1 General Purpose
In the Chap. 8 the effect of categorical
predictors on an continuous outcome has been assessed. Linear
regression could be used for the purpose. However, the categorical
predictor variable had to be restructured prior to the analysis. If
your outcome is binary, the analysis of categorical predictors is
more easy, because SPSS provides an automatic restructure
procedure.
2 Schematic Overview of Type of Data File
3 Primary Scientific Question
Is logistic regression appropriate for
assessing categorical predictors with binary outcomes.
4 Data Example
In 60 patients of four races the effect
of the race category, age, and gender on the physical strength
class was tested. We will use the example of the Chap. 8. The effect of race, gender, and
age on physical strength was assessed. Instead of physical strength
as continuous outcome, a binary outcome (physical
strength < or ≥ 70 points) was applied.
|
Race
|
Age
|
Gender
|
Strength score
|
|
1,00
|
35,00
|
1,00
|
1,00
|
|
1,00
|
55,00
|
,00
|
1,00
|
|
1,00
|
70,00
|
1,00
|
,00
|
|
1,00
|
55,00
|
,00
|
,00
|
|
1,00
|
45,00
|
1,00
|
1,00
|
|
1,00
|
47,00
|
1,00
|
1,00
|
|
1,00
|
75,00
|
,00
|
,00
|
|
1,00
|
83,00
|
1,00
|
1,00
|
|
1,00
|
35,00
|
1,00
|
1,00
|
|
1,00
|
49,00
|
1,00
|
1,00
|
The entire data file is in
“chapter39categoricalpredictors”, and is in extras.springer.com. We
will start by opening the data file in SPSS.
5 Logistic Regression with Categorical Predictors
For analysis the statistical model
Binary Logistic Regression in the module Regression is
required.
Command:
-
Analyze....Regression....Binary Logistic Regression....Dependent: strengthbinary....Covariates: race, gender, age....click Categorical....Categorical Covariates: enter race....Reference Category: mark Last....click Continue....click OK.
Variables in the equation
|
B
|
S.E.
|
Wald
|
df
|
Sig.
|
Exp(B)
|
||
|---|---|---|---|---|---|---|---|
|
Step 1a
|
Race
|
13,140
|
3
|
,004
|
|||
|
Race(1)
|
2,652
|
1,285
|
4,256
|
1
|
,039
|
14,176
|
|
|
Race(2)
|
−2,787
|
1,284
|
4,715
|
1
|
,030
|
,062
|
|
|
Race(3)
|
1,423
|
1,066
|
1,782
|
1
|
,182
|
4,149
|
|
|
Age
|
−,043
|
,029
|
2,199
|
1
|
,138
|
,958
|
|
|
Gender
|
1,991
|
,910
|
4,791
|
1
|
,029
|
7,323
|
|
|
Constant
|
1,104
|
1,881
|
,345
|
1
|
,557
|
3,017
|
|
The above table shows the results of
the analysis. As compared to the hispanics (used as reference
category),
-
blacks are significantly more strengthy (at p = 0,039)
-
asians are significantly less strengthy (at p = 0,030)
-
whites are not significantly different from hispanics.
Age is not a significant predictor of
the presence of strength.
Gender is a significant predictor of
the presence of strength.
The above results are less powerful
than those of the continuous outcome data. Obviously with binary
outcome procedures some statistical power is lost. Nonetheless they
show patterns similar to those with the continuous outcomes.
6 Conclusion
In the Chap. 8 the effect of categorical
predictors on an continuous outcome was shown to be applicable for
categorical predictors. However, the categorical predictor variable
had to be restructured prior to the analysis. If your outcome is
binary, the analysis of categorical predictors is more easy,
because SPSS provides an automatic restructure procedure. The
analysis is presented above.
7 Note
More background, theoretical and
mathematical information of categorical predictors is given in the
Chap. 21, pp 243–252, in Statistics applied to clinical studies,
Springer Heidelberg Germany, 2012, from the same authors.