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

Wald test for more than one
parameter: requires matrices
(See Epidemiol. Res., Chap. 20,
p. 431 for mathematical formula.
Also, see Chapters 14 and 15 here
for how used with correlated data.)

Third testing method:

Score statistic
(See Kleinbaum et al.,Commun.
Stat., 1982 and Chapters 14 and 15
here.)

VI. Interval Estimation:
One Coefficient

Large sample confidence interval:

Estimate(percentage point of
Zestimated standard
error)

Or, alternatively, theZcan be squared and then

compared with percentage points from a chi-

square distribution with one degree of freedom.

The Wald test we have just described considers

a null hypothesis involving only one model

parameter. There is also a generalized Wald

test that considers null hypotheses involving

more than one parameter, such as when com-

paring Models 2 and 3 above. However, the

formula for this test requires knowledge of

matrix theory and is beyond the scope of this

presentation. The reader is referred to the

text by Kleinbaum, Kupper, and Morgenstern

(Epidemiol. Res., Chap. 20, p. 431) for a

description of this test. We refer to this test

again in Chapters 14 and 15 when considering

correlated data.

Yet another method for testing these hypoth-

eses involves the use of ascore statistic(see

Kleinbaum et al., Commun. Stat., 1982).

Because this statistic is not routinely calculated

by standard ML programs, and because its use

gives about the same numerical chi-square

values as the two techniques just presented,

we will not discuss it further in this chaper.

We have completed our discussion of hypothe-

sis testing and are now ready to describeconfi-

dence interval estimation. We first consider

interval estimation when there is only one

regression coefficient of interest. The proce-

dure typically used is to obtain a large sample

confidence interval for the parameter by com-

puting the estimate of the parameter plus or

minus a percentage point of the normal distribu-

tion times the estimated standard error.

EXAMPLE (continued)

or

Z^2 is approximatelyw^2 with 1 df

140 5. Statistical Inferences Using Maximum Likelihood Techniques