Consider the LSAY math
attitude items found in the data in the Assignment section of the Mplus course
web site (see Week 1, LSAY Data, Input for LSAY):
!enj7-10 = "I ENJOY MATH"
!good7-10="I AM GOOD AT MATH"
!und7-10= "USUALLY UNDERSTAND MATH"
!useboy7-10 = "MATH MORE USEFUL FOR BOYS"
!nerv7-10 = "MATH MAKES ME NERVOUS"
!wor7-10= "WORRY ABOUT MATH TEST GRADES"
!scar7-10 = "SCARED WHEN I OPEN MATH BOOK"
!use7-10 = "MATH USEFUL IN EVERYDAY PROBLEMS"
!logic7-10= "MATH HELPS LOGICAL THINKING"
!boybet7-10 = "BOYS BETTER AT MATH THAN GIRLS"
!job7-10 ="NEED MATH FOR A GOOD JOB"
!often7-10 = "WILL USE MATH OFTEN AS AN ADULT"
where each item is measured
on a 5-point Likert scale: 1-Strongly Agree, 2-Agree, 3-Not sure, 4-Disagree, 5-Strongly
Disagree.
Use these data to do a series
of factor analyses covering EFA, EFA within CFA, and simple structure CFA. Show that the EFA within CFA has the
same maximum-likelihood chi-square value and degrees of freedom as the EFA.
Regarding
doing EFA within a CFA framework, the choice of starting values is sometimes
important to avoid non-convergence.
Note that the CFA default loading starting value is 1 while your EFA
solution might indicate many loadings close to 0 or negative 1. In such cases, you may use a variation
on what was shown in class, where instead you specify starting values of 0 for
all loadings in a column and then modify this statement by starting a few key,
large EFA loadings at 1 or -1. For
example, if only y4 and y6 have large positive loadings on f1 in the EFA, you
can say:
f1
by y1-u6*0;
f1 by y4 y6;
which gives a loading
starting value of 0 for y1, y2, y3, and y5, and a loading starting value of 1
for y4 and y6.
You may simplify your
analyses by studying only one grade.
Perhaps it would be interesting to do the analyses separately by gender.
For those with access to only
the demo version of Mplus, choose the subset of 6 items:
enj, good, und, use, job,
often
For the EFA, use Mplus to do
an eigenvalue plot to decide on the number of factors by checking where the
break in the eigenvalue curve (the ³elbow²) is situated and how many factors
are above the ³scree² of similar and small eigenvalues.
Do not include all analysis
output but summarize key points in a 2-3-page report.
As background reading for
these analyses, see (particularly the example in section 4):
Joreskog,
K.G. (1969). A general approach to
confirmatory maximum likelihood factor analysis. Psychometrika, 34.
which is
available as a pdf in the Assignment section of the course web site.