Jon Heron posted on Friday, October 23, 2015 - 4:59 am
I am struggling with the most basic of problems.
As a run-up to a more complex example I want to simulate a simple X-Y relationship where X is standardized and Y is a 2-class mixture. The goal is to examine the impact of ignoring the mixture when regressing Y on X, and then ultimately turn Y latent (so this links to my earlier SP-FA query).
I have no problem simulating Y - for example, the classes may be one unit apart with a standardized distribution for Y within each class - however the introduction of X renders these quantities conditional.
As I see it, I now have the situation where both intercept and residual variance within each class are THE SAME since I do not want C to moderate my X-Y relationship. How might I regain control of Y in it's unconditional state? Any thoughts? I'm thinking that making X binary and doing a multigroup may be the simplest way out of this.
many thanks, Jon
Jon Heron posted on Friday, October 23, 2015 - 5:21 am
As usual, getting the question on paper gets you halfway to a solution.
I need to go back to Linear Regression 1.01 for this one I think + fix my within-class intercepts to functions of my within-class mean(Y), mean(X) and the population gradient b