Using GLIMMIX for 2 binary dependent variables

[BarryS]

Hi.

I was wondering if anyone could help with my query.

I have a data set consisting of 4 variables – 2 binary dependent (response) variables (called “foreign” and “guzzler”) and 2 continuous independent variables (called “weight” and “length”).  Each observation has one value recorded for each of the 4 variables.   The 2 binary dependent (response) variables are correlated.  I am using the probit link function to model the 2 binary dependent variables.

To start off I have just considered one independent variable, length, which relates to the dependent variables as such:

Foreign = A + B * length

Guzzler = C + D * length

where A B C and D are parameters to be estimated.  Below is a sample of the data that I used.  Response is a combination of my foreign and guzzler variables.  ResponseID indicates Foreign (F) or Guzzler (G).

ID	Response	ResponseID	weight	length
50	0	F	3200	199
51	0	F	3420	203
52	0	F	2690	179
53	1	F	2830	189
54	1	F	2070	174
55	1	F	2650	177
50	0	G	3200	199
51	0	G	3420	203
52	1	G	2690	179
53	0	G	2830	189
54	0	G	2070	174
55	1	G	2650	177

I have used the PROC GLIMMIX function as such:

data autodata2;

     set autodata2;

     if responseid="F" then dist="bina1"; else dist="bina2";

run;

proc glimmix data= autodata2 method=rspl;

     class id dist;

     model response(event="1") = dist dist*length /link=probit

     noint s dist=byobs(dist);

     random _residual_/ subject=id type=unr;

run;

and the output I get is:

                                   Covariance Parameter Estimates

                                                                            Standard

                                        Cov Parm     Subject    Estimate       Error

                                        Var(1)            ID           0.7993      0.1332

                                        Var(2)           ID           0.4852     0.08088

                                        Corr(2,1)      ID          -0.1771      0.1147

                                                Solutions for Fixed Effects

                                                            Standard

                        Effect                   dist     Estimate       Error       DF    t Value    Pr > |t|

                        dist                   bina1      8.2139      1.7088       74       4.81      <.0001

                        dist                   bina2     15.2709      2.4099       74       6.34      <.0001

                        length*dist        bina1    -0.04816    0.009543       74      -5.05      <.0001

                        length*dist        bina2    -0.08787     0.01379       74      -6.37      <.0001

I believe that

A = 8.2139    

B = -0.04816  

C = 15.2709    

D = -0.08787   

I have two questions (1) is my approach correct and am I interpreting the parameter values correctly? and more importantly (2) What exactly do the values Var(1), Var(2) and Corr(2,1) under the “Covariance Parameter Estimates” represent?  These values change when I change my independent variable from “length” to “weight”.

Thanks for any replies.

Barry

[SteveDenham]

Var(1) and Var(2) are estimates of the residual error for the two ResponseIDs/dist variables, and Corr(2,1) the estimated correlation between the two.  It is not surprising that the values change when the independent variable changes, as the relationship (solution values) will change, and thus the residual error would be different.

The approach looks great.

Steve Denham

[BarryS]

Thanks for your reply Steve - appreciated.