Since the exposure of all students is fixed at three years, we can model the students article count directly, using a Poisson log-linear model

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Assignment 

1. Suppose {Xn, n ≥ 1} is a sequence of random variables with Xn ∼ Binomial(n, pn) such that npn → λ > 0 as n → ∞. Show that as n → ∞,e−λλkP(Xn = k) → k!, for k = 0, 1, 2, 

The dataset "Long.txt" contains data on the productivity of biochemistry Ph.D. students. The variables are as follows art Number of articles published by the student during last three years of PhD

• fem Gender: 1 if female, 0 if male

• mar Marital status: 1 if married, 0 if not

• kid5 Number of children five years old or younger

• PhD Prestige rating of Ph.D. department

• ment Number of articles published by a mentor during last three years 

Read the dataset into R and attach the data frame.

2. Since the exposure of all students is fixed at three years, we can model the students’ article count directly, using a Poisson log-linear model with no offset. Investigate the bivariate relationships of log(art) with the other variables. Which variables do the article count appear to depend on?

3. Fit a Poisson log-linear model regressing art on the linear effect of the other variables. Notice that the deviance is much greater than the degrees of freedom. Could this be due to a need for second-order terms?

4. Fit a quasi-Poisson model regressing art on the linear effect of the other variables. Do the data appear to be overdispersed?

5. Using a Poisson or quasi-Poisson model as you see fit, select an appropriate model for art. Interpret your final model.

 

 

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