Multigroup analyses for pathmodels
Message/Author
 Claudia Schuchart posted on Friday, January 20, 2017 - 7:13 am
Dear Muthens,
I want to estimate a twolevel path analysis to predict study aspiration by individual and school variables. The clusters are schools (N=80). Furthermore, I have 4 school types and I want to know whether the model is the same for all school types or not. Particularly, I want to know whether 1) the intercept of the dependent variable and 2) the slope of aspiration to study on achievement vary across school types.
I run a multiple group analyses with school type being the grouping variable. I estimated a restricted model for all groups. In a first step I relaxed this constrain for one group:
(...)
within = x1 x2 y1 y2;
between = w;
grouping = a (1 = a1 2 = a2 3 = a3 4 = a4);
cluster = b;
analysis: type = twolevel;
model: %within%
y1 on x1 x2;
y2 on y1 (1);
%between%
y2 on w;
model a2: %within%
y2 on y1;
My questions are: Is this the right procedure to test for group differences regarding path analysis? I am not sure because the output says that estimated sample statistics for groups for between and parameter specification for groups between and within are all zero and I do not understand this. Second, if this is the right procedure, is it possible to fix the intercepts of the dependent variable for all groups?
Thank you very much in advance
Claudia
 Bengt O. Muthen posted on Friday, January 20, 2017 - 1:13 pm
You have to decide if you want to

1) consider school as a fixed mode of variation or

2) a random mode.

In 1) you use multiple group analysis and in 2) you use twolevel analysis. Your input mixes the two which is not right.

If you want to test strict equalities across schools you want to take approach 1), so no twolevel analysis with Within or Between. But it sounds like you want to see if school type influences the slope on level 2 which calls for approach 2) with a random slope:

%Within%

s | y2 on y1;

%Between%
y2 s on w;

where y2 on Between is the intercept.

In this approach there is no Grouping = .
 Claudia Schuchart posted on Monday, January 23, 2017 - 3:06 am
Thank your very much for this reponse. Yes, I consider school (N = 80) as a random mode and I want to know whether one model applies to all the four school types (a1 - a4) or if the models differ from each other within the four school types. As I understood you, school type has to be a variable at level two and not a grouping variable.

%Within%

s | y2 on y1;

%Between%
y2 s on w;
y2 s on a2;
and so on.
 Claudia Schuchart posted on Monday, January 23, 2017 - 3:10 am
Sorry, I have to correct my post: Whether the models differ from each other *between* the four school types.
 Bengt O. Muthen posted on Monday, January 23, 2017 - 3:35 pm
You got it.