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Chapter 6. Building and Applying Logistic
Regression Models
Deyuan Li
School of Management, Fudan University
Feb. 28, 2011
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Outline
•
6.1 Strategies in Model Selection
•
6.2 Logistic Regression Diagnostics
•
6.3 Inference about Conditional Association in 2
××
K
Tables
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6.1 Strategies in model selection
The selection process becomes harder as the number of
explanatory variables increases, because of the rapid increase in
possible e±ects and interactions.
Two competing goals of model selection:
•
the model should be complex enough to ²t the data well;
•
the model should be simple to interpret, smoothing rather
than over²tting the data.
Most models are designed to answer certain questions.
⇒
Those questions guide the choice of model terms:
•
Confrmatory
analysis use a restrict set of models; e.g., a
study hypothesis about an e±ect may be tested by comparing
models with and without that e±ect.
•
For
exploratory
studies, a search among possible models
may provide clues about the dependence structure and raise
questions for future research.
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In either case, it is helpful ²rst to study the e±ect on
Y
of each
predictor by itself using graphics (incorporating smoothing) for a
continuous predictor or a contingency table for a discrete predictor.
This give a “feel” for the marginal e±ects.
Unbalanced data, with relatively few responses of one type, limit
the number of explanatory variables (
x
terms) for the model.
One guideline: at least 10 outcomes of each type should occur for
every
x
term.
For instance, if
y
= 1 only 30 times out of
n
= 1000, the model
should contain no more than about 3
x
terms.
Such guidelines are approximate. This does not mean that if you
have 500 outcomes of each type you are well served by a model
with 50
x
terms.
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View Full Document Many model selection procedures exist, no one of which is always
best.
A model with several predictors may suFer from
multicollinearity
,
i.e., correlations among predictors making it seem that no one
predictor is important when all the others are in the model.
A predictor may seem to have little eFect because it overlaps
considerably with other predictors in the model, i.e., itself being
predicted well by the other predictors.
Deleting such a redundant predictor can be helpful, for instance to
reduce standard errors of other estimated eFects.
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6.1.1 Horseshoe crab example revisited
The horseshoe crab data set in Table 4.3 has four predictors:
color (4 categories), spine condition (3 categories), weight
and width of the carapace shell.
Outcome: The crab has satellites (
y
= 1) or not (
y
=0)
.
Preliminary model:
4 predictors, only main eFects
logit[
P
(
Y
=1)] =
α
+
β
1
weight +
β
2
width
+
β
3
c
1
+
β
4
c
2
+
β
5
c
3
+
β
6
s
1
+
β
7
s
2
,
treating color (
c
i
) and spine condition (
s
j
) as qualitative (factors),
with dummy variables for the ±rst 3 colors and the ±rst 2 spine
conditions. Table 6.1 shows results.
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This note was uploaded on 11/20/2011 for the course ST 3241 taught by Professor Deyuanli during the Spring '11 term at Adams State University.
 Spring '11
 DeyuanLi

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