MLM with interchangeable dyads and le... PreviousNext
Mplus Discussion > Multilevel Data/Complex Sample >
 Andreas Richter posted on Tuesday, August 04, 2015 - 9:45 pm
I have dyadic data, with 2 interchangeable (i.e., arbitrary) dyad members. N = 90 individuals nested in 45 dyads.

At the individual level (within dyad, level 1), I have the independent variable X. At the dyad level (level 2), I have my moderator variable W and the dependent variable Y. All variables are continuous.

I try to specify an interaction model that looks like this: Y (level 2) = X (level 1) + W (level 2) + X*W.

Could you advise what the MPlus syntax for this might look like? Any advice would be very much appreciated!
 Linda K. Muthen posted on Wednesday, August 05, 2015 - 6:15 am
You cannot use a level 1 predictor on level 2. You can use only the between part of it on level 2. See the second part of Example 9.1.
 Andreas Richter posted on Wednesday, August 05, 2015 - 8:31 am
Thank you Linda, I appreciate it. In contrast to Example 9.1, my DV only exists at the between-level (1 rating per dyad). Also, my X predictor shouldn’t be aggregated to level 2 for theoretical reasons.
I specified two alternative models to solve this:

Model 1:
Variable: NAMES ARE Dyad X W Y;

Model 2:
I’ve rearranged the data set by creating separate variables X1 and X2 for each individual within dyads, and removed clustering.

Variable: NAMES ARE X1 X2 W Y;
Analysis: type = random;
Xlatent by X1 X2;
XxW | Xlatent XWITH W;
Y ON W Xlatent XxW;

Both models give me regression outputs. From my understanding, model 2 is a correct, and model 1 a wrong specification of my problem. Is this right? Any advise would be much appreciated!
 Bengt O. Muthen posted on Friday, August 07, 2015 - 5:56 pm
I like the "wide", single-level approach better than the long, two-level approach even though the dyad members are interchangeable as you say. This is like analysis of twins (which we have UG ex's for). So Model 2 instead of Model 1. Although ok, I don't know that you need a factor; each x could interact in the usual way with w (although if they are interchangeable, maybe a factor is better).
 Tor Neilands posted on Monday, August 10, 2015 - 8:50 pm

I have dyadic data from couples measured longitudinally over 5 time points with both missing x-side and y-side data. The data are in the "long" format with up to 10 records per couple. I want to fit so-called "actor-partner" multilevel regression models with lagged predictor scores at time t-1 predicting a single outcome at time t, daily smoking, which is a binary outcome variable (I've created the lagged predictors already). Kenny, Kashy, and Cook's 2006 dyadic analysis textbook points out (p. 347) that although there are three factors - time, person, and dyad - and it is tempting to treat time points as nested within persons and persons nested within dyads, time and person are crossed. If I want to fit this type of model in Mplus, would you recommend I try TYPE=CROSSCLASSIFIED with the syntax following that in UG Ex 9.24, except setting the estimator to Bayes and declaring daily smoking to be categorical? Or is there a different approach you would recommend? Thanks!
 Bengt O. Muthen posted on Tuesday, August 11, 2015 - 1:50 pm
I think Crossclassified would be suitable.
 Tor Neilands posted on Wednesday, August 12, 2015 - 6:38 pm
Thank you, Bengt.

I have a couple of follow-up questions: I am attempting to generate multiple imputations as part of this analysis to share with the lead author who will use the imputed data sets in another software program.

1. When I bring X variables into the model to address missing data, do I need to specify both their variances and covariances - I noticed that unlike in MLE, with BAYES it appears that if I specify variances only for the X variables, I get the means and variances estimated but the WITH covariances are not estimated by default?

2. A number of my X variables are binary, but the imputed values are continuous. What approach would you recommend for obtaining binary imputed values for those missing X variables?

Thanks again and best wishes,

 Bengt O. Muthen posted on Wednesday, August 12, 2015 - 7:33 pm
1. For Bayes you may need to explicitly mention those covariances.

2. You can specify binary X's as such in Mplus multiple imputation using x(c).
 Tor Neilands posted on Thursday, August 13, 2015 - 10:20 am
Thank you, Bengt. Specifying the covariances explicitly resulted in them being included in the model.

I tried using xvarname (c) in the IMPUTE statement of the DATA IMPUTATION command for my each of categorical x variables that are not mentioned as categorical on the CATEGORICAL statement in the VARIABLE command. The model runs and generates imputed data sets, but I noticed that for the 0/1 categorical variables other possible values are imputed. Can you say a little bit more or point me to a resource that can help me understand how the x(c) approach works in DATA IMPUTATION when x is not labeled as categorical on the CATEGORICAL statement in the VARIABLE command? I'm trying to understand why DATA IMPUTATION would produce imputed values other than 0 or 1 for a 0/1 categorical x variable when x(c) is specified for that variable.
 Bengt O. Muthen posted on Friday, August 14, 2015 - 6:27 am
Have a look at UG ex 11.5 which imputes a categorical x variable.
 Tor Neilands posted on Tuesday, August 25, 2015 - 10:02 am

Thanks again for all of your thoughtful replies to my questions on this topic.

We now have a working cross-classified regression model with covariates with missing data brought into the model as random variables by estimating their variances and their covariances with other covariates.

Are the regression coefficients from the regression part of the model probit regression coefficients? If so, and if the investigator desires odds ratios, would it be appropriate to use the MODEL CONSTRAINT techniques outlined in your 2011 causal effects paper to obtain odds ratio estimates?

Thank you again,

 Bengt O. Muthen posted on Tuesday, August 25, 2015 - 10:51 am
Probit is used with Bayes and categorical outcomes. Yes, on your last question too.
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