Between level and within level factor
Message/Author
 Edward Mak posted on Thursday, August 14, 2008 - 5:03 am
Dear Muthen,

I have a question about between level factor and within level factor. How do I set a between level factor affect a within level factor?
Thanks.

Edward
 Bengt O. Muthen posted on Thursday, August 14, 2008 - 8:45 am
You do that through random means of the within-level factor. This assumes that the between-level variation in the indicators is only due to the factor, not item-specific. This then calls for equality of factor loadings across levels:

%within%
fw by y1
y2-y10 (2-10);
%between%
fb by y1
y2-y10 (2-10);

Often, however, the between-level variation is item-specific and the above model doesn't fit.
 Edward Mak posted on Thursday, August 14, 2008 - 9:33 pm
Thank you for your quick reply. ButI do not understand the program you wrote. Could you briefly explan it ?

Thank you very much.

Edward
 Edward Mak posted on Thursday, August 14, 2008 - 9:47 pm
I have three more questions. when i read the user guide, variables such as m, w, etc were used. I know m = mean, and w=within, etc. But is it the default meaning. When we use m, Mplus will think it as mean?

the second question is if m, w, etc were not default, how could i get it?

And the last question is, could you recommend any book to me about how to write Mplus program and how to interpret the results?

Thank you very much.
 Linda K. Muthen posted on Friday, August 15, 2008 - 8:27 am
Please see the examples in Chapter 9 of the user's guide for an explanation of the language.

Please see page 15 of the user's guide for a description of the conventions we use in the user's guide examples. You understanding is not correct. They are only names. They have no impact on the analysis.

See Confirmatory Factor Analysis for Applied Research by Timothy A. Brown.
 Xu, Man posted on Sunday, September 07, 2008 - 4:51 am
But why "... This then calls for equality of factor loadings across levels"?
 Bengt O. Muthen posted on Sunday, September 07, 2008 - 10:46 am
Otherwise, the between-level factor wouldn't be influencing the factor for the individual. The way I see the question is to consider individual i in cluster j,

(1) y_ij = Lambda* eta_ij + e_ij

and decompose the factor into between and within parts

(2) eta_ij = etaB_j + etaW_ij.

Inserting (2) into (1) then means that Lambda is the same for etaB_j and etaW_ij.
 Scott Monroe posted on Wednesday, February 02, 2011 - 11:23 am
Hello Drs.,

I have a related question, that is probably very basic. i'm interested in a cross-level regression path.

The setup is as follows:
- two latent variables (eta1 and eta2)
- each latent variable has its own, separate indicators
- eta2 only varies at the between level
- eta2 influences eta1

My question is this: can i regress eta1W on eta2B? and if so, how do I do so in mplus?

or, will this give me the same results as regressing eta1B on eta2B?