pca.hlp

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{smcl}
{* 06apr2005}{...}
{cmd:help pca} {...}
{right:dialogs:  {bf:{dialog pca}  {dialog pcamat}}{space 7}}
{right:also see:  {help pca postestimation}}
{hline}

{title:Title}

{p 4 18 2}
{hi:[MV] pca} {hline 2} Principal component analysis


{title:Syntax}

{pstd}
Principal component analysis of data

{p 8 12 2}
{cmd:pca} {varlist} {ifin} {weight}
[{cmd:,} {it:{help pca##pcaopts:options}}]

{pstd} 
Principal component analysis of a correlation or covariance matrix

{p 8 15 2}
{cmd:pcamat} {it:matname} {cmd:,} {opt n(#)}
[{it:{help pca##pcaopts:options}}
{it:{help pca##pcamatopts:pcamat_options}}]

{synoptset 19 tabbed}
{marker pcaopts}{...}
{synopthdr}
{synoptline}
{syntab:Model 2}
{synopt:{opt com:ponents(#)}}retain maximum of {it:#} components; synonym is
	{opt fa:ctors()}{p_end}
{synopt:{opt mine:igen(#)}}retain eigenvalues larger than {it:#}; default is
	{cmd:1e-5}{p_end}
{synopt:{opt cor:relation}}perform PCA of the correlation matrix; the
	default{p_end}
{synopt:{opt cov:ariance}}perform PCA of the covariance matrix{p_end}
{synopt:{cmd:vce(}{cmdab:non:e}{cmd:)}}do not compute VCE of the eigenvalues and
	vectors; the default{p_end}
{synopt:{cmd:vce(}{cmdab:nor:mal}{cmd:)}}compute VCE of the eigenvalues and
	vectors assuming multivariate normality{p_end}

{syntab:Reporting}
{synopt:{opt l:evel(#)}}set confidence level; default is {cmd:level(95)}{p_end}
{synopt:{opt bl:anks(#)}}display loadings as blank when
	|loadings| < {it:#}{p_end}
{synopt:{opt novce}}suppress display of SEs even though calculated{p_end}
{p2coldent:# {opt me:ans}}display summary statistics of variables{p_end}

{syntab:Advanced}
{synopt:{opt tol(#)}}advanced; see description below{p_end}
{synopt:{opt ignore}}advanced; see description below{p_end}

{p2coldent:+ {opt norot:ated}}display unrotated results, even if rotated
	results are available (replay only){p_end}
{synoptline}
{p 4 6 2}
# {opt means} is not allowed with {cmd:pcamat}.{p_end}
{p 4 6 2}
+ {opt norotated} is not available in the dialog box.{p_end}

{marker pcamatopts}{...}
{synopthdr:pcamat_options}
{synoptline}
{syntab:Model}
{synopt:{cmdab:sh:ape:(}{cmdab:f:ull}{cmd:)}}{it:matname} is a square symmetric
	matrix; the default{p_end}
{synopt:{cmdab:sh:ape:(}{cmdab:l:ower}{cmd:)}}{it:matname} is a vector with
	the rowwise lower triangle (with diagonal){p_end}
{synopt:{cmdab:sh:ape:(}{cmdab:u:pper}{cmd:)}}{it:matname} is a vector with
	the rowwise upper triangle (with diagonal){p_end}
{synopt:{opt nam:es(namelist)}}variable names; required if {it:matname}
	is triangular{p_end}
{p2coldent:* {opt n(#)}}number of observations; required{p_end}
{synopt:{opt sds(matname2)}}vector with standard deviations of
	variables{p_end}
{synopt:{opt means(matname3)}}vector with means of variables{p_end}
{synoptline}
{p2colreset}{...}
{p 4 6 2}
* {cmd:n()} is required for {cmd:pcamat}.{p_end}

{p 4 6 2}
{cmd:bootstrap}, {cmd:by}, {cmd:jackknife}, {cmd:rolling}, {cmd:statsby}, and
{cmd:xi} are allowed with {cmd:pca}; see {help prefix}.
{p_end}
{p 4 6 2}
{cmd:aweight}s and {cmd:fweight}s are allowed with {cmd:pca}; see help
{help weight}.
{p_end}
{p 4 6 2}
See {help pca postestimation} for features available after estimation.
{p_end}


{title:Description}

{pstd}
Principal component analysis (PCA) is a statistical
technique for data reduction.  The leading eigenvectors from the eigen
decomposition of the correlation or covariance matrix of the variables
describe a series of uncorrelated linear combinations of the variables that
contain most of the variance.  In addition to data reduction, the eigenvectors
from a PCA are often inspected in order to learn more about the underlying
structure of the data.

{pstd}
{cmd:pca} and {cmd:pcamat} display the eigenvalues and eigenvectors from the
PCA eigen decomposition.  The eigenvectors are returned in orthonormal form,
i.e., orthogonal (uncorrelated) and normalized (with unit length, L'L = I).
{cmd:pcamat} provides the correlation or covariance matrix directly.  For
{cmd:pca} the correlation or covariance matrix is computed from the variables
in {it:varlist}.

{pstd}
{cmd:pcamat} allows the correlation or covariance matrix to be specified as a
k by k symmetric matrix with row and column names set to the variable names,
or as a k(k+1)/2 long row or column vector containing the lower or upper
triangle of the correlation or covariance matrix along with the {cmd:names()}
option providing the variable names.  See the {cmd:shape()} option for
details.

{pstd}
The {cmd:vce(normal)} option of {cmd:pca} and {cmd:pcamat} provides standard
errors of the eigenvalues and eigenvectors and aids in the interpretation
of the eigenvectors.  See {help pca##remarks:Remarks} for a discussion of the
underlying assumptions.

{pstd}
Scores, residuals, rotations, scree plots, score plots, loading plots,
and more are available after {cmd:pca} and {cmd:pcamat},
see {help pca postestimation}.


{title:Options}

{dlgtab:Model 2}

{phang}{opt components(#)} and {opt mineigen(#)}
specify the maximum number of components (eigenvectors or factors) to be
retained.  {cmd:components()} specifies the number directly, and
{cmd:mineigen()} specifies it indirectly, keeping all components with
eigenvalues greater than the indicated value.  The options can be specified
individually, together, or not at all.  {cmd:factors()} is a synonym for
{cmd:components()}.

{pmore}{opt components(#)}
sets the maximum number of components (factors) to be retained.  {cmd:pca} and
{cmd:pcamat} always display the full set of eigenvalues, but displays
eigenvectors only for retained components.  Specifying a number larger than
the number of variables in {it:varlist} is equivalent to specifying the number
of variables in {it:varlist}, and is the default.

{pmore}
{opt mineigen(#)}
sets the minimum value of eigenvalues to be retained.  The default is 1e-5 or
the value of {cmd:tol()} if specified.

{pmore}
Specifying {cmd:components()} and {cmd:mineigen()} affects only the number of
components to be displayed and stored in {cmd:e()}, it does not involve the
assumption that the other eigenvalues are 0.  In particular, the standard
errors reported if {cmd:vce(normal)} is specified, do not depend on the number
of retained components.

{phang}{opt correlation} and {opt covariance}
specify that principal components be calculated for the correlation matrix and
covariance matrix, respectively.  The default is {cmd:correlation}.  Unlike
factor analysis, PCA is not scale invariant; the eigenvalues and eigenvectors
of a covariance matrix differ from those of the associated correlation matrix.
Usually, a PCA of a covariance matrix is only meaningful if the variables are
expressed in the same units.

{pmore}
In case of {cmd:pcamat}, do not confuse the type of the matrix to be
analyzed with the type of {it:matname}.  Obviously, if {it:matname} is
a correlation matrix, and the option {cmd:sds()} is not specified, it
is not possible to perform a PCA of the covariance matrix.

{phang}{cmd:vce(}{cmd:none}|{cmd:normal}{cmd:)}
specifies whether standard errors are computed for the eigenvalues, the
eigenvectors, and the (cumulative) percentage of explained variance
("confirmatory PCA"). These standard errors and tests are obtained assuming
multivariate normality of the data and are valid only for a PCA of a
covariance matrix.  Be cautious in applying these to correlation matrices.

{dlgtab:Reporting}

{phang}{opt level(#)}
specifies the confidence level, as a percentage, for confidence intervals.
The default is {cmd:level(95)} or as set by {helpb set level}.  {cmd:level()}
is only allowed in combination with {cmd:vce(normal)}.

{phang}{opt blanks(#)}
shows blanks for loadings with absolute value smaller than {it:#}.  This
option is ignored when specified with {cmd:vce(normal)}.

{phang}{opt novce}
suppresses the display of standard errors, even though they are computed, and