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1 Factor analysisSyntaxMenuDescriptionOptions for factor and factormatOptions unique to factormatRemarks and examplesStored resultsMethods and formulasReferencesAlso seeSyntaxFactor analysis of datafactorvarlist[if][in][weight][,metho d options]Factor analysis of a correlation matrixfactormatmatname, n(#)[method options factormatoptions]methodDescriptionModel 2pfprincipal factor; the defaultpcfprincipal-component factoripfiterated principal factormlmaximum likelihood factoroptionsDescriptionModel 2factors(#)maximum number of factors to be retainedmineigen(#)minimum value of eigenvalues to be retainedciterate(#)communality reestimation iterations (ipfonly)Reportingblanks(#)display loadings as blank when|loadings|<#altdivisoruse trace of correlation matrix as the divisor for reported proportionsMaximizationprotect(#)perform #optimizations and report the best solution (mlonly)randomuse random starting values (mlonly).

2 Seldom usedseed(seed)random-number seed (mlwithprotect()orrandomonly)maximizeopt ionscontrol the maximization process; seldom used (mlonly)norotateddisplay unrotated solution, even if rotated results are available (replay only)norotateddoes not appear in the dialog factor Factor analysisfactormatoptionsDescriptionModel shape(full)matnameis a square symmetric matrix; the defaultshape(lower)matnameis a vector with the rowwise lower triangle (with diagonal)shape(upper)matnameis a vector with the rowwise upper triangle (with diagonal)names(namelist)variable names; required ifmatnameis triangularforcepsdmodifiesmatnameto be positive semidefinite n(#)number of observationssds(matname2)vector with standard deviations of variablesmeans(matname3)vector with means of variables n(#)is required ,by,jackknife,rolling, andstatsbyare allowed withfactor; see[U] Prefix ,bootstrapandjackkniferesults should be interpreted with caution; identification of thefactorparameters involves data-dependent restrictions, possibly leading to badly biased and overdispersed estimates (Milanand Whittaker 1995).

3 Weights are not allowed with thebootstrapprefix; see [R] are not allowed with thejackknifeprefix; see [R] andfweights are allowed withfactor; see[U] [U] 20 Estimation and postestimation commandsfor more capabilities of estimation > multivariate analysis>Factor and principal component analysis>Factor analysisfactormatStatistics> multivariate analysis>Factor and principal component analysis>Factor analysis of a correlation matrixDescriptionfactorandfactormatperfo rm a factor analysis of a correlation produce principal factor, iterated principal factor, principal-component factor, and maximum-likelihood factor the eigenvalues of the correlation matrix,the factor loadings, and the uniqueness (=1 communality)

4 Of the data in the form of variables, allows weights, and can be run for subgroups (see[D]by).factormatis for use with a correlation or covariance matrix in the form of a square Statamatrix or a vector containing the rowwise upper or lower triangle of the correlation or covariancematrix. This concept is explained in more detail below; see optionshape(). If a covariance matrix isprovided tofactormat, it is transformed into a correlation matrix for the factor analysis. To replayestimation results, you may type for factor and factormat Model 2 pf,pcf,ipf, andmlindicate the type of estimation to be performed.

5 The default Factor analysis 3pfspecifies that the principal-factor method be used to analyze the correlation matrix. The factorloadings, sometimes called the factor patterns, are computed using the squared multiple correlationsas estimates of the the that the principal-component factor method be used to analyze the correlation communalities are assumed to be that the iterated principal-factor method be used to analyze the correlation reestimates the communalities the maximum-likelihood factor method, assuming multivariate normal estimation method is equivalent to Rao s canonical-factor method and maximizes the deter-minant of the partial correlation matrix.

6 Hence, this solution is also meaningful as a descriptivemethod for nonnormal not available for singular correlation matrices. At least threevariables must be specified with (#)andmineigen(#)specify the maximum number of factors to be ()specifies the number directly, andmineigen()specifies it indirectly, keeping all factors witheigenvalues greater than the indicated value. The options can be specified individually, together,or not at (#)sets the maximum number of factors to be retained for later use by the prints the full set of eigenvalues but prints the corresponding eigenvectorsonly for retained factors.

7 Specifying a number larger than the number of variables in thevarlistis equivalent to specifying the number of variables in thevarlistand is the (#)sets the minimum value of eigenvalues to be retained. The default for all methodsexceptpcfis 5 10 6(effectively zero), meaning that factors associated with negative eigenvalueswill not be printed or retained. The default forpcfis 1. Many sources recommendmineigen(1),although the justification is complex and uncertain. If#is less than 5 10 6, it is reset to 5 10 (#)is used only withipfand sets the number of iterations for reestimating the commu-nalities.

8 Ifciterate()is not specified, iterations continue until the change in the communalitiesis (0)produces the same results thatpfdoes. Reporting blanks(#)specifies that factor loadings smaller than#(in absolute value) be displayed as that reported proportions and cumulative proportions be computed using thetrace of the correlation matrix,trace(e(C)), as the divisor. The default is to use the sum of alleigenvalues (even those that are negative) as the divisor. Maximization protect(#)is used only withmland requests that#optimizations with random starting valuesbe performed along with squared multiple correlation coefficient starting values and that the bestof the solutions be reported.

9 The output also indicates whether all starting values converged tothe same solution. When specified with a large number, such asprotect(50), this providesreasonable assurance that the solution found is global and not just a local maximum. Iftraceisalso specified (see [R]maximize), the parameters and likelihoods of each maximization will used only withmland requests that random starting values be used. This option is rarelyused and should be used only afterprotect()has shown the presence of multiple factor Factor analysisseed(seed)is used only withmlwhen therandomorprotect()options are also ()specifies the random-number seed; see [R]set seed.

10 Ifseed()is not specified, the random-numbergenerator starts in whatever state it was last :iterate(#),[no]log,trace,tolerance(#), andltolerance(#); see[R]maximize. These options are seldom following option is available withfactorbut is not shown in the dialog box:norotatedspecifies that the unrotated factor solution be displayed, even if a rotated factor solutionis for use only with replaying unique to factormat Model shape(shape)specifies the shape (storage method) for the covariance or correlation following shapes are supported:fullspecifies that the correlation or covariance structure ofkvariables is a symmetrick kmatrix.