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

Presentation

I. Overview

Previous chapter:

 How ML methods work

 Unconditional vs. conditional
approaches

FOCUS

Testing

hypotheses

Computing

confidence

intervals

II. Information for Making
Statistical Inferences

Quantities required from output:

(1) Maximized likelihood value:
Lð^uÞ

(2) Estimated variance–covariance
matrix:V^ðu^Þ

V (q) =

Variances on

diagonal

Covariances off

the diagonal

In the previous chapter, we described how ML

methods work in general and we distinguished

between two alternative approaches to estima-

tion – the unconditional and the conditional

approach.

In this chapter, we describe how statistical

inferences are made using ML techniques in

logistic regression analyses. We focus on pro-

cedures for testing hypotheses and computing

confidence intervals about logistic model para-

meters and odds ratios derived from such

parameters.

Once ML estimates have been obtained, these

estimates can be used to make statistical infer-

ences concerning the exposure–disease rela-

tionships under study. Three quantities are

required from the output provided by standard

ML estimation programs.

The first of these quantities is themaximized

likelihood value, which is the numerical value

of the likelihood functionLwhen the ML esti-

mates are substituted for their corresponding

parameter values; this value is calledLofu^in

our earlier notation.

The second quantity is theestimated variance–

covariance matrix, which we denote asV^of^u.

The estimated variance–covariance matrix has

on its diagonal the estimated variances of

each of the ML estimates. The values off the

diagonal are the covariances of paris of ML

estimates.

132 5. Statistical Inferences Using Maximum Likelihood Techniques