The exhibit below presents a summary of the parameter estimates for a Poisson ge

Question

The exhibit below presents a summary of the parameter estimates for a Poisson generalized linear model (GLM). The model predicts frequency as a function of driver attributes. Each of the predictor variables is coded as a categorical variable: the base class for gender is Male, the base class for age is 30-49, and the base class for speeding tickets is 0. There is an interaction between gender and speeding tickets.

What is the model's predicted frequency for a 31-year-old female with 3 speeding tickets?

The exhibit below presents a summary of the parameter estimates for a Poisson generalized linear model (GLM). The model predicts frequency as a function of driver attributes. Each of the predictor variables is coded as a categorical variable: the base class for gender is Male, the base class for age is 30-49, and the base class for speeding tickets is 0. There is an interaction between gender and speeding tickets.

What is the model's predicted frequency for a 31-year-old female with 3 speeding tickets?

Parameter Estimate Std. Error p-Value Intercept -2.813 0.018 <1e-16 Gender: Female -0.031 0.013 0.017 Age: 18-20 0.176 0.058 0.002 Age: 21-24 0.109 0.032 0.007 Age: 25-29 0.038 0.024 0.113 Age: 50-64 -0.024 0.013 0.065 Age: 65+ 0.018 0.016 0.261 Speeding Tickets: 1 0.105 0.037 0.005 Speeding Tickets: 2+ 0.261 0.086 0.002 Gender: Female AND
Speeding Tickets: 1 -0.017 0.071 0.811 Gender: Female AND
Speeding Tickets: 2+ -0.003 0.129 0.981

Explanation / Answer

The poisson log linear regression model is,
log(frequency) = -2.813 - 0.031(Gender="Female") + 0.176(Age="18-20") + 0.109(Age="21-24") + 0.038(Age="25-29") - 0.024(Age="50-64") + 0.018(Age="65+") + 0.105(SpeedingTickets="1") + 0.261(SpeedingTickets="2+") - 0.017(Gender="Female")(SpeedingTickets="1") - 0.003(Gender="Female")(SpeedingTickets="2+")

For a 31-year-old female with 3 speeding tickets,

(Gender="Female") = 1, (SpeedingTickets="2+") = 1 and all other coefficient variables will be 0.

So,

log(frequency) = -2.813 - 0.031 * 1 + 0.176 * 0 + 0.109 * 0 + 0.038 * 0 - 0.024 * 0 + 0.018 * 0 + 0.105 * 0 + 0.261 * 1 - 0.017 * 1 * 0 - 0.003  * 1 * 1

= -2.813 - 0.031 + 0.261 - 0.003 = -2.586

So, log(frequency) = - 2.586

which gives frequency = exp(-2.586) = 0.0753

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