# Sas Error Communality Greater Than 1.0

Table 33.1 Options Available in the PROC FACTOR Statement Option Description Data Set Options DATA= specifies input SAS data set OUT= specifies output SAS data set OUTSTAT= specifies output data set containing statistical results TARGET= specifies input data set containing the target pattern for rotation Factor Extraction and Communalities HEYWOOD sets to 1 any communality greater than 1 METHOD= specifies the estimation method PRIORS= specifies the method for computing prior communality estimates RANDOM= specifies the seed for pseudo-random number generation ULTRAHEYWOOD allows communalities to exceed 1 Number of Factors MINEIGEN= specifies the smallest eigenvalue for retaining a factor NFACTORS= specifies the number of factors to retain PROPORTION= specifies the proportion of common variance in extracted factors Data Analysis Options ALPHA= specifies the confidence level for interval construction COVARIANCE requests factoring of the covariance matrix COVER= computes the confidence interval and specifies the coverage reference point NOINT omits the intercept from computing covariances or correlations SE requests the standard error estimates in ML estimation VARDEF= specifies the divisor used in calculating covariances or correlations WEIGHT factors a weighted correlation or covariance matrix Rotation Method and Properties GAMMA= specifies the orthomax weight HKPOWER= specifies the power in Harris-Kaiser rotation NORM= specifies the method for row normalization in rotation NOPROMAXNORM turns off row normalization in promax rotation POWER= specifies the power to be used in promax rotation PREROTATE= specifies the prerotation method in promax rotation RCONVERGE= specifies the convergence criterion for rotation cycles RITER= specifies the maximum number of cycles for rotation ROTATE= specifies the rotation method TAU= specifies the oblimin weight ODS Graphics PLOTS= specifies ODS Graphics selection Control Display Output ALL displays all optional output except plots CORR displays the (partial) correlation matrix EIGENVECTORS displays the eigenvectors of the reduced correlation matrix FLAG= specifies the minimum absolute value to be flagged in the correlation and loading matrices FUZZ= specifies the maximum absolute value to be displayed as missing in the correlation

FACTOR This page was developed by the Consulting group of the Division of Statistics and Scientific Computing at the University of Texas at Austin. We thank them for permission to distribute it via our web site. 26 June 1995 Usage Note: Stat-53 Copyright 1995-1997, ACITS, The University of Texas at Austin Statistical Services, 475-9372 Originally available online at: http://ssc.utexas.edu/docs/stat53.html Factor Analysis Using SAS PROC FACTOR This usage note describes how to run a factor analysis, specifically an exploratory common factor analysis, using the SAS FACTOR procedure. This document is composed of three sections: Introduction, Outline of Use, and An https://support.sas.com/documentation/cdl/en/statug/63347/HTML/default/statug_factor_sect006.htm Illustrative Example. The Introduction section explains what factor analysis is and when one should use it. The next section is a detailed outline for conducting a factor analysis. Finally the last section illustrates the use of common factor analysis using actual data. What Is Factor Analysis? Factor analysis is a generic term for a family of statistical techniques concerned with the reduction of a set of observable variables in http://www.ats.ucla.edu/stat/sas/library/factor_ut.htm terms of a small number of latent factors. It has been developed primarily for analyzing relationships among a number of measurable entities (such as survey items or test scores). The underlying assumption of factor analysis is that there exists a number of unobserved latent variables (or "factors") that account for the correlations among observed variables, such that if the latent variables are partialled out or held constant, the partial correlations among observed variables all become zero. In other words, the latent factors determine the values of the observed variables. Each observed variable (y) can be expressed as a weighted composite of a set of latent variables (f's) such that y = a f + a f + ... + a f + e i i1 1 i2 2 ik k i where y_i is the iith observed variable on the factors, and e_i is the residual of y_i on the factors. Given the assumption that the residuals are uncorrelated across the observed variables, the correlations among the observed variables are accounted for by the factors. The following is an example of a simple path diagram for a factor analysis model. This diagram is a schematic representation of the above formula. F1 and F2 are two

Total = 8.94349781 Average = 1.78869956 Eigenvalue Difference Proportion Cumulative 1 7.81003142 5.75597699 0.8733 0.8733 2 2.05405443 2.16118801 0.2297 1.1029 3 -.10713358 0.21620672 -0.0120 1.0910 4 -.32334030 http://www.stat.ncsu.edu/people/bloomfield/courses/st731/stocks-factor-analysis4.html 0.16677387 -0.0362 1.0548 5 -.49011417 -0.0548 1.0000 2 factors will http://sites.stat.psu.edu/~ajw13/stat505/fa06/17_factor/10_factor_example.html be retained by the PROPORTION criterion. Iteration Criterion Ridge Change Communalities 1 0.0704728 0.0313 0.5248 1.21812 0.67556 0.79974 0.46740 0.54849 ERROR: Communality greater than 1.0. Method = Maximum Likelihood Heywood fixup The FACTOR Procedure Initial Factor Method: Maximum Likelihood Prior Communality Estimates: SMC sas error cvx dd dow hon xom 0.69329826 0.58565226 0.62362806 0.41489432 0.74382163 Preliminary Eigenvalues: Total = 8.94349781 Average = 1.78869956 Eigenvalue Difference Proportion Cumulative 1 7.81003142 5.75597699 0.8733 0.8733 2 2.05405443 2.16118801 0.2297 1.1029 3 -.10713358 0.21620672 -0.0120 1.0910 4 -.32334030 0.16677387 -0.0362 1.0548 5 -.49011417 -0.0548 1.0000 2 factors will be retained by the PROPORTION sas error communality criterion. Iteration Criterion Ridge Change Communalities 1 0.1078566 0.0313 0.3067 1.00000 0.63819 0.72654 0.44558 0.62967 2 0.0223267 0.0000 0.1200 1.00000 0.69347 0.78560 0.47234 0.74971 3 0.0218857 0.0000 0.0137 1.00000 0.70631 0.77194 0.47549 0.74932 4 0.0218752 0.0000 0.0021 1.00000 0.70625 0.77233 0.47340 0.75013 5 0.0218750 0.0000 0.0003 1.00000 0.70656 0.77201 0.47346 0.75012 Convergence criterion satisfied. Significance Tests Based on 66 Observations Test DF Chi-Square Pr > ChiSq H0: No common factors 10 176.4415 <.0001 HA: At least one common factor H0: 2 Factors are sufficient 1 1.3380 0.2474 HA: More factors are needed Chi-Square without Bartlett's Correction 1.4218728 Akaike's Information Criterion -0.5781272 Schwarz's Bayesian Criterion -2.7677819 Tucker and Lewis's Reliability Coefficient 0.9796914 Squared Canonical Correlations Factor1 Factor2 1.0000000 0.8550749 Eigenvalues of the Weighted Reduced Correlation Matrix: Total = 5.90011651 Average = 1.47502913 Eigenvalue Difference Proportion Cumulative 1 Infty Infty 2 5.90011671 5.75633734 1.0000 1.0000 3 0.14377937 0.13813367 0.0244 1.0244 4 0.00564570 0.15507097 0.0010 1.0253 5 -.1494252

of factors. You will notice that this program is missing the "hey" option. We will start out without this option to see what type of error may occur here, and how it may be remedied. This is something that could very easily happen with your own data analysis. For m = 3 factors, maximum likelihood estimation fails to converge. An examination of the records of each iteration reveals that the communality of the first variable (climate) exceeds one during the first iteration. Since the communality must lie between 0 and 1, this is the cause for failure. We have to fix this. SAS provides a number of different fixes for this kind of error. Most of these fixes have to do with the initial guess for the communalities; that is, changing the starting values for the communalities. Remedies Attempt adding a priors option to the procedure, setting an initial guess for the communalities. Available priors include: priors=smc: Sets the prior communality of each variable proportional to the R 2 of that variable with all other variables as an initial guess. priors=asmc: As above, but an adjustment is made so that the sum of the communalities is equal to the maximum of the absolute correlations. priors=max: Sets the prior communality of each variable to the maximum absolute correlation within any other variable. priors=random: Sets the prior communality of each variable to a random number between 0 and 1. The idea here is that if we start out with better starting values then we might have better luck at convergence. Unfortunately in trying each of these options, (including running the random option multiple times), we find that these options are ineffective for our Places Rated Data case. The second option needs to be considered. Attempt adding the "hey" (Heywood) option to the procedure. This sets communalities greater than one back to on

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