Interpretaton of regression coefficients
Message/Author
 Fuzhong Li posted on Tuesday, May 26, 2009 - 5:42 pm
Hi, I have a question regarding how to interpret the linear regression of the random intercept c#1 of the categorical latent variable c on the cluster-level covariate w (Example 10.9 in the Guide).
In a multilevel mixture model of the between part, suppose I have two trajectory classes with c#1 representing a decline trajectory in body mass index (BMI) and c#2 (reference) representing a increase trajectory and that I have a positive relation between the cluster-level covariate (e.g., neighborhood land use mix) and the random intercept (c#1) in the between-part of the model, does that positive linear regression coefficient means "increases in neighborhood land mix lead to decreases in BMI decline in Class 1 compared to Class 2” This seems to be a very basis regression analysis question, but I guess I do not completely understand the meaning of this intercept. I cut and paste that part of Mplus output below (Land means urban land use mix). Any insight would be appreciated. Thank you. Fuzhong
Between Level
C#1 ON
SES -0.002 0.009 -0.201 0.841
LAND 0.025 0.012 1.999 0.046
 Bengt O. Muthen posted on Thursday, May 28, 2009 - 11:15 am
We talk about such interpretation in our latest version of the Topic 8 short course. The handout is on our web site. It's about how a cluster-level phenomenom influences an individual's outcome via a random intercept.

Using words of your application, an increasing land use mix (on Between) increases the c#1 intercept (on Between) which means an increase in the odds that an individual (in that Between unit) belongs to class 1, namely the declining class, as opposed to class 2.
 Fuzhong Li posted on Monday, June 15, 2009 - 5:15 pm
Many thanks. Follwing your suggestion, i did watch the clip (course 8) a couple of times and it was very helpful.

(sorry for not being able to respond early. I had to make an unpected overseas trip the last couple of weeks).
fuzhong