help factor postestimation dialogs: predict estat loadingplot
rotate scoreplot screeplot
also see: factor
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Title
[MV] factor postestimation -- Postestimation tools for factor and
factormat
Description
The following postestimation commands are of special interest after
factor and factormat:
command description
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estat anti anti-image correlation and covariance matrices
estat common correlation matrix of the common factors
estat factors AIC and BIC model-selection criteria for different
numbers of factors
estat kmo Kaiser-Meyer-Olkin measure of sampling adequacy
estat residuals matrix of correlation residuals
estat rotatecompare compare rotated and unrotated loadings
estat smc squared multiple correlations between each
variable and the rest
estat structure correlations between variables and common factors
+ estat summarize estimation sample summary
loadingplot plot factor loadings
rotate rotate factor loadings
scoreplot plot score variables
screeplot plot eigenvalues
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+ estat summarize is not available after factormat.
The following standard postestimation commands are also available:
command description
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* estimates cataloging estimation results
+ predict predict regression or Bartlett scores
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* estimates table is not allowed, and estimates stats is allowed only
with the ml factor method.
+ predict after factormat works only if you have variables in memory that
match the names specified in factormat. predict assumes mean zero and
standard deviation one unless the means() and sds() options of
factormat were provided.
Special-interest postestimation commands
estat anti displays the anti-image correlation and anti-image covariance
matrices. These are minus the partial covariance and minus the partial
correlation matrices of all pairs of variables, holding all other
variables constant.
estat common displays the correlation matrix of the common factors. For
orthogonal factor loadings, the common factors are uncorrelated, and
hence an identity matrix is shown. estat common is of more interest
after oblique rotations.
estat factors displays model-selection criteria (AIC and BIC) for models
with 1, 2, ..., # factors. Each model is estimated using maximum
likelihood (i.e., using the ml option of factor).
estat kmo specifies that the Kaiser-Meyer-Olkin (KMO) measure of sampling
adequacy be displayed. KMO takes values between 0 and 1, with small
values meaning that overall the variables have too little in common to
warrant a factor analysis. Heuristically, the following labels are given
to values of KMO:
0.00 to 0.49 unacceptable
0.50 to 0.59 miserable
0.60 to 0.69 mediocre
0.70 to 0.79 middling
0.80 to 0.89 meritorious
0.90 to 1.00 marvelous
estat residuals displays the raw or standardized residuals of the
observed correlations with respect to the fitted (reproduced) correlation
matrix.
estat rotatecompare displays the unrotated factor loadings and the most
recent rotated factor loadings.
estat smc displays the squared multiple correlations between each
variable and all other variables. SMC is a theoretical lower bound for
communality, so it is an upper bound for uniqueness. The pf factor
method estimates the communalities by smc.
estat structure displays the factor structure, i.e., the correlations
between the variables and the common factors.
estat summarize displays summary statistics of the variables in the
factor analysis over the estimation sample. This subcommand is, of
course, not available after factormat.
rotate modifies the results of the last factor or factormat command to
create a set of loadings that are more interpretable than those
originally produced. A variety of orthogonal and oblique rotations are
available, including varimax, orthomax, promax, and oblimin. See [MV]
rotate for more details. rotate stores results along with the original
estimation results so that replaying factor or factormat and other
postestimation commands may refer to the unrotated as well as the rotated
results.
Syntax for predict
predict [type] {stub*|newvarlist} [if] [in] [, statistic options]
statistic description
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Main
regression regression scoring method
bartlett Bartlett scoring method
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options description
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Main
norotated use unrotated results, even when rotated results are
available
notable suppress table of scoring coefficients
format(%fmt) format for displaying the scoring coefficients
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Menu
Statistics > Postestimation > Predictions, residuals, etc.
Options for predict
+------+
----+ Main +-------------------------------------------------------------
regression produces factors scored by the regression method.
bartlett produces factors scored by the method suggested by Bartlett.
This method produces unbiased factors, but they may be less accurate
than those produced by the default regression method suggested by
Thomson. Regression-scored factors have the smallest mean squared
error from the true factors but may be biased.
norotated specifies that unrotated factors be scored even when you have
previously issued a rotate command. The default is to use rotated
factors if they are available and unrotated factors otherwise.
notable suppresses the table of scoring coefficients.
format(%fmt) specifies the display format for scoring coefficients.
Syntax for estat
Anti-image correlation/covariance matrices
estat anti [, nocorr nocov format(%fmt)]
Correlation of common factors
estat common [, norotated format(%fmt)]
Model-selection criteria
estat factors [, factors(#) detail]
Sample adequacy measures
estat kmo [, novar format(%fmt)]
Residuals of correlation matrix
estat residuals [, fitted obs sresiduals format(%fmt)]
Comparison of rotated and unrotated loadings
estat rotatecompare [, format(%fmt)]
Squared multiple correlations
estat smc [, format(%fmt)]
Correlations between variables and common factors
estat structure [, norotated format(%fmt)]
Summarize variables for estimation sample
estat summarize [, label noheader noweights]
Menu
Statistics > Postestimation > Reports and statistics
Options for estat
+------+
----+ Main +-------------------------------------------------------------
nocorr, an option used with estat anti, suppresses the display of the
anti-image correlation matrix.
nocov, an option used with estat anti, suppresses the display of the
anti-image covariance matrix.
format(%fmt) specifies the display format. The defaults differ between
the subcommands.
norotated, an option used with estat common and estat structure, requests
that the displayed and returned results be based on the unrotated
original factor solution rather than on the last rotation (orthogonal
or oblique).
factors(#), an option used with estat factors, specifies the maximum
number of factors to include in the summary table.
detail, an option used with estat factors, presents the output from each
run of factor (or factormat) used in the computations of the AIC and
BIC values.
novar, an option used with estat kmo, suppresses the KMO measures of
sampling adequacy for the variables in the factor analysis,
displaying the overall KMO measure only.
fitted, an option used with estat residuals, displays the fitted
(reconstructed) correlation matrix on the basis of the retained
factors.
obs, an option used with estat residuals, displays the observed
correlation matrix.
sresiduals, an option used with estat residuals, displays the matrix of
standardized residuals of the correlations. Be careful when
interpreting these residuals.
label, noheader, and noweights are the same as for the generic estat
summarize command; see [R] estat.
Examples
Setup
. webuse bg2
. factor bg2cost1-bg2cost6
Residuals of correlation matrix
. estat residuals
Estimation sample
. estat summ
Varimax rotation
. rotate
Use 1st 2 factors if > 2 retained
. rotate, factors(2)
Promax rotation
. rotate, promax
Oblique oblimin rotation
. rotate, oblimin(0.5) oblique
Score first two, rotated factors
. predict f1 f2
Score first two, unrotated factors
. predict raw1 raw2, norotate
Scree plot
. screeplot
Factor score plot
. scoreplot
Scatterplot of factor loadings
. loadingplot
Saved results
Let p be the number of variables and f, the number of factors.
predict, in addition to generating variables, also saves the following in
r():
Macros
r(method) regression or Bartlett
Matrices
r(scoef) p x f matrix of scoring coefficients
estat anti saves the following in r():
Matrices
r(acov) p x p anti-image covariance matrix
r(acorr) p x p anti-image correlationmatrix
estat common saves the following in r():
Matrices
r(Phi) f x f correlation matrix of common factors
estat factors saves the following in r():
Matrices
r(stats) k x 5 matrix with log likelihood, degrees of
freedom, AIC, and BIC for models with 1 to k
factors estimated via maximum likelihood
estat kmo saves the following in r():
Scalars
r(kmo) the Kaiser-Meyer-Olkin measure of sampling
adequacy
Matrices
r(kmow) column vector of KMO measures for each
variable
estat residuals saves the following in r():
Matrices
r(fit) fitted matrix for the correlations, hat C =
hat Lambda hat Phi hat Lambda' + hat Psi
r(res) raw residual matrix C - hat C
r(SR) standardized residuals (sresiduals option
only)
estat smc saves the following in r():
Matrices
r(smc) vector of squared multiple correlations of
variables with all other variables
estat structure saves the following in r():
Matrices
r(st) p x f matrix of correlations between variables
and common factors
See [R] estat for the returned results of estat summarize.
rotate after factor and factormat add to the existing e():
Scalars
e(r_f) number of factors in rotated solution
e(r_fmin) rotation criterion value
Macros
e(r_class) orthogonal or oblique
e(r_criterion) rotation criterion
e(r_ctitle) title for rotation
e(r_normalization) kaiser or none
Matrices
e(r_L) rotated loadings
e(r_T) rotation
e(r_Phi) correlations between common factors
e(r_Ev) explained variance by common factors
The factors in the rotated solution are in decreasing order of e(r_Ev).
Also see
Manual: [MV] factor postestimation
Help: [MV] factor;
[MV] rotate, [MV] scoreplot, [MV] screeplot
