Confirmatory Factor Analysis With SAS Calis

Read a brief description of the data here. See the SAS output here.

The data for this lesson are available at T&F’s data site and also from my SPSS data page, file CFA-Wisc.sav. The data are also in the file CFA-Wisc.xls on my StatData page. Download that Excel file. Bring the data into SAS.

Paste the following code into the Program Editor and run it.

optionsformdlim='-'nodatepagno=min;

proccaliscovpAll; var info -- coding;

LINEQS

info = v1 F_Verbal + e1,

comp = v2 F_Verbal + e2,

arith = v3 F_Verbal + e3,

simil = v4 F_Verbal + e4,

vocab = v5 F_Verbal + e5,

digit = v6 F_Verbal + e6,

pictcomp = p1 F_Perform + e7,

parang = p2 F_Perform + e8,

block = p3 F_Perform + e9,

object = p4 F_Perform + e10,

coding = p5 F_Perform + e11;

STD

F_VerbalF_Perform = 1.01.0,

e1-e11 = e_var1-e_var11;

COV

F_VerbalF_Perform = phi;

run;

Each of the measured variables is related to one or the other of the two factors, with parameters v1 – v6 and p1 – p6 to be estimated. The variances of the two factors are fixed at 1. Phi is the covariance between the two factors, which is to be estimated.

Look at the output. The null hypothesis of good fit is rejected, but this may be simply from having too much power. The fit indices are OK. GFI (.931) exceeds .9, CFI (.941) does not quite reach the .95 standard, and RMSEA (.06) is between good (.05) and adequate (.08).. The standardized residual for PictComp-Comp is high, with the same value T&F got with EQS. The path from Performance IQ to Coding is not significant (t = .81). The correlation between factors is .59. The standardized path coefficients are the same reported by Amos. If you square the coefficients for the error terms you get 1  the R2 reported by Amos. The Lagrange Multiplier test suggests adding a path from Performance IQ to Comp, with the obtained value of Chi-square (9.767) being the same that T&F reported getting from EQS. The Wald test indicates that the fit of the model would not be significantly reduced by dropping the path from Performance IQ to Coding.

Model 2. Here I have added a path from Performance IQ to Comp. The model fit Chi-square has dropped from 70.236 to 60.295, a drop of 9.94, which, on one df, is significant. Adding that path from Performance IQ to Comp has significantly improved the fit of the model. GFI has increased from .931 to .942, CFI from .941 to .960, and RMSEA has dropped from .06 to .05.

Notice that the path from Performance IQ to Coding is not statistically significant. Perhaps we should just drop that variable. Drop it and see what happens.

Model 3. With Coding out of the model, the goodness of fit Chi-square is no longer significant, 2(33) = 45.018, p = .079. GFI has increased from .94 to .952, CFI from .960 to .974, and RMSEA has dropped from .05 to .046.

  • David Kenney on Fit Indices
  • CFA with AMOS
  • CFA with SAS ProcCalisCFA on Big Five Instrument
  • Draw an SEM Diagram in Power Point
  • Return to Wuensch’s Stats Lessons Page

Karl L. Wuensch
Dept. of Psychology, East Carolina Univ., Greenville, NC 27858 USA

April, 2016