Cox path model and the effects of col...
Message/Author
 Brian Steinmeyer posted on Thursday, May 03, 2007 - 11:01 am
Hi Bengt/Linda,

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,

"survival(t) ON x1 x2;
x1 WITH X2@0.9;"

Any suggestions or ideas on how to better compare the joint effect of the two predictors on survival? Should it be done, given the two effects are so highly collinear?

Brian

P.S. - I fit the path model in Mplus,
specified a correlation of 0.9 (above) and received the following message:

"*** FATAL ERROR
THIS MODEL CAN BE DONE ONLY WITH
MONTECARLO INTEGRATION."

What does this mean?
 Linda K. Muthen posted on Friday, May 04, 2007 - 8:07 am
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:

f BY x1 x2;

and regress survival on the factor:

survival(t) ON f;
 Brian Steinmeyer posted on Friday, May 04, 2007 - 11:31 am
Linda,

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,
Brian
 Linda K. Muthen posted on Friday, May 04, 2007 - 2:55 pm
I would have both factor loadings free and set the metric of the factor by fixing the factor variance to one. Then you can look at the two factor loadings.
 Brian Steinmeyer posted on Tuesday, May 08, 2007 - 9:20 am
Hi Linda,

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?

Thanks,
Brian
 Linda K. Muthen posted on Tuesday, May 08, 2007 - 9:50 am
To free the first factor loading, place an asterik behind it.

f BY y1* y2;

This is described in the user's guide under the BY option.