Using GLIMMIX for 2 binary dependent variables

BarryS — Wed, 02 Nov 2011 12:33:42 GMT

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

Using GLIMMIX for 2 binary dependent variables

SteveDenham — Thu, 03 Nov 2011 12:03:34 GMT

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

Using GLIMMIX for 2 binary dependent variables

BarryS — Mon, 07 Nov 2011 15:06:17 GMT

Thanks for your reply Steve - appreciated.

topic Using GLIMMIX for 2 binary dependent variables in Statistical Procedures

Using GLIMMIX for 2 binary dependent variables

Using GLIMMIX for 2 binary dependent variables

Using GLIMMIX for 2 binary dependent variables