best British Game from BAFTA.[122] At IGN's Best of 2013 Awards, it received multiple wins, including Best Xbox 360 Graphics,[131] Best Xbox 360 Sound,[134] and Best Action Game on Xbox 360,[119] PlayStation 3[135] and overall.[136]

text: Sales

text: Within 24 hours of its release, Grand Theft Auto V generated more than US$800 million in worldwide revenue, equating to approximately 11.21 million copies sold for Take-Two Interactive.[137][m] The numbers nearly doubled analysts' expectations for the title.[139][140] Three days after release, the game had surpassed one billion dollars in sales, making it the fastest selling entertainment product in history.[141][n] Six weeks after its release, Rockstar had shipped nearly 29 million copies of the game to retailers, exceeding the lifetime figures of Grand Theft Auto IV.[143] On 7 October 2013, the game became the best-selling digital release on PlayStation Store for PlayStation 3, breaking the previous record set by The Last of Us, though numerical sales figures were not disclosed.[144][145] It broke seven Guinness World Records on 8 October: best-selling video game in 24 hours, best-selling action-adventure video game in 24 hours, highest grossing video game in 24 hours, fastest entertainment property to gross US$1 billion, fastest video game to gross US$1 billion, highest revenue generated by an entertainment product in 24 hours, and most viewed trailer for an action-adventure video game.[2] A digital version was released on 18 October for the Xbox 360,[146] which went on to become the highest grossing day-one and week-one release on Xbox Live.[147] As of May 2014, the game has generated over US$1.98 billion in revenue.[148] As of August 2014, the game has sold-in over 34 million units to retailers for the PlayStation 3 and Xbox 360.[149] By December 2014, the game had shipped 45 million copies, including 10 million copies of the re-released version.[150] As of May 2018, the game has shipped over 95 million copies worldwide across all platforms,[151] and generated over US$6 billion by April 2018, making it the most profitable entertainment product of all time.[152][153]

text: In the United Kingdom, the game became the all time fastest-selling, selling more than 2.25 million copies in five days. This broke the record set by Call of Duty: Black Ops at two million copies over the same period. It broke the day one record by selling 1.57 million copies and generating £65 million.[154] In two weeks, the game sold more than 2.6 million copies and generated £90 million, which accounted for 52% of games sold September 2013.[155] After three weeks on sale, it beat Grand Theft Auto IV's lifetime sales in the United Kingdom.[156] In its fourth week, it became the fastest-selling title to break the three million barrier in the UK, thus overtaking Black Ops II's lifetime sales.[157] In November 2014, the game became the best-selling game of all time in the UK, overtaking Black Ops.[158] The game was similarly successful in North America: it was the best selling game in September, representing over 50% of software sales[159] and boosting overall software sales by 52% compared to September 2012.[160]

text: Grand Theft Auto Online

text: Developed in tandem with the single-player mode, the online multiplayer mode Grand Theft Auto Online was conceived as a separate experience to be played in a continually evolving world.[161] Up to 30 players[o] freely roam across the game world and enter lobbies to complete jobs (story-driven competitive and cooperative modes).[162] The Content Creator toolset lets players create their own parameters for custom jobs, like racetracks and deathmatch weapon spawn points.[163] Players may band together in organised player teams called crews to complete jobs together. Rockstar Games Social Club extends crews formed in Max Payne 3's multiplayer mode to those of Grand Theft Auto Online. Players may create their own crews and join up to five total. Crews win multiplayer matches to earn experience points and climb online leaderboards.[164]

text: Grand Theft Auto Online launched on 1 October 2013, two weeks after Grand Theft Auto V's release.[165] Many players reported connection difficulties and game freezes during load screens.[166][167] Rockstar released a technical patch on 5 October in an effort to resolve the issues,[168] but problems persisted the second week following launch as some players reported their character progress as having disappeared.[169] Another technical patch was released on 10 October combating the issues[170] and Rockstar offered a GTA$500,000 (in-game currency) stimulus to the accounts of all players connected to Online since launch as recompense.[171] Because of the widespread technical issues present at launch, many reviewers bemoaned their Grand Theft Auto Online experience, but generally recognised its open-ended exploration and dynamic content as strengths.[172][173][174][175][176]

text: Post-release content is continually added to Grand Theft Auto Online through free title updates. Some updates add new game modes and features,[177][178] and others feature themed gameplay content, such as the Independence Day Special update that added patriotic-themed content on 1 July 2014.[179] The widely anticipated[180][181] Online Heists update launched on 10 March 2015 and suffered some initial technical difficulties due to the increased user load.[182] Shortly after the game's PC release, some players reported being banned from Grand Theft Auto Online for using field of view and cosmetic mods in single-player.[183] Rockstar stated in their official blog that nobody had been banned from Online for using single-players mods, but that recent updates to the PC version had the "unintentional effect" of making such mods unplayable. They stated that mods are unauthorised and may cause unforeseen technical problems and instabilities.[184]

text: Controversies

text: The game has generated several controversies related to its violence and depiction of women. A mission that requires players to use torture equipment in a hostage interrogation polarised reviewers, who noted its political commentary but felt that the torture sequence was in poor taste.[78][185] The mission also received criticism from politicians and anti-torture charity groups.[186] The game became subject to widespread online debate over its portrayal of women, particularly in the wake of backlash against GameSpot journalist Carolyn Petit when she claimed the game was misogynistic in her review.[76][187] After Petit's review webpage received more than 20,000 largely negative comments, many journalists defended her right to an opinion and lamented the gaming community's defensiveness towards criticism.[188][189] Television personality Karen Gravano and actress Lindsay Lohan both filed lawsuits against Rockstar in allegation that characters in the game were based on their likenesses.[190][191] Their lawsuits were later dismissed.[192] Australian department store Target pulled the game from their 300 stores following a Change.org petition against depictions of violence towards women in the game.[193]

text: Legacy

text: Critics concurred that Grand Theft Auto V was among seventh generation console gaming's best[27] and a great closing title before the eighth generation's emergence.[194][195] Polygon's Plante observed that the game would "bridge between games' present and the future", and declared it "the closure of this generation, and the benchmark for the next".[86] VideoGamer.com's Simon Miller considered it "the ultimate swansong for this console cycle" that would "cast a long shadow over the next".[196] Three days after its release, the game ranked second on IGN's "Top 25 Xbox 360 Games" list. Editor Ryan McCaffrey considered that the open world's scale and detail succeeded the majority of other Xbox 360 games. He called the game "a triumph both for gamers and for the medium itself, and it deserves its runaway success".[197] In November 2013, Hardcore Gamer placed the game third on their "Top 100 Games of the Generation" list. They cited its improved shooting and driving mechanics over its predecessors, and considered the multiple protagonist design "a welcome change of pace" that could become an eighth generation gaming benchmark.[198] In December, The Daily Telegraph listed the game among their "50 best games of the console generation". They called it a "cultural behemoth" that "will be Rockstar's lasting legacy".[199]

text: In January 2014, Computer and Video Games ranked the game fourth on their "Games of the Generation 20–1" list. Editor Rob Crossley said that for the first time, Rockstar created an "utterly beautiful" open world. He found that the game did away with Grand Theft Auto IV's repetitive mission design and focused instead on fun gameplay.[200] In May, IGN ranked it eighth on their "Top 100 Games of a Generation" list and called it a "huge, raucous, and wildly ambitious bridge towards the [eighth] generation of console gaming".[201] The next month, it placed third on IGN's "Games of a Generation: Your Top 100" list as voted by the site's readers.[202] In August, Game Informer ranked it third on their "Top 10 Action Games Of The Generation" list. They compared the game's quality to that of its predecessor, but thought that its ensemble character set-up, varied missions and multiplayer superseded Grand Theft Auto IV's placement on the list. They wrote of the story's absurd drama and the open world's vastness, and did not "regret a single second" spent playing the game.[203] In November, Edge named it the fifth best game of its generation and commented that "no other game studio is even daring to attempt an open world game in its tradition because there is simply no possibility of measuring up to [its] standards."[204] In 2015, the publication rated it the second greatest video game of all time.[205] The game ranked high on several best game lists determined by the public; it featured eighth on Empire's "100 Greatest Video Games Of All Time" list, and fifth on Good Game's "Top 100 Games" list, as voted by the magazine and programme's respective audiences.[206][207] It was the most tweeted game of 2015, despite being released over a year earlier.[208]

text: Notes

text:
Jump up ^ Additional work by Rockstar San Diego, Rockstar Leeds, Rockstar Toronto, Rockstar New England and Rockstar London.[1]
Jump up ^ The first-person view is only available in the Microsoft Windows, PlayStation 4 and Xbox One versions of the game.[3]
Jump up ^ Art director Aaron Garbut estimated that it is large enough to fit the game worlds of Red Dead Redemption, Grand Theft Auto: San Andreas and Grand Theft Auto IV inside of it.[7]
Jump up ^ Accessed via a pop-up "weapon wheel" that features eight slots corresponding to different weapon types.[9]
Jump up ^ Players can alternatively hail taxicabs that drive to specific destinations.[10]
Jump up ^ Health is fully replenished by using first aid kits or consuming food and drink.[10]
Jump up ^ Players arrested or killed by officers during missions may restart from the last checkpoint.[15]
Jump up ^ Players may take alternative evasive measures like respraying their vehicle at chop shops, which instantly erases the wanted level.[17]
Jump up ^ In Grand Theft Auto V, the FIB and IAA are fictionalised parodies of the Federal Bureau of Investigation (FBI) and Central Intelligence Agency (CIA), respectively.[29]
Jump up ^ Media analyst Arvind Bhatia estimated that the development budget exceeded US US$137 million.[39] The Scotsman reporter Marty McLaughlin estimated that the combined budget of the development and marketing efforts exceeded GB£170 million (US$265 million).[38]
Jump up ^ The Microsoft Windows, PlayStation 4 and Xbox One versions add another 162 tracks to the in-game radio.[53]
Jump up ^ Grand Theft Auto V shares its status as fifth-highest rated game on Metacritic with Super Mario Galaxy, Super Mario Galaxy 2, Super Mario Odyssey, The Legend of Zelda: Breath of the Wild, Tony Hawk's Pro Skater 3, Perfect Dark, Metroid Prime, Grand Theft Auto III, Halo: Combat Evolved and NFL 2K1. The games that are rated higher than Grand Theft Auto V are The Legend of Zelda: Ocarina of Time, Tony Hawk's Pro Skater 2, Soulcalibur and Grand Theft Auto IV.[83]
Jump up ^ The game's first-day sales record beat the previous record of US$500 million set by Call of Duty: Black Ops II.[138]
Jump up ^ The game's US$1 billion revenue broke the previous record set by Call of Duty: Black Ops II, which took 15 days to surpass US$1 billion in sales.[142]
Jump up ^ The PlayStation 3 and Xbox 360 versions of Grand Theft Auto Online allow up to 16 concurrent players,[162] while the PlayStation 4 and Xbox One versions allow up to 30 concurrent players.[65]