Interpreting multi-level interaction
Message/Author
 Andrew Li posted on Monday, February 13, 2017 - 2:13 pm
Hello,
I am trying to interpret the interaction of two L-2 variables in the prediction of a L-1 variable. In this case, X and W are L-2 variables and Y is a L-1 Variable. I hypothesize that the cross-level relationship between X and Y will be moderated by W. I have the codes below. In particular, I am not sure the last few lines with respect to simple slope analyses are correct. Would you please take a look? BTW, all the variables are continuous variables and I have grandmean centered the two level-2 variables. Thank you.

usevariables = a1 x w y inter ;
cluster = a1;
between = x w inter;
define:
center x w (grandmean);
inter = x * w;
analysis: type = twolevel;
model:
%between%
y on x (b1)
w (b2)
inter (b3);
model constraint:
new (x1 x2 x3);
x1 = b1 + b3*(1);
x2 = b1;
x3 = b1 + b3*(-1);
output: Sampstat stdyx;
 Bengt O. Muthen posted on Monday, February 13, 2017 - 5:51 pm
This looks fine. Except you want to add

%Within%
y;
 Andrew Li posted on Tuesday, February 14, 2017 - 7:02 am
Dear Dr. Muthen,
Thank you so much for your reply. I use the Mplus code from the Geiser book (p. 216). In the demonstration of the codes for the Mean-as-outcomes model (a model where there is no L-1 predictor but one L-2 predictor), the code does not include a %within line. I wonder why this line is included as you suggested. Is it because now I have more than one L-2 predictor and also the interaction between two L-2 predictors? Thank you.
 Bengt O. Muthen posted on Wednesday, February 15, 2017 - 11:09 am
Make sure that the within-level variance is estimated - check your output. If it isn't, add it.
 Andrew Li posted on Wednesday, February 15, 2017 - 5:03 pm
Dear Dr. Muthen,
Thank you for your response. I really appreciate it.
You mention variance in your response. I use Tech3 to get the variance/covariance matrix. However, I don't quite understand the numbering on the x and y axes. I know that I can get the info with Tech1 in the output. The problem is I have a really hard time figuring out which number matches which parameter. I am sure there is a very intuitive way but I guess it gets lost in me. I read the relevant section in the manual and I still have no clues. Your help is greatly appreciate.
 Linda K. Muthen posted on Wednesday, February 15, 2017 - 5:42 pm
TECH1 gives a number to each free parameter in the model. Those numbers are used in the TECH3 variance/covariance matrix. For example the 1,1 entry is the variance of parameter 1. The 1,2 entry is the covariance between parameter 1 and parameter 2 etc.
 Andrew Li posted on Thursday, February 16, 2017 - 7:23 am
Dear Dr. Muthen,
Thank you for your response.
I understood the variance/covariance matrix in the TECH3 output. The problem I have is related to the TECH1 output. Specifically, I don't know which parameter is related to which number. The TECH1 output includes a lot of symbols like beta, alpha, etc. I don't know how each number corresponds to the specific variables/parameters in my model.
Andrew
 Linda K. Muthen posted on Thursday, February 16, 2017 - 8:21 am
See pages 757-760 of the current user's guide on the website. The matrices are described there.
 Andrew Li posted on Thursday, February 16, 2017 - 12:04 pm
Dear Dr. Muthen,
Thank you so much. I was finally able to figure out what each number means.

Sorry to pepper you with questions, but where can I find the degrees of freedom for the slope and intercept? I don't see them in the output (tech1 tech8, tech3 cinterval)?
 Bengt O. Muthen posted on Thursday, February 16, 2017 - 6:47 pm
Perhaps you are referring to degrees of freedom for F tests. Mplus provides z-tests instead (no df's). See chapter 1 of our new book.
 Andrew Li posted on Friday, February 17, 2017 - 6:05 am
Thank you Dr. Muthen. I appreciate your help. I will go ahead to buy the book.
 Bengt O. Muthen posted on Saturday, February 18, 2017 - 5:05 pm
ok.