help pca postestimation dialogs: predict estat rotate
loadingplot scoreplot screeplot
also see: pca
-------------------------------------------------------------------------------
Title
[MV] pca postestimation -- Postestimation tools for pca and pcamat
Description
The following postestimation commands are of special interest after pca
and pcamat:
command description
-------------------------------------------------------------------------
estat anti anti-image correlation and covariance matrices
estat kmo Kaiser-Meyer-Olkin measure of sampling adequacy
estat loadings component-loading matrix in one of several
normalizations
estat residuals matrix of correlation or covariance residuals
estat rotatecompare compare rotated and unrotated components
estat smc squared multiple correlations between each
variable and the rest
+ estat summarize display summary statistics over the estimation
sample
loadingplot plot component loadings
rotate rotate component loadings
scoreplot plot score variables
screeplot plot eigenvalues
-------------------------------------------------------------------------
+ estat summarize is not available after pcamat.
The following standard postestimation commands are also available:
command description
-------------------------------------------------------------------------
+ estat examine the VCE matrix
estimates cataloging estimation results
* lincom point estimates, standard errors, testing, and
inference for linear combinations of
coefficients
* nlcom point estimates, standard errors, testing, and
inference for nonlinear combinations of
coefficients
predict score variables, predictions, and residuals
* predictnl point estimates, standard errors, testing, and
inference for generalized predictions
* test Wald tests of simple and composite linear
hypotheses
* testnl Wald tests of nonlinear hypotheses
-------------------------------------------------------------------------
+ estat is available after pca and pcamat with the vce(normal) option.
* lincom, nlcom, predictnl, test, and testnl are available only after pca
with the vce(normal) option.
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 of all pairs of variables, holding all other variables
constant.
estat kmo displays the Kaiser-Meyer-Olkin (KMO) measure of sampling
adequacy. KMO takes values between 0 and 1, with small values indicating
that overall the variables have too little in common to warrant a PCA
analysis. Historically, the following labels are often 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 loadings displays the component-loading matrix in one of several
normalizations of the columns (eigenvectors).
estat residuals displays the difference between the observed correlation
or covariance matrix and the fitted (reproduced) matrix using the
retained factors.
estat rotatecompare displays the unrotated (principal) components next to
the most recent rotated components.
estat smc displays the squared multiple correlations between each
variable and all other variables. SMC is a theoretical lower bound for
communality and thus an upper bound for the unexplained variance.
estat summarize displays summary statistics of the variables in the
principal component analysis over the estimation sample. This subcommand
is not available after pcamat.
Syntax for predict
predict [type] {stub*|newvarlist} [if] [in] [, statistic options ]
statistic # of vars.
description (k = # of orig. vars.; f = # of
components)
-------------------------------------------------------------------------
Main
score 1,...,f scores based on the components; the default
fit k fitted values using the retained components
residual k raw residuals from the fit using the retained
components
q 1 residual sum of squares
-------------------------------------------------------------------------
options description
-------------------------------------------------------------------------
Main
norotated use unrotated results, even when rotated results
are available
center base scores on centered variables
notable suppress table of scoring coefficients
format(%fmt) format for displaying the scoring coefficients
-------------------------------------------------------------------------
Menu
Statistics > Postestimation > Predictions, residuals, etc.
Options for predict
Note on pcamat: predict requires that variables with the correct names be
available in memory. Apart from centered scores, means() should have
been specified with pcamat. If you used pcamat because you have access
only to the correlation or covariance matrix, you cannot use predict.
+------+
----+ Main +-------------------------------------------------------------
score calculates the scores for components 1, ..., #, where # is the
number of variables in newvarlist.
fit calculates the fitted values, using the retained components, for each
variable. The number of variables in newvarlist should equal the
number of variables in the varlist of pca.
residual calculates for each variable the raw residuals (residual =
observed - fitted), with the fitted values computed using the
retained components.
q calculates the Rao statistics (i.e., the sum of squares of the omitted
components) weighted by the respective eigenvalues. This equals the
residual sum of squares between the original variables and the fitted
values.
norotated uses unrotated results, even when rotated results are
available.
center bases scores on centered variables. This option is relevant only
for a PCA of a covariance matrix, in which the scores are based on
uncentered variables by default. Scores for a PCA of a correlation
matrix are always based on the standardized variables.
notable suppresses the table of scoring coefficients.
format(%fmt) specifies the display format for scoring coefficients. The
default is format(%8.4f).
Syntax for estat
Display the anti-image correlation and covariance matrices
estat anti [, nocorr nocov format(%fmt) ]
Display the Kaiser-Meyer-Olkin measure of sampling adequacy
estat kmo [, novar format(%fmt) ]
Display the component-loading matrix
estat loadings [, cnorm(unit|eigen|inveigen) format(%fmt) ]
Display the differences in matrices
estat residuals [, obs fitted format(%fmt) ]
Display the unrotated and rotated components
estat rotatecompare [, format(%fmt) ]
Display the squared multiple correlations
estat smc [, format(%fmt) ]
Display the summary statistics
estat summarize [, label noheader noweights]
Menu
Statistics > Postestimation > Reports and statistics
Options for estat
nocorr, an option used with estat anti, suppresses the display of the
anti-image correlation matrix, i.e., minus the partial correlation
matrix of all pairs of variables, holding constant all other
variables.
nocov, an option used with estat anti, suppresses the display of the
anti-image covariance matrix, i.e., minus the partial covariance
matrix of all pairs of variables, holding constant all other
variables.
format(%fmt) specifies the display format. The defaults differ between
the subcommands.
novar, an option used with estat kmo, suppresses the Kaiser-Meyer-Olkin
measures of sampling adequacy for the variables in the principal
component analysis, displaying the overall KMO measure only.
cnorm(unit|eigen|inveigen), an option used with estat loadings, selects
the normalization of the eigenvectors, the columns of the
principal-component loading matrix. The following normalizations are
available,
unit ssq(column) = 1 (default)
eigen ssq(column) = eigenvalue
inveigen ssq(column) = 1/eigenvalue
with ssq(column) being the sum-of-squares of the elements in a column
and eigenvalue, the eigenvalue associated with the column
(eigenvector).
obs, an option used with estat residuals, displays the observed
correlation or covariance matrix for which the PCA was performed.
fitted, an option used with estat residuals, displays the fitted
(reconstructed) correlation or covariance matrix based on the
retained components.
label, noheader, and noweights are the same as for the generic estat
summarize command; see [R] estat.
Examples
Setup
. sysuse auto
. pca trunk weight length headroom
Statistics
. estat residuals, fitted
. estat loadings, cnorm(eigen)
Scree plot
. screeplot,
. screeplot, ci(normal)
Plots of component loadings and scores
. loadingplot, component(3)
. scoreplot, component(3) mlabel(country)
Rotation of loadings
. rotate
. rotate, varimax
. rotate, oblimin(0.5) oblique
Individual scores for the components are obtained via predict
. predict f1
. predict f1 f2
Residual sum of squares
. predict t, q
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():
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 correlation matrix
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 loadings saves the following in r():
Macros
r(cnorm) component normalization: eigen, inveigen, or unit
Matrices
r(A) p x f matrix of normalized component loadings
estat residuals saves the following in r():
Matrices
r(fit) p x p matrix of fitted values
r(residual) p x p matrix of residuals
estat smc saves the following in r():
Matrices
r(smc) vector of squared multiple correlations of
variables with all other variables
See [R] estat for the returned results of estat summarize and estat vce
(available when vce(normal) is specified with pca or pcamat).
rotate after pca and pcamat add to the existing e():
Scalars
e(r_f) number of components 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_Ev) explained variance by rotated components
The components in the rotated solution are in decreasing order of
e(r_Ev).
Also see
Manual: [MV] pca postestimation
Help: [MV] pca;
[MV] rotate, [MV] scoreplot, [MV] screeplot
