transport safety practise-poisson regression

Assignment #3

(Count Data – Poisson Regression Analysis)

Name: Student Number:

There are 204 observations from a travel survey conducted in the Central Business District in Suzhou, Jiangsu. The purpose of the survey was to study the number of times (per week) commuters' changed their departure time on their work-to-home trip to avoid traffic congestion. The data are non-negative integers with the mean approximately equal to the variance thus the data are well suited to approach. Remember in a Poisson regression, you are estimating the Poisson regression a parameter vector βsuch that:

λ= EXP (βX)

where λ is the Poisson parameter that in this case is the expected number of departure changes per week.

Your task is to estimate a model of number of departure changes per week using the Poisson family regression techniques. In your analysis, please provide the solutions to the following questions:

1. Please give the probability density function of Poisson distribution.

As is shown in Fig.1, my best model is

λy e−λ

P(Y=y)=

λ=EXP⁡(0.5483106x4−0.3261742x15+2.683363x17−3.01086)

2. Provide the results of your best model specification.

Fig.1 The best Poisson model

3. Compute the likelihood ratio test statistic χ2 and the ρ2 statistic.

As is shown in Fig.1, χ2 = 177.76, ρ2 = 0.3031

4. A discussion of the logical process that led you to the selection of your final specification (discuss

the theory behind the inclusion of your selected variables). Include t-statistics and justify the sign of your variables.

In this case, x5 is the dependent variable y and in my view, x4, x7, x8, x12, x13, x15, x16, x17 could be the independent variables (assuming that x22 refers to the catering employment in work zone). The result is presented in Fig.2.

Fig.2 The first model

We can find that the p-values of x7, x8, x12, x13 and x16 are more than 0.1. It means x7, x8, x12, x13 and x16 may have no significant relationship with Y and we should delete them in next models one by one. Finally, we can get a model with independent variables of x4, x15 and x17 as shown in Fig.1. All p-values are smaller than 0.05 so we can conclude that there is a highly significant relationship between Y and x4, x15 and x17 under 95% confidence level.

5. Compute elasticities for each variable to determine the marginal effects of the independent

variables.

Using .margins, dydx(*) command we can obtain the elasticity for each variable.

Fig.3 The marginal effects of the independent variables