Hi, I am trying to plot a growth model that uses MLR and probit link, with intercept, slope, and quadratic growth parameters. I was using the formula below to get the predicted probabilities for values of x: P(y|x) = phi(-(t)+(s*x)+(q*x^2)) Where t = threshold (I have the intercept@0 which is the default) and phi = cum normal distribution. All in the unstandardized output. However, when I check the estimated intercept that is presented in the PLOT3 output, my intercept is different.
Am I using the correct formula? Because we are talking about latent probabilities, should I be doing something different?
Related to this, I am also using knownclass to examine the growth in two groups. When this is estimated, the intercept is only @0 for the second group, and so I am not sure what combination of threshold and intercept estimates I should be using in the formula?
That formula does not look correct. You have latent variables i, s, and q which have variation that needs to be accounted for in the probability expression. There is an explicit Phi formula due to using probit link but it has to be expressed in line with slides 162-164 of the Topic 4 handout on our website using the example of a single latent variable. Note that the residual variance of that latent variable comes into play in the probability calculation.
Thank you for your reply. I have had a look at the Topic 4 handout pages 162-164 (on this page http://www.statmodel.com/course_materials.shtml; I have checked both the old and new versions of the pdfs) and unfortunately I cannot see any formula related to how I can use the parameters from the model to plot my growth with a probit link. Is this something that can be done simply using a formula as per a simple linear growth model?