I chose to use the africa data. To see if poission reggression was right for this data I created a histogram of coups. The histogram is very skewed right which means poisson regression is a good fit.

hist(africa$miltcoup)

I started by creating a model with all of the variables and then took its summary to see what variables were significant. Oilgarchy,pollib, and parties were the only variables that had p values below .1 so I chose those to be the variables in my first model. From there I will perform a drop in deviance test.

fullmod<- glm(africa$miltcoup~africa$oligarchy+africa$pollib+africa$parties+africa$pctvote+africa$popn+africa$numelec+africa$numregim,family = poisson)
summary(fullmod)
## 
## Call:
## glm(formula = africa$miltcoup ~ africa$oligarchy + africa$pollib + 
##     africa$parties + africa$pctvote + africa$popn + africa$numelec + 
##     africa$numregim, family = poisson)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -1.3331  -0.9768  -0.2003   0.5297   1.7477  
## 
## Coefficients:
##                   Estimate Std. Error z value Pr(>|z|)   
## (Intercept)      -0.552324   0.903536  -0.611  0.54101   
## africa$oligarchy  0.066744   0.034111   1.957  0.05039 . 
## africa$pollib    -0.701259   0.271330  -2.585  0.00975 **
## africa$parties    0.032119   0.011169   2.876  0.00403 **
## africa$pctvote    0.014033   0.009808   1.431  0.15249   
## africa$popn       0.008972   0.006666   1.346  0.17836   
## africa$numelec   -0.027105   0.064708  -0.419  0.67530   
## africa$numregim   0.198305   0.230035   0.862  0.38865   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for poisson family taken to be 1)
## 
##     Null deviance: 65.945  on 35  degrees of freedom
## Residual deviance: 29.281  on 28  degrees of freedom
##   (11 observations deleted due to missingness)
## AIC: 110.09
## 
## Number of Fisher Scoring iterations: 6
mod1<- glm(africa$miltcoup~africa$oligarchy+africa$pollib+africa$parties,family = poisson) 

Here I performed a drop in deviance test. I started by taking the summary of my current mod and found parties to be the least significant, so I would test to see if it was a good variable. I will be testing it at the .05 significance level. Since the p value is greater than the significance level it is ok to drop parties.

summary(mod1)
## 
## Call:
## glm(formula = africa$miltcoup ~ africa$oligarchy + africa$pollib + 
##     africa$parties, family = poisson)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -1.4495  -1.0868  -0.3699   0.5723   1.7526  
## 
## Coefficients:
##                  Estimate Std. Error z value Pr(>|z|)    
## (Intercept)       0.27416    0.36432   0.753  0.45172    
## africa$oligarchy  0.09892    0.02012   4.916 8.82e-07 ***
## africa$pollib    -0.51592    0.19511  -2.644  0.00819 ** 
## africa$parties    0.01641    0.00865   1.897  0.05778 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for poisson family taken to be 1)
## 
##     Null deviance: 79.124  on 41  degrees of freedom
## Residual deviance: 42.242  on 38  degrees of freedom
##   (5 observations deleted due to missingness)
## AIC: 123.92
## 
## Number of Fisher Scoring iterations: 5
mod2<-glm(africa$miltcoup~africa$oligarchy+africa$pollib,family = poisson)
teststat<-deviance(mod2)-deviance(mod1)
pchisq(teststat,df=1,lower.tail = FALSE)
## [1] 0.07118606

Here I performed a 95% confidence interval

confint(mod2,parm=2,level=.95)
## Waiting for profiling to be done...
##      2.5 %     97.5 % 
## 0.06218165 0.13982861

Lastly I calculated the dispersion parameter of my model. The DP ending up being about 1.12 which means the variance is 1.12 times larger than the mean.

dp<-sum(residuals(mod2,type="pearson")^2/mod2$df.res)
dp
## [1] 1.119648