Evaluating Logistical Regression
Results
Question; A previous post presented
results from a logistical regression model where the impact of age on the likelihood
a person was employed varied based on the value of a disease index.
The coefficients
of the logistical regression model are presented below.
A Logistical Regression
Model for Employment


Variable

Coef.

P>z

male

0.35

0.00

ba_deg

0.53

0.00

no_college

0.09

0.43

age5859

1.16

0.00

age6061

0.77

0.00

age62

0.41

0.03

age6364

0.41

0.01

age6566

0.22

0.16

disease_age5859

1.56

0.00

disease_age6061

1.28

0.00

disease_age62

0.92

0.00

disease_age6364

1.38

0.00

disease_age6566

1.42

0.00

Model
based on 3314 respondents between the age of 58 and 66 from the Medical
Expenditures Panel Survey.
Statistics
summarizing the value of the disease index are presented in the table below.
The Disease Statistic


Percentiles


0%

0

1%

0

5%

0

10%

0

25%

0

50%

0.37

75%

0.69

90%

1.06

95%

1.34

99%

2.09

100%

3.43

n

3314

Mean

0.43

STD

0.48

Skew

1.50

Using
this information, provide the estimate of the employment probability for a male
with a BA degree and with disease index 0 at ages 5859, 6061, 62, 6364, and
66.
Also provide
estimated employment probabilities for a male with a BA degree and disease
index at the 75^{th} percentile for a person at same ages.
Discuss
how disease impacts the relationship between age and employment for people
nearing retirement age & discuss policy implications.
Analysis;
The
conditional employment probabilities or
a person with characteristics displayed by vector X based on logit coefficients
B are obtained from the formula.
P= Exp(XB)/(1+Exp(XB))
Here is
the layout of the spreadsheet for the probability calculations when disease
index is 0.
Calculation of Probabilities from Logit Model Disease=0


X Variables


Variable

Coef. B

Person 1

Person 2

Person 3

Person 4

Person 5

male

0.35

1

1

1

1

1

ba_deg

0.53

1

1

1

1

1

no_college

0.09

0

0

0

0

0

age5859

1.16

1

0

0

0

0

age6061

0.77

0

1

0

0

0

age62

0.41

0

0

1

0

0

age6364

0.41

0

0

0

1

0

age6566

0.22

0

0

0

0

1

disease_age5859

1.56

0

0

0

0

0

disease_age6061

1.28

0

0

0

0

0

disease_age62

0.92

0

0

0

0

0

disease_age6364

1.38

0

0

0

0

0

disease_age6566

1.42

0

0

0

0

0

Here
are the calculations of the employment probability when the disease index is 0.
Calculations of
employment probability when disease index is 0


Sumproduct (XB)

2.040

1.650

1.294

1.294

0.658

Exp(SUMP)

7.691

5.205

3.646

3.646

1.930

Employment Probability

0.885

0.839

0.785

0.785

0.659

Here is
the layout for the calculation of the employment probability when the disease
index is at the 75^{th} percentile at a value of 0.69.
Calculation of Probabilities from Logit Model Disease=0


X Variables


Variable

Coef.

Person 1

Person 2

Person 3

Person 4

Person 5

male

0.35

1

1

1

1

1

ba_deg

0.53

1

1

1

1

1

no_college

0.09

0

0

0

0

0

age5859

1.16

1

0

0

0

0

age6061

0.77

0

1

0

0

0

age62

0.41

0

0

1

0

0

age6364

0.41

0

0

0

1

0

age6566

0.22

0

0

0

0

1

disease_age5859

1.56

0.69

0

0

0

0

disease_age6061

1.28

0

0.69

0

0

0

disease_age62

0.92

0

0

0.69

0

0

disease_age6364

1.38

0

0

0

0.69

0

disease_age6566

1.42

0

0

0

0

0.69

Here
are the employment probabilities when disease index is at the 75^{th}
percentile or 0.69.
Calculations of employment probability when disease index is
0.69, the 75th percentile


Sumproduct (XB)

0.963

0.767

0.659

0.338

0.321

Exp(SUMP)

2.619

2.153

1.933

1.402

0.725

p EXP(SUMP)/(1+EXP(SUMP))

0.724

0.683

0.659

0.584

0.420

Observations:
A
substantial number of people with disease have left the workforce prior to age
62.
Reaching
age 62 has a much larger impact on the likelihood a person remains employed for
people with no disease than for people with disease.
After age
62 people with a disease leave the workforce much more rapidly than people with
no disease.
Go to
the previous post for a larger discussion of policy discussions and other issues
like the construction of the disease index.
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