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PC

The PC command is available to extract principal components from a set of data and, as an option, do a varimax rotation for factor analysis. A good reference on principal components is Jolliffe [1986]. Output may include the eigenvalues, eigenvectors, components, factor matrix, and rotated factor matrix. It is possible to specify conditions under which factors are retained. Multicollinearity diagnostics including condition numbers, condition indexes, and variance proportions may also be printed. The command may also be used for Principal Components Regression. For more details see the SHAZAM Reference Manual.

In general, the format is:

PC vars / options

The available options are:

OPTION DESCRIPTION
cor Specifies that the analysis is to be done on the CORrelation matrix. If this option is not specified, the analysis is done on the deviations from the means cross-product matrix. Since the components are sensitive to transformations, it is important that the user be sure this option is needed. If all the variables are measured in the same units, it is probably better to use the cross-product matrix. This is often the case for economists. If the variables are all measured differently, it may be more appropriate to use the correlation matrix which, in effect, normalizes all variables.
beg= Specifies the BEGinning observation to be used in estimation. This option overrides the SAMPLE command and defaults to the sample range in effect.
end= Specifies the ENDing observation to be used in estimation. This option overrides the SAMPLE command and defaults to the sample range in effect.
eval= Saves the EigenVALues in the vector specified. The values are sorted in descending order (that is, the largest eigenvalue is first).
evec= Saves the EigenVECtors in the (K x K) matrix specified. The first column of the matrix is the eigenvector that corresponds to the largest eigenvalue.
list LISTs the matrix of principal components. If there are many observations the list of all the components will be very long.
max Sets the PEVEC, PFM and PRM options.
maxfact= Specifies the MAXimum number of FACTors to be retained. If no value of MINEIG is specified MAXFACT will be the actual number retained. If MAXFACT is not specified, all will be included.
mineig= Specifies the MINimum EIGenvalue allowed to be retained. If the COR option is specified, the eigenvalues will range from 0 to the number of variables in the analysis. Sometimes a convenient value is MINEIG=1. This rule of thumb does not work if the analysis is done on the cross-product matrix. The default is MINEIG=0.
nc= The normalization code which must be specified if a listing of the actual retained components is desired. The codes are: 1. No normalization, variance is lambda/(n-1) 2. Variance is 1/(n-1) 3. Variance is lambda 4. Variance is 1 where lambda is the eigenvalue corresponding to the component and n is the number of observations
pcinfo= Saves a matrix of INFOrmation needed for regressions on Principal Components.
pcollin Prints the table of variance-decomposition proportions that can be used for the detection of multiCOLLINearity.
pcomp= Saves the matrix of Principal COMPonents in the NxK matrix specified. The first column of the matrix is the principal component that corresponds to the largest eigenvalue.
pevec Prints all the EigenVECtors for the retained components. If there are many variables this option could yield a lot of costly output which may have little value.
pfm Prints the Factor Matrix for the retained factors.
prm Computes and Prints the Rotated factor Matrix by a varimax rotation. The method is described in Kaiser [1959]. The varimax rotation is one of the most common types of rotation.
raw Specifies that the analysis is to be done on the RAW cross-product matrix. If this option is not specified, the analysis is done on the deviations from the means cross-product matrix. The same warnings specified for the COR option apply here.
scale Specifies that the analysis is to be done on a scaled cross-product matrix. The scaled matrix transforms a RAW cross-product matrix into one where the data vectors all have unit length so that the diagonals of the cross-product matrix are all equal to 1. Note that this is not the same as the COR option. If the SCALE option is not specified, the analysis is done on the deviations from the means cross-product matrix. The same warnings specified for the COR option apply here.