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

Get to know your data!

Perform thorough descriptive ana-
lyses before modeling.

 Useful for finding data errors

 Gain insight about your data

Descriptive analyses include the
following:

 Frequency tables

 Summary statistics

 Correlations

 Scatter plots

 Histograms

VII. Hierarchically Well-
Formulated Models

Initial model structure: HWF

Model contains all lower-order
components

It is important to do thorough descriptive ana-

lyses before modeling. Get to know your data!

It is possible to run many models and not know

that you have only two smokers in your dataset.

Also descriptive analyses are useful for finding

errors. An individual’s age may be incorrectly

recorded at 699 rather than 69 and you may

never know that from reading model output.

Descriptive analyses include obtaining fre-

quency tables for categorical variables, uni-

variate summary statistics (means, variance,

quartiles, max, min, etc.) for continuous vari-

able, bivariate cross tables, bivariate correla-

tions, scatter plots, and histograms. Descriptive

analyses can be performed both before and after

the variable specification stage. Often more

insight is gained from a descriptive analysis

than from modeling.

When choosing theVand Wvariables to be

included in the initial model, the investigator

must ensure that the model has a certain struc-

ture to avoid possibly misleading results. This

structure is called ahierarchically well-formulated

model, abbreviated as HWF, which we define

and illustrate in this section.

A hierarchically well-formulated model is a

model satisfying the following characteristic:

Given any variable in the model, all lower-

order components of the variable must also

be contained in the model.

To understand this definition, let us look at an

example of a model that isnothierarchically

well formulated. Consider the model given in

logit form as logit P(X) equalsaplusbEplus

g 1 V 1 plusg 2 V 2 plus the product termsd 1 EV 1

plusd 2 EV 2 plusd 3 EV 1 V 2.

For this model, let us focus on the three-factor

product termEV 1 V 2. This term has the follow-

ing lower-order components:E, V 1 ,V 2 ,EV 1 ,

EV 2 , andV 1 V 2. Note that the last component

V 1 V 2 is not contained in the model. Thus, the

model is not hierarchically well formulated.

EXAMPLE

NotHWF model:

logitP



X



¼aþbEþg 1 V 1 þg 2 V 2

þd 1 EV 1 þd 2 EV 2 þd 3 EV 1 V 2

Components ofEV 1 V 2 :

E,V 1 ,V 2 ,EV 1 ,EV 2 ,V 1 V 2

"not in model

Presentation: VII. Hierarchically Well-Formulated Models 181