Logistic Regression: A Self-learning Text, Third Edition (Statistics in the Health Sciences)

Estimated Covariance Matrix

Variable Intercept cat age chl ecg

Intercept 1.575061 0.66288 0.01361 0.00341 0.04312
CAT 0.66288 9.638853 0.00207 0.003591 0.02384
AGE 0.01361 0.00207 0.00026 3.66E-6 0.00014
CHL 0.00341 0.003591 3.66E-6 0.000018 0.000042
ECG 0.04312 0.02384 0.00014 0.000042 0.107455
SMK 0.1193 0.02562 0.000588 0.000028 0.007098
HPT 0.001294 0.001428 0.00003 0.00025 0.01353
CH 0.054804 0.00486 0.00104 0.000258 0.00156
CC 0.003443 0.04369 2.564E-6 0.00002 0.00033

Variable smk hpt ch cc

Intercept 0.1193 0.001294 0.054804 0.003443

CAT 0.02562 0.001428 0.00486 0.04369

AGE 0.000588 0.00003 0.00104 2.564E-6

CHL 0.000028 0.00025 0.000258 0.00002

ECG 0.007098 0.01353 0.00156 0.00033

SMK 0.107104 0.00039 0.002678 0.000096

HPT 0.00039 0.109982 0.108 0.000284

CH 0.002678 0.108 0.551555 0.00161

CC 0.000096 0.000284 0.00161 0.000206

The negative 2 log likelihood statistic (i.e.,2 Log L) for the model, 347.230, is
presented in the table titled “Model Fit Statistics.” A likelihood ratio test statistic
to assess the significance of the two interaction terms can be obtained by running a
no-interaction model and subtracting the negative 2 log likelihood statistic for the
current model from that of the no-interaction model.

The parameter estimates are given in the table titled “Analysis of Maximum Likeli-
hood Estimates.” The point estimates of the odds ratios, given in the table titled
“Odds Ratio Estimates,” are obtained by exponentiating each of the parameter
estimates. However, these odds ratio estimates can be misleading for continuous
predictor variables or in the presence of interaction terms. For example, for continu-
ous variables like AGE, exponentiating the estimated coefficient gives the odds ratio
for a one-unit change in AGE. Also, exponentiating the estimated coefficient for CAT
gives the odds ratio estimate (CAT¼1 vs. CAT¼0) for a subject whose cholesterol
count is zero, which is impossible.

B. PROC GENMOD

Next, we illustrate the use of PROC GENMOD with the Evans County data. PROC
GENMOD can be used to run generalized linear models (GLM) and generalized
estimating equations (GEE) models, including unconditional logistic regression,
which is a special case of GLM. The link function and the distribution of the outcome
are specified in the model statement. LINK¼LOGIT and DIST¼BINOMIAL are
the MODEL statement options that specify a logistic regression. Options requested

SAS 605