Syntax

You can specify the following statements with the FACTOR procedure:

• PROC FACTOR < options > ;

  • VAR variables ;

  • PRIORS communalities ;

  • PARTIAL variables ;

  • FREQ variable ;

  • WEIGHT variable ;

  • BY variables ;

Usually only the VAR statement is needed in addition to the PROC FACTOR statement. The descriptions of the BY, FREQ, PARTIAL, PRIORS, VAR, and WEIGHT statements follow the description of the PROC FACTOR statement in alphabetical order.

PROC FACTOR Statement

• PROC FACTOR < options > ;

The options available with the PROC FACTOR statement are listed in the following table and then are described in alphabetical order:

Table 27.1: Options Available in the PROC FACTOR Statement

Task	Option
Data sets	DATA= OUT= OUTSTAT= TARGET=
Extract factors and communalities	HEYWOOD METHOD= PRIORS= RANDOM= ULTRAHEYWOOD
Analyze data	ALPHA= COVARIANCE COVER= NOINT SE VARDEF= WEIGHT
Specify number of factors	MINEIGEN= NFACTORS= PROPORTION=
Specify numerical properties	CONVERGE= MAXITER= SINGULAR=
Specify rotation method and properties	GAMMA= HKPOWER= NORM= NOPROMAXNORM POWER= PREROTATE= RCONVERGE= RITER= ROTATE= TAU=
Control displayed output	ALL CORR EIGENVECTORS FLAG= FUZZ= MSA NOPRINT NPLOT= PLOT PREPLOT PRINT REORDER RESIDUALS ROUND SCORE SCREE SIMPLE
Exclude the correlation matrix from the OUTSTAT= data set	NOCORR
Miscellaneous	NOBS=

ALL

• displays all optional output except plots. When the input data set is TYPE=CORR, TYPE=UCORR, TYPE=COV, TYPE=UCOV, or TYPE=FACTOR, simple statistics, correlations , and MSA are not displayed.

ALPHA= p

• specifies the level of confidence 1 ˆ’ p for interval construction. By default, p = 0.05, corresponding to 1 ˆ’ p = 95% confidence intervals. If p is greater than one, it is interpreted as a percentage and divided by 100. Because the coverage probability is not controlled simultaneously , you may consider supplying a nonconventional p using methods such as Bonferroni adjustment.

CONVERGE= p

CONV= p

• specifies the convergence criterion for the METHOD=PRINIT, METHOD=ULS, METHOD=ALPHA, or METHOD=ML option. Iteration stops when the maximum change in the communalities is less than the value of the CONVERGE= option. The default value is 0.001. Negative values are not allowed.

CORR

C

• displays the correlation matrix or partial correlation matrix.

COVARIANCE

COV

• requests factoring of the covariance matrix instead of the correlation matrix. The COV option can be used only with the METHOD=PRINCIPAL, METHOD=PRINIT, METHOD=ULS, or METHOD=IMAGE option.

COVER < = p>

CI < = p>

• computes the confidence intervals and optionally specifies the value of factor loading for coverage detection. By default, p = 0. The specified value is represented by an asterisk ˜* in the coverage display. This is useful for determining the salience of loadings. For example, if COVER=.4, a display ˜0*[ ] indicates that the entire confidence interval is above 0.4, implying strong evidence for the salience of the loading. See the section Confidence Intervals and the Salience of Factor Loadings on page 1327 for more details.

DATA= SAS-data-set

• specifies the input data set, which can be an ordinary SAS data set or a specially structured SAS data set as described in the section Input Data Set beginning on page 1322. If the DATA= option is omitted, the most recently created SAS data set is used.

EIGENVECTORS

EV

• displays the eigenvectors of the reduced correlation matrix, of which the diagonal elements are replaced with the communality estimates. When METHOD=ML, the eigenvectors are for the weighted reduced correlation matrix. PROC FACTOR chooses the solution that makes the sum of the elements of each eigenvector nonnegative. If the sum of the elements is equal to zero, then the sign depends on how the number is rounded off.

FLAG= p

• flags absolute values larger than p with an asterisk in the correlation and loading matrices. Negative values are not allowed for p . Values printed in the matrices are multiplied by 100 and rounded to the nearest integer (see the ROUND option). The FLAG= option has no effect when standard errors or confidence intervals are also printed.

FUZZ= p

• prints correlations and factor loadings with absolute values less than p printed as missing. For partial correlations, the FUZZ= value is divided by 2. For residual correlations, the FUZZ= value is divided by 4. The exact values in any matrix can be obtained from the OUTSTAT= and ODS output data sets. Negative values are not allowed. The FUZZ= option has no effect when standard errors or confidence intervals are also printed.

GAMMA= p

• specifies the orthomax weight used with the option ROTATE=ORTHOMAX or PREROTATE=ORTHOMAX. Alternatively, you can use ROTATE=ORTHOMAX( p ) with p representing the orthomax weight. There is no restriction on valid values for the orthomax weight, although the most common values are between 0 and the number of variables. The default GAMMA= value is one, resulting in the varimax rotation.

HEYWOOD

HEY

• sets to 1 any communality greater than 1, allowing iterations to proceed.

HKPOWER= p

HKP= p

• specifies the power of the square roots of the eigenvalues used to rescale the eigenvectors for Harris-Kaiser (ROTATE=HK) rotation, assuming that the factors are extracted by the principal factor method. If the principal factor method is not used for factor extraction, the eigenvectors are replaced by the normalized columns of the unrotated factor matrix, and the eigenvalues replaced by the column normalizing constants. HKPOWER= values between 0.0 and 1.0 are reasonable. The default value is 0.0, yielding the independent cluster solution, in which each variable tends to have a large loading on only one factor. An HKPOWER= value of 1.0 is equivalent to an orthogonal rotation, with the varimax rotation as the default. You can also specify the HKPOWER= option with ROTATE=QUARTIMAX, ROTATE=BIQUARTIMAX, ROTATE=EQUAMAX, or ROTATE=ORTHOMAX, and so on. The only restriction is that the Harris-Kaiser rotation must be associated with an orthogonal rotation.

MAXITER= n

• specifies the maximum number of iterations for factor extraction. You can use the MAXITER= option with the PRINIT, ULS, ALPHA, or ML methods. The default is 30.

METHOD= name

M= name

• specifies the method for extracting factors. The default is METHOD=PRINCIPAL unless the DATA= data set is TYPE=FACTOR, in which case the default is METHOD=PATTERN. Valid values for name are as follows :

  ALPHA A	produces alpha factor analysis.
  HARRIS H	yields Harris component analysis of S ˆ’ 1 RS ˆ’ 1 (Harris 1962), a noniterative approximation to canonical component analysis.
  IMAGE I	yields principal component analysis of the image covariance matrix, not Kaiser s (1963, 1970) or Kaiser and Rice s (1974) image analysis. A nonsingular correlation matrix is required.
  ML M	performs maximum likelihood factor analysis with an algorithm due, except for minor details, to Fuller (1987). The option METHOD=ML requires a nonsingular correlation matrix.
  PATTERN	reads a factor pattern from a TYPE=FACTOR, TYPE=CORR, TYPE=UCORR, TYPE=COV or TYPE=UCOV data set. If you create a TYPE=FACTOR data set in a DATA step, only observations containing the factor pattern ( _TYPE_ = PATTERN ) and, if the factors are correlated, the interfactor correlations ( _TYPE_ = FCORR ) are required.
  PRINCIPAL PRIN P	yields principal component analysis if no PRIORS option or statement is used or if you specify PRIORS=ONE; if you specify a PRIORS statement or a PRIORS= value other than PRIORS=ONE, a principal factor analysis is performed.
  PRINIT	yields iterated principal factor analysis.
  SCORE	reads scoring coefficients ( _TYPE_ = SCORE ) from a TYPE=FACTOR, TYPE=CORR, TYPE=UCORR, TYPE=COV, or TYPE=UCOV data set. The data set must also contain either a correlation or a covariance matrix. Scoring coefficients are also displayed if you specify the OUT= option.
  ULS U	produces unweighted least squares factor analysis.

MINEIGEN= p

MIN= p

• specifies the smallest eigenvalue for which a factor is retained. If you specify two or more of the MINEIGEN=, NFACTORS=, and PROPORTION= options, the number of factors retained is the minimum number satisfying any of the criteria. The MINEIGEN= option cannot be used with either the METHOD=PATTERN or the METHOD=SCORE option. Negative values are not allowed. The default is 0 unless you omit both the NFACTORS= and the PROPORTION= options and one of the following conditions holds:

  • If you specify the METHOD=ALPHA or METHOD=HARRIS option, then MINEIGEN=1.

  • If you specify the METHOD=IMAGE option, then

    

  • For any other METHOD= specification, if prior communality estimates of 1.0 are used, then

    

    When an unweighted correlation matrix is factored , this value is 1.

MSA

• produces the partial correlations between each pair of variables controlling for all other variables (the negative anti-image correlations) and Kaiser s measure of sampling adequacy (Kaiser 1970; Kaiser and Rice 1974; Cerny and Kaiser 1977).

NFACTORS= n

NFACT= n

N= n

• specifies the maximum number of factors to be extracted and determines the amount of memory to be allocated for factor matrices. The default is the number of variables. Specifying a number that is small relative to the number of variables can substantially decrease the amount of memory required to run PROC FACTOR, especially with oblique rotations . If you specify two or more of the NFACTORS=, MINEIGEN=, and PROPORTION= options, the number of factors retained is the minimum number satisfying any of the criteria. If you specify the option NFACTORS=0, eigenvalues are computed, but no factors are extracted. If you specify the option NFACTORS= ˆ’ 1, neither eigenvalues nor factors are computed. You can use the NFACTORS= option with the METHOD=PATTERN or METHOD=SCORE option to specify a smaller number of factors than are present in the data set.

NOBS= n

• specifies the number of observations. If the DATA= input data set is a raw data set, nobs is defined by default to be the number of observations in the raw data set. The NOBS= option overrides this default definition. If the DATA= input data set contains a covariance, correlation, or scalar product matrix, the number of observations can be specified either by using the NOBS= option in the PROC FACTOR statement or by including a _TYPE_ = N observation in the DATA= input data set.

NOCORR

• prevents the correlation matrix from being transferred to the OUTSTAT= data set when you specify the METHOD=PATTERN option. The NOCORR option greatly reduces memory requirements when there are many variables but few factors. The NOCORR option is not effective if the correlation matrix is required for other requested output; for example, if the scores or the residual correlations are displayed (using SCORE, RESIDUALS, ALL options).

NOINT

• omits the intercept from the analysis; covariances or correlations are not corrected for the mean.

NOPRINT

• suppresses the display of all output. Note that this option temporarily disables the Output Delivery System (ODS). For more information, see Chapter 14, Using the Output Delivery System.

NOPROMAXNORM NOPMAXNORM

• turns off the default row normalization of the pre- rotated factor pattern, which is used in computing the promax target matrix.

NORM=COV KAISER NONE RAW WEIGHT

• specifies the method for normalizing the rows of the factor pattern for rotation. If you specify the option NORM=KAISER, Kaiser s normalization is used . If you specify the option NORM=WEIGHT, the rows are weighted by the Cureton-Mulaik technique (Cureton and Mulaik 1975). If you specify the option NORM=COV, the rows of the pattern matrix are rescaled to represent covariances instead of correlations. If you specify the option NORM=NONE or NORM=RAW, normalization is not performed. The default is NORM=KAISER.

NPLOT= n

• specifies the number of factors to be plotted. The default is to plot all factors. The smallest allowable value is 2. If you specify the option NPLOT= n , all pairs of the first n factors are plotted, producing a total of n ( n ˆ’ 1) / 2 plots.

OUT= SAS-data-set

• creates a data set containing all the data from the DATA= data set plus variables called Factor1 , Factor2 , and so on, containing estimated factor scores. The DATA= data set must contain multivariate data, not correlations or covariances. You must also specify the NFACTORS= option to determine the number of factor score variables. Note that OUT= option is disabled if you specify partial variables in the PARTIAL statement. In order to use the OUT= option with partialed variables, you can first regress the target variables on the partial variables. This can be done using PROC REG or PROC IML. You can then factor analyze the residuals without the PARTIAL statement. In this case, the OUT= option will not be disabled. If you want to create a permanent SAS data set, you must specify a two-level name. Refer to SAS Files in SAS Language Reference: Concepts for more information on permanent data sets.

OUTSTAT= SAS-data-set

• specifies an output data set containing most of the results of the analysis. The output data set is described in detail in the section Output Data Sets on page 1325. If you want to create a permanent SAS data set, you must specify a two-level name. Refer to SAS Files in SAS Language Reference: Concepts for more information on permanent data sets.

PLOT

• plots the factor pattern after rotation.

POWER= n

• specifies the power to be used in computing the target pattern for the option ROTATE=PROMAX. Valid values must be integers ‰ 1. The default value is 3. You can also specify the power= value in the ROTATE= option, e.g., ROTATE=PROMAX(4).

PREPLOT

• plots the factor pattern before rotation.

PREROTATE= name

PRE= name

• specifies the prerotation method for the option ROTATE=PROMAX. Any rotation method other than PROMAX or PROCRUSTES can be used. The default is PREROTATE=VARIMAX. If a previously rotated pattern is read using the option METHOD=PATTERN, you should specify the PREROTATE=NONE option.

PRINT

• displays the input factor pattern or scoring coefficients and related statistics. In oblique cases, the reference and factor structures are computed and displayed. The PRINT option is effective only with the option METHOD=PATTERN or METHOD=SCORE.

PRIORS= name

• specifies a method for computing prior communality estimates. You can specify numeric values for the prior communality estimates by using the PRIORS statement. Valid values for name are as follows:

  ASMC A	sets the prior communality estimates proportional to the squared multiple correlations but adjusted so that their sum is equal to that of the maximum absolute correlations (Cureton 1968).
  INPUT I	reads the prior communality estimates from the first observation with either _TYPE_ = PRIORS or _TYPE_ = COMMUNAL in the DATA= data set (which must be TYPE=FACTOR).
  MAX M	sets the prior communality estimate for each variable to its maximum absolute correlation with any other variable.
  ONE O	sets all prior communalities to 1.0.
  RANDOM R	sets the prior communality estimates to pseudo-random numbers uniformly distributed between 0 and 1.
  SMC S	sets the prior communality estimate for each variable to its squared multiple correlation with all other variables.

• The default prior communality estimates are as follows:

  METHOD=	PRIORS=
  PRINCIPAL	ONE
  PRINIT	ONE
  ALPHA	SMC
  ULS	SMC
  ML	SMC
  HARRIS	(not applicable )
  IMAGE	(not applicable)
  PATTERN	(not applicable)
  SCORE	(not applicable)

• By default, the options METHOD=PRINIT, METHOD=ULS, METHOD=ALPHA, and METHOD=ML stop iterating and set the number of factors to 0 if an estimated communality exceeds 1. The options HEYWOOD and ULTRAHEYWOOD allow processing to continue.

PROPORTION= p

PERCENT= p

P= p

• specifies the proportion of common variance to be accounted for by the retained factors using the prior communality estimates. If the value is greater than one, it is interpreted as a percentage and divided by 100. The options PROPORTION=0.75 and PERCENT=75 are equivalent. The default value is 1.0 or 100%. You cannot specify the PROPORTION= option with the METHOD=PATTERN or METHOD=SCORE option. If you specify two or more of the PROPORTION=, NFACTORS=, and MINEIGEN= options, the number of factors retained is the minimum number satisfying any of the criteria.

RANDOM= n

• specifies a positive integer as a starting value for the pseudo-random number generator for use with the option PRIORS=RANDOM. If you do not specify the RANDOM= option, the time of day is used to initialize the pseudo-random number sequence. Valid values must be integers ‰ 1.

RCONVERGE= p

RCONV= p

• specifies the convergence criterion for rotation cycles. Rotation stops when the scaled change of the simplicity function value is less than the RCONVERGE= value. The default convergence criterion is

  

  where f _new and f _old are simplicity function values of the current cycle and the previous cycle, respectively, K = max (1 , f _old ) is a scaling factor, and ˆˆ is 1E-9 by default and is modified by the RCONVERGE= value.

REORDER

RE

• causes the rows (variables) of various factor matrices to be reordered on the output. Variables with their highest absolute loading (reference structure loading for oblique rotations) on the first factor are displayed first, from largest to smallest loading, followed by variables with their highest absolute loading on the second factor, and so on. The order of the variables in the output data set is not affected. The factors are not reordered.

RESIDUALS

RES

• displays the residual correlation matrix and the associated partial correlation matrix. The diagonal elements of the residual correlation matrix are the unique variances.

RITER= n

• specifies the maximum number of cycles n for factor rotation. Except for promax and Procrustes, you can use the RITER= option with all rotation methods. The default n is the maximum between 100 and 10 times of the number of variables.

ROTATE= name

R= name

• specifies the rotation method. The default is ROTATE=NONE.

• Valid name s for orthogonal rotations are as follows:

  BIQUARTIMAX BIQMAX	specifies orthogonal biquartimax rotation. This corresponds to the specification ROTATE=ORTHOMAX(.5).
  EQUAMAX E	specifies orthogonal equamax rotation. This corresponds to the specification ROTATE=ORTHOMAX with GAMMA= number of factors /2.
  FACTORPARSIMAX FPA	specifies orthogonal factor parsimax rotation. This corresponds to the specification ROTATE=ORTHOMAX with GAMMA= number of variables .
  NONE N	specifies that no rotation be performed, leaving the original orthogonal solution.
  ORTHCF ( p1 , p2 ) ORCF ( p1 , p2 )	specifies the orthogonal Crawford-Ferguson rotation with the weights p1 and p2 for variable parsimony and factor parsimony, respectively. See the definitions of weights in the section Simplicity Functions for Rotations on page 1329.
  ORTHGENCF ( p1 , p2 , p3 , p4 ) ORGENCF ( p1 , p2 , p3 , p4 )	specifies the orthogonal generalized Crawford-Ferguson rotation with the four weights p1 , p2 , p3 , and p4 . See the definitions of weights in the section Simplicity Functions for Rotations on page 1329.
  ORTHOMAX < ( p ) > ORMAX < ( p ) >	specifies the orthomax rotation with orthomax weight p . If ROTATE=ORTHOMAX is used, the default p value is 1 unless specified otherwise in the GAMMA= option. Alternatively, ROTATE=ORTHOMAX( p ) specifies p as the orthomax weight or the GAMMA= value. See the definition of the orthomax weight in the section Simplicity Functions for Rotations on page 1329.
  PARSIMAX PA	specifies orthogonal parsimax rotation. This corresponds to the specification ROTATE=ORTHOMAX with
  	where nvar is the number of variables, and nfact is the number of factors.
  QUARTIMAX QMAX Q	specifies orthogonal quartimax rotation. This corresponds to the specification ROTATE=ORTHOMAX(0).
  VARIMAX V	specifies orthogonal varimax rotation. This corresponds to the specification ROTATE=ORTHOMAX with GAMMA=1.

  Valid name s for oblique rotations are as follows:

  BIQUARTIMIN BIQMIN	specifies biquartimin rotation. It corresponds to the specification ROTATE=OBLIMIN(.5) or ROTATE=OBLIMIN with TAU=.5.
  COVARIMIN CVMIN	specifies covarimin rotation. It corresponds to the specification ROTATE=OBLIMIN(1) or ROTATE=OBLIMIN with TAU=1.
  HK < ( p ) > H < ( p ) >	specifies Harris-Kaiser case II orthoblique rotation. When specifying this option, you can use the HKPOWER= option to set the power of the square roots of the eigenvalues by which the eigenvectors are scaled, assuming that the factors are extracted by the principal factor method. For other extraction methods, the unrotated factor pattern is column normalized. The power is then applied to the column normalizing constants, instead of the eigenvalues. You can also use ROTATE=HK( p ), with p representing the HKPOWER= value. The default associated orthogonal rotation with ROTATE=HK is the varimax rotation without Kaiser normalization. You may associate the Harris-Kaiser with other orthogonal rotations using the ROTATE= option together with the HKPOWER= option.
  OBBIQUARTIMAX OBIQMAX	specifies oblique biquartimax rotation.
  OBEQUAMAX OE	specifies oblique equamax rotation.
  OBFACTORPARSIMAX OFPA	specifies oblique factor parsimax rotation.
  OBLICF( p1 , p2 ) OBCF( p1 , p2 )	xspecifies the oblique Crawford-Ferguson rotation with the weights p1 and p2 for variable parsimony and factor parsimony, respectively. See the definitions of weights in the section Simplicity Functions for Rotations on page 1329.
  OBLIGENCF( p1 , p2 , p3 , p4 ) OBGENCF( p1 , p2 , p3 , p4 )	specifies the oblique generalized Crawford-Ferguson rotation with the four weights p1 , p2 , p3 , and p4 . See the definitions of weights in the section Simplicity Functions for Rotations on page 1329.
  OBLIMIN < ( p ) > OBMIN < ( p ) >	specifies the oblimin rotation with oblimin weight p . If ROTATE=OBLIMIN is used, the default p value is zero unless specified otherwise in the TAU= option. Alternatively, ROTATE=OBLIMIN( p ) specifies p as the oblimin weight or the TAU= value. See the definition of the oblimin weight in the section Simplicity Functions for Rotations on page 1329.
  OBPARSIMAX OPA	specifies oblique parsimax rotation.
  OBQUARTIMAX OQMAX	specifies oblique quartimax rotation. This is the same as the QUARTIMIN method.
  OBVARIMAX OV	specifies oblique varimax rotation.
  PROCRUSTES	specifies oblique Procrustes rotation with the target pattern provided by the TARGET= data set. The unrestricted least squares method is used with factors scaled to unit variance after rotation.
  PROMAX < ( p ) > P < ( p ) >	specifies oblique promax rotation. You can use the PREROTATE= option to set the desirable pre-rotation method, orthogonal or oblique. When using with ROTATE=PROMAX, the POWER= option lets you specify the power for forming the target. You can also use ROTATE=PROMAX( p ), where p represents the POWER= value.
  QUARTIMIN QMIN	specifies quartimin rotation. It is the same as the oblique quartimax method. It also corresponds to the specification ROTATE=OBLIMIN(0) or ROTATE=OBLIMIN with TAU=0.

ROUND

• prints correlation and loading matrices with entries multiplied by 100 and rounded to the nearest integer. The exact values can be obtained from the OUTSTAT= and ODS output data sets. The ROUND option also flags absolute values larger than the FLAG= value with an asterisk in correlation and loading matrices (see the FLAG= option). If the FLAG= option is not specified, the root mean square of all the values in the matrix printed is used as the default FLAG= value. The ROUND option has no effect when standard errors or confidence intervals are also printed.

SCORE

• displays the factor scoring coefficients. The squared multiple correlation of each factor with the variables is also displayed except in the case of unrotated principal components . Unless you specify the NOINT option in PROC FACTOR, the scoring coefficients should be applied to standardized variables “variables that are centered by subtracting the original variable means and then divided by the original variable standard deviations. With the NOINT option, the scoring coefficients should be applied to data without centering.

SCREE

• displays a scree plot of the eigenvalues (Cattell 1966, 1978; Cattell and Vogelman 1977; Horn and Engstrom 1979).

SE

STDERR

• computes standard errors for various classes of unrotated and rotated solutions under the maximum likelihood estimation.

SIMPLE

S

• displays means, standard deviations, and the number of observations.

SINGULAR= p

SING= p

• specifies the singularity criterion, where 0 < p < 1. The default value is 1E ˆ’ 8.

TARGET= SAS-data-set

• specifies an input data set containing the target pattern for Procrustes rotation (see the description of the ROTATE= option). The TARGET= data set must contain variables with the same names as those being factored. Each observation in the TARGET= data set becomes one column of the target factor pattern. Missing values are treated as zeros. The _NAME_ and _TYPE_ variables are not required and are ignored if present.

TAU= p

• specifies the oblimin weight used with the option ROTATE=OBLIMIN or PREROTATE=OBLIMIN. Alternatively, you can use ROTATE=OBLIMIN( p ) with p representing the oblimin weight. There is no restriction on valid values for the oblimin weight, although for practical purposes a negative or zero value is recommended. The default TAU= value is 0, resulting in the quartimin rotation.

ULTRAHEYWOOD

ULTRA

• allows communalities to exceed 1. The ULTRAHEYWOOD option can cause convergence problems because communalities can become extremely large, and ill-conditioned Hessians may occur.

VARDEF=DFNWDFWEIGHT WGT

• specifies the divisor used in the calculation of variances and covariances. The default value is VARDEF=DF. The values and associated divisors are displayed in the following table where i = 0 if the NOINT option is used and i = 1 otherwise, and where k is the number of partial variables specified in the PARTIAL statement.

  Value	Description	Divisor
  DF	degrees of freedom	n ˆ’ k ˆ’ i
  N	number of observations	n ˆ’ k
  WDF	sum of weights DF	ˆ‘ i w i ˆ’ k ˆ’ i
  WEIGHT WGT	sum of weights	ˆ‘ i w i ˆ’ k

WEIGHT

• factors a weighted correlation or covariance matrix. The WEIGHT option can be used only with the METHOD=PRINCIPAL, METHOD=PRINIT, METHOD=ULS, or METHOD=IMAGE option. The input data set must be of type CORR, UCORR, COV, UCOV, or FACTOR, and the variable weights are obtained from an observation with _TYPE_ = WEIGHT .

BY Statement

• BY variables ;

You can specify a BY statement with PROC FACTOR to obtain separate analyses on observations in groups defined by the BY variables. When a BY statement appears, the procedure expects the input data set to be sorted in order of the BY variables.

If your input data set is not sorted in ascending order, use one of the following alternatives:

• Sort the data using the SORT procedure with a similar BY statement.

• Specify the BY statement option NOTSORTED or DESCENDING in the BY statement for the FACTOR procedure. The NOTSORTED option does not mean that the data are unsorted but rather that the data are arranged in groups (according to values of the BY variables) and that these groups are not necessarily in alphabetical or increasing numeric order.

• Create an index on the BY variables using the DATASETS procedure (in Base SAS software). For more information on creating indexes and using the BY statement with indexed datasets, refer to SAS Files in SAS Language Reference: Concepts .

If you specify the TARGET= option and the TARGET= data set does not contain any of the BY variables, then the entire TARGET= data set is used as a Procrustean target for each BY group in the DATA= data set.

If the TARGET= data set contains some but not all of the BY variables, or if some BY variables do not have the same type or length in the TARGET= data set as in the DATA= data set, then PROC FACTOR displays an error message and stops.

If all the BY variables appear in the TARGET= data set with the same type and length as in the DATA= data set, then each BY group in the TARGET= data set is used as a Procrustean target for the corresponding BY group in the DATA= data set. The BY groups in the TARGET= data set must be in the same order as in the DATA= data set. If you specify the NOTSORTED option in the BY statement, there must be identical BY groups in the same order in both data sets. If you do not specify the NOTSORTED option, some BY groups can appear in one data set but not in the other.

For more information on the BY statement, refer to the discussion in SAS Language Reference: Concepts . For more information on the DATASETS procedure, refer to the discussion in the SAS Procedures Guide .

FREQ Statement

• FREQ variable ;

If a variable in the data set represents the frequency of occurrence for the other values in the observation, include the variable s name in a FREQ statement. The procedure then treats the data set as if each observation appears n times, where n is the value of the FREQ variable for the observation. The total number of observations is considered to be equal to the sum of the FREQ variable when the procedure determines degrees of freedom for significance probabilities.

If the value of the FREQ variable is missing or is less than one, the observation is not used in the analysis. If the value is not an integer, the value is truncated to an integer.

The WEIGHT and FREQ statements have a similar effect, except in determining the number of observations for significance tests.

PARTIAL Statement

• PARTIAL variables ;

If you want the analysis to be based on a partial correlation or covariance matrix, use the PARTIAL statement to list the variables that are used to partial out the variables in the analysis.

PRIORS Statement

• PRIORS communalities ;

The PRIORS statement specifies numeric values between 0.0 and 1.0 for the prior communality estimates for each variable. The first numeric value corresponds to the first variable in the VAR statement, the second value to the second variable, and so on. The number of numeric values must equal the number of variables. For example,

  proc factor;   var     x  y  z;   priors .7 .8 .9;   run;  

You can specify various methods for computing prior communality estimates with the PRIORS= option of the PROC FACTOR statement. Refer to the description of that option for more information on the default prior communality estimates.

VAR Statement

• VAR variables ;

The VAR statement specifies the numeric variables to be analyzed. If the VAR statement is omitted, all numeric variables not specified in other statements are analyzed .

WEIGHT Statement

• WEIGHT variable ;

If you want to use relative weights for each observation in the input data set, specify a variable containing weights in a WEIGHT statement. This is often done when the variance associated with each observation is different and the values of the weight variable are proportional to the reciprocals of the variances. If a variable value is negative or is missing, it is excluded from the analysis.