Metric of ordinal dependent >and< ind...
Message/Author
 Michael Windzio posted on Thursday, March 24, 2005 - 7:20 am
Dear Linda and Bengt,
I have a question concering a path model with ordinal dependent variables (dv).
The model is the following:

CATEGORICAL ARE ot s;
MODEL: f1 by g16 g17 g18 g1 g2;
f2 by q1 q2 q3 q4 q5;
f1 on un ab mi a o;
f2 on f1 un a fr;
ot on un ab a fr f1;
ot with f2;
s on ot un ab a o fr f1 f2;

"ot" is an ordinal dv, explained by un, ab, fr and f1. But the model is a path model, so that "ot" is an independent variable explaining "s" in the subsequent step.
My questions:
1. what is the metric of "ot" if it is modeled as an independent variable explaining "s" in the last equation? Is it now considered as interval scaled with an underlying latent distribution, as usual in ordinal regression?
2. If so, then I couldn't compare the effect with other standardized variables, because "ot" is defined as categorical (ordinal) and has not been standardized ?

Best whishes and thanks a lot,

Michael Windzio, Hannover (KFN), Germany
 bmuthen posted on Thursday, March 24, 2005 - 7:57 am
The answer differs between using WLSMV and ML estimation. For WLSMV, probit regressions are used and when ot is an independent variable it is the latent response variable ("ot*") underlying the observed ot that is used. For ML, logit regressions are used and when ot is an independent variable it is the variable itself, approximated as a continuous variable, that is used. You can use a standardized solution in either case. The two models have somewhat different meaning, however, in terms of the role that ot vs ot* plays.