My SEM model includes: f1 by y1-y4 f2 by y5-y8 f3 by y9-y11 f4 by u1-u6 (3-ordered categories each) f5 by f1-f4 1 outcome (ordered categorical) 1 covariate (binary) I use public data and apply panel weights.
Questions related to the calculations of probabilities from the probit regression:
1. Do I need to account for the weights (I read a post on accounting for frequency weights; I am not sure if this applies to the type of weights in my study and in what way).
2. When the outcome is regressed on both f4 and f5, how should I calculate probabilities on the outcome 1SD above/below the means? Should I only change either x1 or x2 and keep the other at the mean, or is there another, more sophisticated way?
3. I am interested in group differences on the outcome. How should I explore these? One way would be to run two separate analyses - one per group. This will result in estimated probabilities that are group-specific (meaning, an individual compared to her group-specific mean). Rights? Another way would be to run a MIMIC model. Then, I will have the following estimates: b1 for f5 on covariate b2 for outcome on f5 3 thresholds (t1-t3) Considering the outcome does not directly regress on both b weights, how would I calculate the probabilities?
where y_1 represents the socio economic status, x is the maternal educational, lat is a latent variable (lipids) and y*_2 denotes the underlying latent response variable in the probit model (b and g are regression coefficients). It follows that
where tau_2 is the threshold for y_2 and F is the standard normal distribution function found in tables. I know that I have to fix x and lat to get these probabilities, but it is not clear to me in what values I can fix lat as it is a latent variable.
Any help on calculated/interpretting predicted probabilities or using some other approach to interpretation would be greatly appreciated.