I have what seems to be a simple modeling problem, but one that has caused some serious head scratching. I would like to determine which one of two continuous effects (x1 and x2), measured on the same individual at one occasion, better predicts a given survival outcome, knowing that the two effects are highly collinear (i.e. 0.90)! I know that multicollinearity poses a problem in the Cox Model just as in regression, but could you model this correlation while you fit a path model in Mplus? For example,
When you use the WITH statement for the two independent variables, you in effect turn them into dependent variables. Because they have missing data, observations will have zero, one, or two dimensions of integration. When the number of dimensions of integration vary over observations, Monte Carlo integration is needed.
I would not recommend doing what you are doing. Instead I would create a factor behind the two independent variables:
Thanks for contacting me. I appreciate your comments.
Per your suggestion, can you estimate effects for x1 and x2 with the introduction of the latent factor, f if your main interest is to determine which indicator (x1,x2) is stronger (i.e. more predictive of survival) or is inference now based on f, which influences the joint effect of x1 and x2 on survival?
Thanks for your response! I fit the model and fixed the factor variance to one. However, the first factor loading was estimated at one? How do you free both factor loading parameters, per your suggestion, given the default that Mplus fixes the first factor loading to one in order to establish the scale for the latent factor?