Problem on Poisson Regression: Sub-Sahara Africa has experienced a high proportion of regime…

Problem on Poisson Regression: Sub-Sahara Africa has experienced a

high proportion of regime changes due to military takeover of governments for a variety of reasons. We intend to use the data to explain military coups. The variables are:

MILTICOUP: n. of coups
MILITARY: n. of years of military oligarchy
POLLIB: (0 =no civil rights, 1 =limited, 2=extensive) PARTY93: n. of political parties
PCTVOTE: % legislative voting
PCTTURN: % registered voting
SIZE: of country (1000 km2)
POP: (in millions)
NUMREGIM: Number of regimes
NUMELEC: Number of elections

a) AnappropriatemodelisthePoissonregressionmodel.Writedown the model and the likelihood function.

b) Run a standard GLM on the data and get the estimated mean and variance of the parameters.

c) UsenormalcandidatedensitieswithmeanandvarianceattheGLM estimates in the Metropolis-Hastings algorithm. Implement the algorithm and run it. Adjust your proposal density to get a reasonable acceptance rate.

d) Plot traces and diagnostic ACF plots to assess convergence.

e) Plot the posterior densities of the regression parameters and

compare those to the prior densities.