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

III. Screening Variables

Scenario:

Logistic Model

E(0,1) vs.D(0,1)

C 1 ,C 2 ,...,Cp

“large”p

Desired initial model:

Logit PðXÞ¼aþbEþ~

p

j¼ 1

gjCj

þ~

p

j¼ 1

djECj

Follow hierarchical BW elimina-

tion strategy (Chap. 7)

However, suppose:

 Computer program does not run

or

 Fitted model unreliable (“large”

p)

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What do you do?

OPTIONS (large-number-of-vari-

ables problem)

1. Screening:
    Exclude someCjone-at-a-
   time
    Begin again with reduced
   model


2. Collinearity diagnostics on
   initial model:
    Exclude someCjand/or
   ECjstrongly related to
   other variables in the model


3. Forward algorithm for
   interactions:
    Start withEand allCj,
   j¼1,...,p
    Sequentially add significant
   ECj

In this section, we address the following sce-

nario: Suppose you wish to fit a binary logistic

model involving a binary exposure and out-

come variablesE and Dcontrolling for the

potential confounding and effect-modifying

effects of a “large” number of variables Cj,

j¼1, 2,...,pthat you have identified from

the literature.

You would like to begin with a model contain-

ingE, the main effects of eachCj, and all prod-

uct terms of the formECj, and then follow

the hierarchical backward elimination strategy

described in Chap. 7 to obtain a “best” model.

However, when you run a computer program

(e.g., SAS’s Proc Logistic) to fit this model, you

find that the model does not run or you decide

that, even if the model runs, the resulting fitted

model is too unreliable because of the large

number of variables being considered. What

do you do in this situation?

There are several possible options:

1. Use some kind of “screening” technique to
   exclude some of the Cj variables from the
   model one-at-a-time, and then begin again
   with a reduced-sized model that you hope is
   reasonably reliable and/or at least will run.


2. Use “collinearity” diagnostic methods
   starting with the initial model to exclude vari-
   ables (typically product terms) that are
   strongly related to other variables in the model.


3. Use a forward regression algorithm that
   starts with a model containing all main effect
   Cjterms and proceed to sequentially add statis-
   tically significant product terms.

Presentation: III. Screening Variables 263