Using only the within or between matrix
Message/Author
 Anonymous posted on Thursday, June 12, 2003 - 12:31 pm
I’m a novice in analysing multilevel data. A couple of weeks ago, I bought Mplus and now I have several questions that I’d like you to answer.

1. Two-level option

Hox’s program SPLIT2 produces three kinds of matrices: (1) pooled within groups, (2) scaled between groups, (3) rough estimate of between groups. All of them are included in Mplus. Am I correct in assuming that the third is the one Mplus uses to calculate the between model? Please explain to me why it is the third and not the second one.

2. Using only the within or between matrix

Is it appropriate to do analysis only on either the within or between level, in conjunction with the corresponding matrix?

If I would do so, what is the proper meaning of the results? For an analysis done on the pooled within matrix, do the results reflect the “pure” relationships on the individual level adjusted for the fact of cluster-membership?

When only working on the between level, which of the two between matrices do I have to use? Do the results reflect the “real” relationships on the between level? Have they been adjusted at all?

Could I use the matrices for further calculations e.g. in SPSS (with corrected N in the case of the within matrix: N-nCluster)?

Does it make any sense to calculate on one level and are the results reliable enough to be published in a paper (e.g. in the case of only a few clusters)?

3. How does one do an analysis only on the within or between level in Mplus? Does one need to use SAVEDATA?

I would be very grateful to you for an answer.
 Linda K. Muthen posted on Friday, June 13, 2003 - 6:32 am
1. I am not familiar with Hox's terminology. With the MUML estimator, Mplus analyzes SW and SB. See formulas 197 and 198 on page 380-381 of the Mplus User's Guide. With maximum likelihood estimation, Mplus analyzes raw data.

2. You can analyze the pooled-within matrix or the estimated simga B matrix separately. It is likely that the pooled-within matrix will give very similar results to those from a multilevel model. The estimated sigma B results will not be as good. We recommend doing this before doing the multilevel model.

Both of these matrices can be saved in Mplus and then analyzed separately. See pages 89-91 of the Mplus User's Guide. You can use them in other programs.

By the way, be sure to get the Addendum to the Mplus User's Guide from www.statmodel.com under Product Support. It describes many new multilevel features in Mplus.
 Anonymous posted on Tuesday, June 22, 2004 - 4:57 am
I have the following problem with multilevel modeling: I have data with students nested within classrooms and I'm longitudinally predicting students' feelings of insecurity from the degree of experienced and observed violence in the classroom. At the student level, everything is fine. At the classroom level, I get standardized path coefficients of 3.24, 10.68, etc. for the paths from observed and exeprienced violence at T1 to feelings of insecurity at T2. Also the stand path from insecurity at T1 to insecurity at T2 is 8.99.
I don't know how to proceed with the analysis and would be really greatful for help..
 Linda K. Muthen posted on Tuesday, June 22, 2004 - 8:22 am
Which standardized coefficients are you referring to? STD or STDYX?
 Anonymous posted on Tuesday, June 22, 2004 - 11:05 pm
I am referring to STDYX. At the same time, the Est./S.E.'s are near zero.

I was now trying to do the same model with latent variables, and this seems to work better. The paths coefficients are reasonable. However, in this model, I have one correlation at the between level which is -1.14. Can I interpret the results from this model, or I better try something else?
 Linda K. Muthen posted on Wednesday, June 23, 2004 - 8:21 am
It sounds like you have an inadmissible model and need to make some changes.
 Jan Hochweber posted on Monday, April 23, 2007 - 2:32 am
I’d like to do regression analysis and SEM with covariates using the within and between covariance matrices only (SAMPLE IS / SIGB IS). Will results be correct if some of my covariates are dummy variables?

Thank you!
 Linda K. Muthen posted on Monday, April 23, 2007 - 8:01 am
Yes.
 Daniel Leopold posted on Saturday, May 16, 2015 - 4:16 pm
Drs. Muthen,

My question is whether to include my dependent variable in the WITHIN = statement, or leave it out so that it's in both the WITHIN and BETWEEN levels.

I'm trying to explore the magnitude/significance of A, B, C and their interactions on Y (i.e., reaction time). The raw data for Y has already been mean centered within each subject. I will eventually test some indirect effects at the between level, but I want to explore and refine the within level model prior to estimating the between level as well. Furthermore, the B*C beta is significant when I include Y in the WITHIN= statement, but nonsignificant when I leave Y out of that statement. Which of these syntaxes is correct, and how does the interpretation differ?

WITHIN = A B C A*B A*C B*C;
CLUSTER = Subject;

Analysis:
TYPE = TWOLEVEL;
Estimator = MLR;

Model:

%WITHIN%
Y ON A;
Y ON B;
Y ON C;
Y ON A*B;
Y ON A*C;
Y ON B*C;

Many thanks!
 Daniel Leopold posted on Saturday, May 16, 2015 - 5:28 pm
After reading through another set of posts in "Explaining a significant interaction...", I tried your suggestion of TWOLEVEL BASIC to explore ICCs:

When I include Y in the WITHIN= statement:
Average cluster size = 120.9; Y's ICC = .000

When I do not include Y in the WITHIN= statement:
Average cluster size = 120.9; Y's ICC = .252

My dependent variable (Y, which is reaction time) is certainly measured within subjects, but I also want it to be the dependent variable in my between level analyses as well. Just thought I'd provide this additional information in case it changes your response or suggestion(s).
 Bengt O. Muthen posted on Monday, May 18, 2015 - 12:29 pm
Don't put Y on Within=, the reason being that it has between-level variation. Putting variables on Within= means that no between-level variance is modeled for them, so assuming it is zero.