Introduction to Categorical Data Analysis

CHAPTER 7: LOGLINEAR MODELS FOR CONTINGENCY TABLES 337
PROC GENMOD can fit the proportional odds version of cumulative logit models
using the DIST=MULTINOMIAL and LINK=CLOGIT options. Table A.7 fits
it to Table 6.9. When the number of response categories exceeds two, by default
PROC LOGISTIC fits this model. It also gives a score test of the proportional odds
assumption of identical effect parameters for each cutpoint.
Table A.7. SAS Code for Cumulative Logit Model with Mental Impairment Data
of Table 6.9
data impair;
input mental ses life;
datalines;
1 1 1
....
4 0 9
;
proc genmod ;
model mental = life ses / dist=multinomial link=clogit lrci type3;
proc logistic;
model mental = life ses;
One can fit adjacent-categories logit models in SAS by fitting equivalent baselinecategory
logit models (e.g., see Table A.12 in the Appendix in Agresti, 2002). With
the CMH option, PROC FREQ provides the generalized CMH tests of conditional
independence. The statistic for the “general association” alternative treats X and Y as
nominal, the statistic for the “row mean scores differ” alternative treats X as nominal
and Y as ordinal, and the statistic for the “nonzero correlation” alternative treats X
and Y as ordinal.
CHAPTER 7: LOGLINEAR MODELS FOR CONTINGENCY TABLES
Table A.8 uses GENMOD to fit model (AC, AM, CM) to Table 7.3. Table A.9 uses
GENMOD to fit the linear-by-linear association model (7.11) to Table 7.15 (with
column scores 1,2,4,5). The defined variable “assoc” represents the cross-product of
row and column scores, which has β parameter as coefficient in model (7.11).
Table A.8. SAS Code for Fitting Loglinear Models to Drug Survey Data of Table 7.3
data drugs;
input a c m count ©©;
datalines;
1 1 1 911 1 1 2 538 1 2 1 44 1 2 2 456
2 1 1 3 2 1 2 43 2 2 1 2 2 2 2 279
;
proc genmod; class a c m;
model count = a c m a∗m a∗c c∗m / dist=poi link=log lrci type3 obstats;