Cross-Level Interaction
Message/Author
 Kai Rödiger posted on Monday, September 30, 2013 - 2:29 am
Dear Linda and Bengt,

I'm quite new to MPlus and Multilevel Modelling but I figured out most of the basic stuff quite well. Now I have serious problems with a Cross-Level Interaction and need your help to know if it is possible at all to have a model like this.

So in short: I have LVL 2 measurements at the employee lvl (customer attitude) and LVL 1 measures at the customer LVL (perception of behavior).

I want this path to be moderated by the age difference between employee and customer modelled by (AE - AC). Each employee has up to 3 matched customers so there are up to 3 different values for Delta Age.

--------------------------Delta Age (I think this has to be a Within-Variable)
-----------------------------|
-----------------------------|
-----------------------------|
-----------------------------v
Employee Behavior (L2) ----> Customer Perception (L1)

I tried various ways to define the slopes in the within and between part of the model but none of them worked out. Could you give me a hint if at all (and if yes how) such a relationship can be modelled?

Best regards and thank you very very much in advance,
Kai
 Linda K. Muthen posted on Monday, September 30, 2013 - 6:40 am
Example 9.2 shows how to model a cross-level interaction.
 Kai Rödiger posted on Tuesday, October 01, 2013 - 2:22 am
Thank you for your quick answer but I think my problem is a different one.

Example 9.2 shows a a LVL 2 Variable moderating a LVL 1 -> LVL 1 path.

What I want to model is a LVL 2 Variable moderating a LVL 2 -> LVL 1 path.

Is this possible at all? Thank you very much in advance for your answer again and I hope you can help me.

Best regards,
Kai
 Linda K. Muthen posted on Tuesday, October 01, 2013 - 9:51 am
I think what you want is

USEVARIABLES = y x z w zw;
WITHIN = x;
BETWEEN = z w;
DEFINE:
zw = z*w;

MODEL:
%WITHIN%
y ON x;
%BETWEEN%
y ON z w zw;

Note that the y on between is the between part of y. Latent variable decomposition is discussed in Example 9.1 and 9.2.
 Kai Rödiger posted on Wednesday, October 02, 2013 - 4:44 am
Thank you again for your quick response. What we want is the following:

USEVARIABLES = y1 y2 x z;
WITHIN = z;
BETWEEN = x;

MODEL:
%WITHIN%
y2 ON y1;

%BETWEEN%
y1 ON x;

S|y1 ON x; !Path to be moderated is a LVL2 on LVL1 Path

S ON z; !Moderator z is a within-variable. No matter in which part of the model this path is defined, MPlus produces error messages.

Is modelling the interaction via multiplication a common option in multilevel analysis? I thought it is necessary to use the random slope method.

Thanks again and best regards,
Kai
 Linda K. Muthen posted on Wednesday, October 02, 2013 - 12:06 pm
In multilevel modeling, you can't have a random slope on the highest level.
 Kai Rödiger posted on Monday, November 25, 2013 - 3:02 am
Dear Linda,

thank you very much for your response. Do you have any suggestion how to solve this problem? Which method / approach might be best if cross-level interactions won't work here. Is a multilevel multigroup analysis a valid approach for this problem?

Thank you very much for your response,
Kai
 Linda K. Muthen posted on Monday, November 25, 2013 - 9:22 am
This seems a reasonable approach.
 Yanxia WANG posted on Thursday, March 19, 2015 - 7:44 pm
Hello,

I am new to Mplus, and recently met a similar problem which the level 2 moderator moderates the relationship between independent variable from level 2 and dependent variable from level 1. I did what Linda suggested, however, Mplus reported error with undefined zw (the interaction item). I really could not figure it out. Would you please help me to handle with this problem?

Thanks a lot.
 Linda K. Muthen posted on Friday, March 20, 2015 - 6:58 am
 Bep Uink posted on Thursday, December 03, 2015 - 6:10 pm
Hello,
I am running a 2 level model in the uni variate format, with experience sampling data. I am trying to predict an outcome at time 1, controlling for a co-variate a t-1. However, I do not want between-day lags (i.e. I do not want participants ratings in the morning to be predicted by their last rating on the previous day). However, I am not sure the syntax for this? I have thought of excluding observations the occur in the first time point of the following day, but these are are also used as t-1 covariates for the following time point. Any help would be very appreciated. Thank you.
 Tihomir Asparouhov posted on Friday, December 04, 2015 - 8:59 am
You can consider three level modeling where the middle level = day. Alternatively and probably the easiest is to have 0 for that covariate in the data for the first observation in the day.
 Bep Uink posted on Sunday, December 06, 2015 - 10:09 pm
Thank you, Tihomir. I am not clear on what covariate. To be more clear, I am trying to regress mood at time 1 onto event at time 1, controlling for mood at t-1. Because I do not want events from the previous nights' time point predicting the next mornings' mood, should I replace data for night time events with 0?
 Tihomir Asparouhov posted on Monday, December 07, 2015 - 3:31 pm
I would recommend reading these three papers

Ellen L. Hamaker, Conor V. Dolan, and Peter C. M. Molenaar (2002) On the Nature of SEM Estimates of ARMA Parameters, Structural Equation Modeling, 9(3), 347–368

Joran Jongerling, Jean-Philippe Laurenceau, Ellen L. Hamaker (2015) A Multilevel AR(1) Model: Allowing for Inter-Individual Differences in Trait-Scores, Inertia, and Innovation Variance, Multivariate Behavioral Research, 50:3, 334-349

Zhiyong Zhang, Ellen L. Hamaker, John R. Nesselroade (2008) Comparisons of Four Methods for Estimating a Dynamic Factor Model Structural Equation Modeling, 15:377–402,
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