I am trying to run 4-period cross-lagged model involving a continuous Y and a categorical X (nominal, 4 levels, say: Xa, Xb, Xc, Xd).
So my model looks something like this (using Xd as reference)
Y2 ON Y1 Xa1 Xb1 Xc1; Xa2 ON Y1 Xa1 Xb1 Xc1; Xb2 ON Y1 Xa1 Xb1 Xc1; Xc2 ON Y1 Xa1 Xb1 Xc1;
Y3 ON Y2 Xa2 Xb2 Xc2; Xa3 ON Y2 Xa2 Xb2 Xc2; Xb3 ON Y2 Xa2 Xb2 Xc2; Xc3 ON Y2 Xa2 Xb2 Xc2;
Note that I'm also adding time-variant and - invariant covariates.
I have a couple of questions:
1) I specified the LINK function to be LOGIT. Does that mean that the estimates in MODEL results are all logit-transformed? Or those are only for when the outcome is categorical (ie. when looking at when the outcome is Y, I would just read the results as ordinary non-transformed/standardized parameter estimates)?
2) I'm not sure if I'm reading my results right. Say if I look at Odds Ratios for when my outcome is Xc3, am I looking at the odds ratio for being in Xc3 vs not, or is it the odds ratio of being in Xc3 vs being in Xd3 (my reference)?
3) I can't seem to correlate categorical variables without having to specify a mixture type analysis. Is there a way around this?
4) If you know of articles with similar methodology, please send them my way
I assume that you mean that you have created 3 binary variables from the 4-category nominal. The modeling is a little tricky in this case both because the binary variables are part of the same nominal variable and for the following reason. Link=logit goes with ML and ML does has the issue for this kind of model where the binary variable appears as both a DV and an IV. As a DV, the model is logistic (so a non-linear model) but as an IV, it is the observed binary variable that is the predictor (so a linear model). Indirect effects can then not be computed easily. Things are a bit clearer with WLSMV where you do the regressions via continuous latent response variables so all regressions are linear. In WLSMV as opposed to ML, it is straightforward to correlate binary variables.
It may also be clearer to do one analysis at a time for each binary variable.
Thanks for the response. I'm working on your suggestions now but I'm not sure if I'm interpreting the estimates correctly. I know that when I'm looking at my coefficient estimates for when my IV is categorical I'm looking at probits. But if my outcome is continuous, would I interpret my coefficients just as how I would do with a standard linear model?