Event Probabilities from Logit Models
Question: The table below contains coefficients of a
logit regression model for whether people age 58 to 66 are employed or not
employed. Use the estimated
coefficients to obtain the employment probabilities for three people.
All three people are 58year
males with a college degree. The first
person does not have diabetes. The
second person has diabetes but does not have complications from diabetes. The third person has both diabetes and some
diabetic related complication.
Data:
A Logit Model for Work Status  Age 58 to 66


working

Coef.

z

male

0.4130

5.59

age5859

0.5112

3.82

age6061

0.2282

1.69

age6364

0.2251

1.64

age6566

0.8567

6.11

College Degree

0.6273

4.15

no_college

0.0071

0.06

diabetes

0.5045

5.1

complications

1.1857

5.15

_cons

0.0645

0.43

Formula for event probabilities from logit models:
Define XB as the dot product
of the explanatory variables with the coefficients for the explanatory
variables. The formula for the event
probability (in this case the probability of being employed) is:
P= Exp(XB)/(1+Exp(XB))
Calculations: The first step is to set up a table with the
logit coefficient next to the variable vectors for the three people.
Logit Coefficients and Variable Values
for Three People


working

Coef.

Person 1

Person 2

Person 3

male

0.4130

1

1

1

age5859

0.5112

1

1

1

age6061

0.2282

0

0

0

age6364

0.2251

0

0

0

age6566

0.8567

0

0

0

college_deg

0.6273

1

1

1

no_college

0.0071

0

0

0

diabetes

0.5045

0

1

1

complications

1.1857

0

0

1

_cons

0.0645

0

0

0

The next steps are to
calculate XB with the SUMPRODUCT function in Excel and then plug this value
into the formula to get p.
Calculation of Employment Probabilities for Three People


Person 1

Person 2

Person 3


SUMPRODUCT

1.552

1.047

0.139

EXP SUMPRODUCT

4.719

2.849

0.871

P

0.825

0.740

0.465

Concluding Remarks: The person without diabetes
has an 82.5 percent likelihood of being employed. The person with diabetes but no
complications has a 74.0 percent chance of being employed. The person with diabetes and
diabetesrelated complications has a 46.5 percent chance of being employed.
Other exercises for students of statistics. Use the data
presented here to calculate employment likelihoods for a female age 66 with a
college degree and with and without diabetes or diabetes related
complications.