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

Model Summary

Step

2 Log

likelihood

Cox & Snell

R square

Nagelkerke

R square

1 347.230 .139 .271

Variables in the Equation

B S.E. Wald df Sig.

Exp

(B)

95.0% C.I. for

EXP(B)

Lower Upper

Step 1a CAT 12.688 3.104 16.705 1 .000 .000 .000 .001

AGE .035 .016 4.694 1 .030 1.036 1.003 1.069

CHL .005 .004 1.700 1 .192 .995 .986 1.003

ECG .367 .328 1.254 1 .263 1.444 .759 2.745

SMK .773 .327 5.582 1 .018 2.167 1.141 4.115

HPT 1.047 .332 9.960 1 .002 2.848 1.487 5.456

CH 2.332 .743 9.858 1 .002 .097 .023 .416

CC .069 .014 23.202 1 .000 1.072 1.042 1.102

Constant 4.050 1.255 10.413 1 .001 .017

aVariable(s) entered on step 1: CAT, AGE, CHL, ECG, SMK, HPT, CH, CC.

The estimated coefficients for each variable (labeled B) and their standard errors,
along with the Wald chi-square test statistics and correspondingp-values, are given in
the table titled “Variables in the Equation.” The intercept is labeled “Constant” and is
given in the last row of the table. The odds ratio estimates are labeled EXP(B) in the
table, and are obtained by exponentiating the corresponding coefficients. As noted
previously in the SAS section, these odds ratio estimates can be misleading for
continuous variables or in the presence of interaction terms.

The negative 2 log likelihood statistic for the model, 347.23, is presented in the table
titled “Model Summary.” A likelihood ratio test statistic to asses the significance of
the two interaction terms can be performed 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.

SupposewewishtoestimatetheoddsratioforCAT¼1vs.CAT¼0 among those
with HPT¼0andCHOL¼220. This odds ratio isexp(b 1 þ 220 b 8 ). From the output,
this is estimated atexp(12.688þ 220
.069). This is an example of an odds ratio
ascertained as a linear combination of parameters. Obtaining a linear combination
of parameter estimates along with the corresponding standard error and 95%
confidence interval is not straightforward in SPSS as it is in SAS (with an ESTI-
MATE statement) or in Stata (with the LINCOM command). However, there is a way
to “trick” SPSS into doing this. Since, in this example, we are interested in estimat-
ing the odds ratio for CAT among those who have a cholesterol level of 220 (CHL¼
220), the trick is to create a new variable for cholesterol such that when the choles-
terol level is 220, the new variable takes the value zero. For that situation the

SPSS 637