The equation for binary distal outcomes (for GGMM) is provided in several sources, but I cannot find the equations for ordered and continuous distal variables (with hopefully at least brief explanations). Can someone point me in the direction of these? Much thanks.
For continuous and ordinal distals predicted by a latent class variable I don't think we have equations written out per se in a publication. But it is simple to describe that they would be. This is based on a distal outcome being just like another latent class indicator.
For a continuous distal you have
where k indexes the different classes (so the mean varies across classes). Variances can also vary across classes.
For an ordinal distal you have
where tau refers to the set of thresholds that vary both across the C categories of the distal (c=0, 1, ...C-1; thresholds ordered) and across the classes k of the latent class variable. The relationship between thresholds and probabilities for various categories of the distal is shown in the appendices to the UG (e.g. appendix 1).