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# Mixed Models: Is there a way to incorporate bilinear random effects in SAS?

I’d like to fit a mixed model with a bilinear random effect as discussed in (Hoff, P.D. Bilinear mixed-effects models for dyadic data. Journal of the American Statistical Association, 100: 286-295, 2005).

In a “normal” mixed modeling situation if we have two random effects, say A and B, then the code

random A B;

assumes that A~Normal(0,Sigma_A) and B~Normal(0,Sigma_B). However, in the bilinear case the random effect is C = A*B or ATB (if A and B are vectors). Is there a way to incorporate the bilinear effect “C” into any of the mixed procedures in SAS?

Thanks.

Valued Guide
Posts: 684

## Re: Mixed Models: Is there a way to incorporate bilinear random effects in SAS?

If you are doing dyadic data analysis (the subject of the Hoff article), then you will have to be careful. I suggest you read the book Dyadic Data Analysis by Kenny, Kashy, and Cook (2011). Follow the links on this page to get to a description of the book.

Chapter 8 of Kenny et al. book deals with the subject of Hoff's article, and the website for chapter 8 has a link to another article where SAS is used extensively for dyadic analysis. I have not pursued this, but you might be able to find the appropriate MIXED code. Good luck.

New Contributor
Posts: 3

## Re: Mixed Models: Is there a way to incorporate bilinear random effects in SAS?

Thanks for the response and link. I actually have skimmed through that book and Ch.8 in particular. It mentions Hoff's model and the fact that it can account for triadic effects through the multiplicative random effects, but it doesn't discuss its implementation. I've spoken with Hoff directly, but he's not a SAS user and the analyses I'm doing are best suited for SAS. I'm hoping SAS is capable of allowing for multiplicative random effects, but it may not be... Thanks!

Valued Guide
Posts: 684

## Re: Mixed Models: Is there a way to incorporate bilinear random effects in SAS?

MIXED and GLIMMIX do have the capability for certain types of multiplicative random effects, with the factor analytic structure, such as FA1(1) or FA(1) (options on the RANDOM statement). But I don't think this is what you need, so I won't explain any more. I have not studied the Hoff article in detail, but it appears that you will need something more complex than the usual MIXED code. You might be able to construct the structure of the variance-covariance matrix (a consequence of random effects of A, B, and A*B), and place the terms in an LDATA= file. Unfortunately, I don't have time to really study the Hoff article, so I cannot give specifics. Maybe my response will encourage someone else to make suggestions.

New Contributor
Posts: 3

## Re: Mixed Models: Is there a way to incorporate bilinear random effects in SAS?

I emailed David Kenny and he also doesn't think that the bilinear random effect model can be fitted with the usual MIXED code. I'll look into using the LDATA functionality. I also plan to look into whether SAS IML provides a way to fit this model. If others have suggestions please let me know.

Thanks!

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