Friday, April 6, 2018

Evaluating Logistical Regression Results

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 58-59, 60-61, 62, 63-64, and 66.

Also provide estimated employment probabilities for a male with a BA degree and disease index at the 75th 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 75th 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 75th 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.