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📄 factor_postestimation.hlp

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{smcl}
{* 02may2005}{...}
{cmd:help factor postestimation}{...}
{right:dialogs:  {bf:{dialog factor_estat:estat}}  {bf:{dialog loadingplot}}  {bf:{dialog factor_p:predict}} }
{right:{bf:{dialog rotate}}  {bf:{dialog scoreplot}}  {bf:{dialog screeplot}}}
{right:also see:  {helpb factor}{space 22}}
{hline}

{title:Title}

{p 4 36 2}
{hi:[MV] factor postestimation} {hline 2} Postestimation tools for
{cmd:factor} and {cmd:factormat}


{title:Description}

{pstd}
The following postestimation commands are of special interest after
{cmd:factor} and {cmd:factormat}:

{synoptset 21 tabbed}{...}
{p2coldent:command}description{p_end}
{synoptline}
{synopt:{helpb factor postestimation##anti:estat anti}}anti-image correlation
	and covariance matrices{p_end}
{synopt:{helpb factor postestimation##common:estat common}}correlation matrix
	of the common factors{p_end}
{synopt:{helpb factor postestimation##factors:estat factors}}AIC and BIC model
	selection criteria for different numbers of factors{p_end}
{synopt:{helpb factor postestimation##kmo:estat kmo}}Kaiser-Meyer-Olkin
	measure of sampling adequacy{p_end}
{synopt:{helpb factor postestimation##residuals:estat residuals}}matrix of
        correlation residuals{p_end}
{synopt:{helpb factor postestimation##rotatecomp:estat rotatecompare}}compare
        rotated and unrotated loadings{p_end}
{synopt:{helpb factor postestimation##smc:estat smc}}squared multiple
        correlations between each variable and the rest{p_end}
{synopt:{helpb factor postestimation##structure:estat structure}}correlations
	between variables and common factors{p_end}
{p2coldent:+ {helpb factor postestimation##summarize:estat summarize}}estimation
	sample summary{p_end}
{synopt:{helpb scoreplot:loadingplot}}plot factor loadings{p_end}
{synopt:{helpb rotate}}rotate factor loadings{p_end}
{synopt:{helpb scoreplot}}plot score variables{p_end}
{synopt:{helpb screeplot}}plot eigenvalues{p_end}
{synoptline}
{p 4 6 2}
+ {cmd:estat summarize} is not available after {cmd:factormat}.
{p_end}

{pstd}
In addition, the following standard postestimation commands are available:

{p2coldent:command}description{p_end}
{synoptline}
{p2coldent:* {helpb estimates}}cataloging estimation results{p_end}
{p2coldent:+ {helpb factor postestimation##predict:predict}}predict 
	regression or Bartlett scores{p_end}
{synoptline}
{p2colreset}{...}
{p 4 6 2}
* {cmd:estimates table} is not allowed and {cmd:estimates stats} is only
allowed with the {cmd:ml} factor method.
{p_end}

{p 4 6 2}
+ {cmd:predict} after {cmd:factormat} works only if you have variables in
memory that match the names specified in {cmd:factormat}.  {cmd:predict}
assumes mean zero and standard deviation one unless the {cmd:means()}
and {cmd:sds()} options of {cmd:factormat} were provided.


{title:Special-interest postestimation commands}

{pstd}
{cmd: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.

{pstd}
{cmd: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.  {cmd:estat common} is of more interest after oblique rotations.

{pstd}
{cmd: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
{cmd:ml} option of {cmd:factor}).

{pstd}
{cmd:estat kmo}
specifies that the Kaiser-Meyer-Olkin measure of sampling adequacy (KMO) 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 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

{pstd}
{cmd:estat residuals}
displays the raw or standardized residuals of the observed correlations with
respect to the fitted (reproduced) correlation matrix.

{pstd}
{cmd:estat rotatecompare}
displays the unrotated factor loadings and the most recent rotated factor
loadings.

{pstd}
{cmd:estat smc}
displays the squared multiple correlations between each variable and all other
variables.  SMC is a theoretical lower bound for communality, and so an upper
bound for uniqueness.  Note that the {cmd:pf} factor method estimates the
communalities by {cmd:smc}.

{pstd}
{cmd:estat structure}
displays the factor structure, i.e., the correlations between the variables
and the common factors.

{pstd}
{cmd:estat summarize}
displays summary statistics of the variables in the factor analysis over the
estimation sample.  This subcommand is, of course, not available after
{cmd:factormat}.

{pstd}
{cmd:rotate} modifies the results of the last {cmd:factor} or {cmd: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
{helpb rotate} for additional details.  {cmd:rotate} stores results along with
the original estimation results so that replaying {cmd:factor} or
{cmd:factormat} and other post estimation commands may refer to the unrotated
as well as the rotated results.


{marker predict}{...}
{title:Syntax for predict}

{p 8 16 2}
{cmd:predict} {newvar:list} {ifin}
[{cmd:,} {it:statistic} {it:options}]

{synoptset 16 tabbed}{...}
{p2coldent:statistic}description{p_end}
{synoptline}
{syntab:Main}
{p2col:{opt r:egression}}regression scoring method{p_end}
{p2col:{opt b:artlett}}Bartlett scoring method{p_end}
{synoptline}

{synopthdr}
{synoptline}
{syntab:Main}
{synopt:{opt norot:ated}}use unrotated results, even when rotated results are
	available{p_end}
{synopt:{opt not:able}}suppress table of scoring coefficients{p_end}
{synopt:{opth for:mat(%fmt)}}format for displaying the scoring
	coefficients{p_end}
{synoptline}
{p2colreset}{...}


{title:Options for predict}

{dlgtab:Main}

{phang}
{opt regression}
produces factors scored by the regression method.

{phang}
{opt 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.

{phang}
{opt norotated}
specifies that unrotated factors be scored even when you have previously
issued a {cmd:rotate} command.  The default is to use rotated factors if
available and unrotated factors otherwise.

{phang}
{opt notable}
suppresses the table of scoring coefficients.

{phang}
{opth format(%fmt)}
specifies the display format for scoring coefficients.


{title:Syntax for estat}

{marker anti}{...}
{pstd}
Anti-image correlation/covariance matrices

{p 8 12 2}
{cmd:estat anti}
[{cmd:,} {opt nocorr} {opt nocov} {opth for:mat(%fmt)}]

{marker common}{...}
{pstd}
Correlation of common factors

{p 8 12 2}
{cmd:estat} {cmdab:com:mon}
[{cmd:,} {opt norot:ated} {opth for:mat(%fmt)}]

{marker factors}{...}
{pstd}
Model selection criteria

{p 8 12 2}
{cmd:estat} {cmdab:fac:tors}
[{cmd:,} {opt fac:tors(#)} {opt det:ail}]

{marker kmo}{...}
{pstd}
Sample adequacy measures

{p 8 12 2}
{cmd:estat kmo}
[{cmd:,} {opt nov:ar} {opth for:mat(%fmt)}]

{marker residuals}{...}
{pstd}
Residuals of correlation matrix

{p 8 12 2}
{cmd:estat} {cmdab:res:iduals}
[{cmd:,} {opt f:itted} {opt o:bs} {opt sr:esiduals} {opth for:mat(%fmt)}]

{marker rotatecomp}{...}
{pstd}
Comparison of rotated and unrotated loadings

{p 8 12 2}
{cmd:estat} {cmdab:rot:atecompare} [{cmd:,} {opth for:mat(%fmt)}]

{marker smc}{...}
{pstd}
Squared multiple correlations

{p 8 12 2}
{cmd:estat smc}
[{cmd:,} {opth for:mat(%fmt)}]

{marker structure}{...}
{pstd}
Correlations between variables and common factors

{p 8 12 2}
{cmd:estat} {cmdab:str:ucture}
[{cmd:,} {opt norot:ated} {opth for:mat(%fmt)}]

{marker summarize}{...}
{pstd}
Summarize variables for estimation sample

{p 8 12 2}
{cmd:estat} {cmdab:su:mmarize}
[{cmd:,} {opt lab:el} {opt nohea:der} {opt nowei:ghts}]


{title:Options for estat}

{dlgtab:Main}

{phang}
{opt nocorr},
an option of {cmd:estat anti},
suppresses the display of the anti-image correlation matrix.

{phang}
{opt nocov},
an option of {cmd:estat anti},
suppresses the display of the anti-image covariance matrix.

{phang}
{opt format(%fmt)}
specifies the display format.  The defaults differ between the subcommands.

{phang}
{opt norotated},
an option of {cmd:estat common} and {cmd: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).

{phang}
{opt factors(#)},
an option of {cmd:estat factors},
specifies the maximum number of factors to include in the summary table.

{phang}
{opt detail},
an option of {cmd:estat factors},
presents the output from each run of {cmd:factor} (or {cmd:factormat}) used in
the computation of the AIC and BIC values.

{phang}
{opt novar},
an option of {cmd:estat kmo},
suppresses the KMO measures of sampling adequacy for the variables in the
factor analysis, displaying the overall KMO measure only.

{phang}
{opt fitted},
an option of {cmd:estat residuals},
displays the fitted (reconstructed) correlation matrix based on the retained
factors.

{phang}
{opt obs},
an option of {cmd:estat residuals},
displays the observed correlation matrix.

{phang}
{opt sresiduals},
an option of {cmd:estat residuals},
displays the matrix of standardized residuals of the correlations.  Caution is
warranted in the interpretation of these residuals.

{phang}
{opt label}, {opt noheader}, and {opt noweights}
are the same as for the generic {cmd:estat summarize} command; see
{helpb estat}.


{title:Examples}

{p 4 47 2}
{cmd:. estat residuals} {space 15} (residuals of correlation matrix){p_end}
{p 4 47 2}
{cmd:. estat summ} {space 20} (estimation sample){p_end}

{p 4 47 2}
{cmd:. rotate} {space 24} (varimax rotation){p_end}
{p 4 47 2}
{cmd:. rotate, factors(2)} {space 12} (use 1st 2 factors if > 2 retained){p_end}
{p 4 47 2}
{cmd:. rotate, promax} {space 16} (promax rotation){p_end}
{p 4 47 2}
{cmd:. rotate, oblimin(0.5) oblique} {space 2} (oblique oblimin rotation){p_end}

{p 4 47 2}
{cmd:. predict f1 f2} {space 17} (score first two, rotated factors){p_end}
{p 4 47 2}
{cmd:. predict raw1 raw2, norotate} {space 3} (score first two, unrotated factors){p_end}

{p 4 47 2}
{cmd:. screeplot} {space 21} (scree plot){p_end}

{p 4 47 2}
{cmd:. scoreplot, mlabel(country)} {space 4} (factor score plot){p_end}

{p 4 47 2}
{cmd:. loadingplot} {space 19} (scatter plot of factor loadings){p_end}


{title:Also see}

{psee}
Manual:  {bf:[MV] factor postestimation}{p_end}

{psee}
Online:  {helpb factor};{break}
{helpb estimates},
{helpb pca},
{helpb rotate},
{helpb scoreplot},
{helpb screeplot}
{p_end}

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