Association between categorical laten...
Message/Author
 Dave posted on Friday, August 27, 2010 - 7:16 am
I am new to this, so please excuse my naivety.

I am interested in assessing the association between two categorical latent variables (c1, with 2 latent classes and 4 categorical indicators, and c2, with 3 latent classes and 3 categorical indicators). If I include a WITH command then I get the following output:

C1#1 WITH
C2#1 1.659 0.506 3.277 0.001
C2#2 2.788 2.762 1.010 0.313

1. Are these loglinear parameters? Is it possible to interpret them in terms of overall association between the two categorical latent variables?

2. Is there an alternative approach which assesses overall association between two categorical latent variables (e.g. a Chi-2 test equivalent)?

Selected input code below:

VARIABLE:
USEVARIABLES = u1-u7;
CATEGORICAL = u1-u7;
CLASSES = c1 (2) c2 (3);

ANALYSIS:
TYPE = MIXTURE;
PARAMETERIZATION = LOGLINEAR;

MODEL:
%OVERALL%
c1 WITH c2;
MODEL c1:
%c1#1%
[u1\$1 u2\$1 u3\$1 u4\$1];
[u1\$2 u2\$2 u3\$2 u4\$2];
%c1#2%
[u1\$1 u2\$1 u3\$1 u4\$1];
[u1\$2 u2\$2 u3\$2 u4\$2];
MODEL c2:
%c2#1%
[u5\$1 u6\$1 u7\$1];
[u5\$2 u6\$2 u7\$2];
%c2#2%
[u5\$1 u6\$1 u7\$1];
[u5\$2 u6\$2 u7\$2];
%c2#3%
[u5\$1 u6\$1 u7\$1];
[u5\$2 u6\$2 u7\$2];
 Linda K. Muthen posted on Saturday, August 28, 2010 - 8:02 am
Yes, the are loglinear parameters. To assess fit, you would need to obtain the loglikelihood for the analysis model versus a more restrictive model where all associations are zero. -2 times the loglikelihood difference is distributed as chi-square.