## Logistic regression exercise

In my Bayesian class, I assigned a problem (exercise 8.3 from BCWR) where one is using logistic regression to model the trajectory of Mike Schmidt’s home run rates.

First, I have written a function to compute the log posterior for a logistic regression model with a vague prior placed on the regression vector. The function together with a short example how it works can be found here.

Second, it seems that there is a problem getting the laplace function to converge if you don’t use a really good starting value. Here is an alternative way of getting the posterior mode.

Suppose y is a vector containing the home run counts and n is a vector with the sample sizes. Let age be the vector of ages and age2 be the vector of ages squared. Define the response to be a matrix containing the vectors of successes and failures.

response=cbind(y,n-y)

Then the mle of beta is found using the glm command with the family=binomial option

fit=glm(response~age+age2,family=binomial)

The posterior mode is the mle:

beta=coef(fit)

The approximation to the posterior variance-covariance matrix is found by

V=vcov(fit)

Now you should be able to use the random walk metropolis algorithm to simulate from the posterior.