could you please elaborate on the advantages/disadvantages of the two types of parameterization with more than one catgeroical latent variable: a) Logistic Regression e.g., c2#1 on c1#1 b) loglinear modeling e.g., c2#1 with c1#1.
bmuthen posted on Wednesday, May 19, 2004 - 4:38 pm
ON should be used with regression relationships and WITH when you merely want the variables to correlate. If you only have 2 c's, it won't make a difference to model fit because you are using the same number of parameters for the two c's. See also the end of chapter 13 where in that 3 x 3 example you would use 8 parameters in both cases (counting the 2 c1 parameters in the loglinear version).
thank you for your quick reply. As you know, I am aware of the syntax difference between "on" and "with". However, I was interested in the logic to use either type of parameterization. Are there any applications you are aware off, where one is prefferrable over the second one? For example, I am currently investigating a parallel process (Grades 1-3: Growth of aggression and peer rejection) leading to later growth in conduct problems (grade 6-9). For this purpose, which parameterization would you suggest?
bmuthen posted on Wednesday, May 19, 2004 - 7:08 pm
The two parameterizations of logistic and loglinear go with multiple c's (multiple latent class variables). The ON statement goes with logistic regression and WITH with loglinear. Loglinear is useful with loglinear modeling activities typically used with frequency tables for observed categorical variables, but here applied to studying associations between different c's (so standard loglinear modeling is a special case). Logistic is useful when you want to study the influence of one c on another c. You can read about both parameterizations in loglinear books such as Fienberg's. Sometimes you have a combination situation. Let's say you have c1 for aggression trajectory classes, c2 for peer rejection, and c3 for conduct problems and that c1 and c2 are contemperaneous and c3 happens later and is influenced by c1 and c2. Then I would use the logistic parameterization and say c3 on c1 c2 and in this parameterization you can still say c1 with c2.