HHernandez_DATA621_Discussion12

ELMR Exercise 5.4

require("faraway")
library(MASS)

data("africa")
summary(africa)

##     miltcoup       oligarchy          pollib         parties     
##  Min.   :0.000   Min.   : 0.000   Min.   :0.000   Min.   : 0.00  
##  1st Qu.:0.000   1st Qu.: 0.000   1st Qu.:1.000   1st Qu.:10.00  
##  Median :1.000   Median : 1.000   Median :2.000   Median :13.00  
##  Mean   :1.404   Mean   : 4.447   Mean   :1.667   Mean   :15.96  
##  3rd Qu.:2.000   3rd Qu.: 9.000   3rd Qu.:2.000   3rd Qu.:19.00  
##  Max.   :6.000   Max.   :18.000   Max.   :2.000   Max.   :62.00  
##                                   NA's   :5                      
##     pctvote           popn              size           numelec      
##  Min.   : 0.00   Min.   :  0.067   Min.   :   0.5   Min.   : 0.000  
##  1st Qu.:18.90   1st Qu.:  1.450   1st Qu.:  33.0   1st Qu.: 4.000  
##  Median :28.95   Median :  5.600   Median : 274.0   Median : 6.000  
##  Mean   :31.88   Mean   : 10.953   Mean   : 516.7   Mean   : 6.191  
##  3rd Qu.:43.04   3rd Qu.: 11.450   3rd Qu.: 813.0   3rd Qu.: 8.500  
##  Max.   :77.40   Max.   :113.800   Max.   :2506.0   Max.   :14.000  
##  NA's   :6                                                          
##     numregim    
##  Min.   :1.000  
##  1st Qu.:2.000  
##  Median :3.000  
##  Mean   :2.511  
##  3rd Qu.:3.000  
##  Max.   :4.000  
## 

#Plot reponse against all predictors

pairs(africa)

# Fit model 1
lm_pois <- glm(formula = miltcoup ~ ., family= "poisson", data=na.omit(africa))
summary(lm_pois)

## 
## Call:
## glm(formula = miltcoup ~ ., family = "poisson", data = na.omit(africa))
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -1.3443  -0.9542  -0.2587   0.3905   1.6953  
## 
## Coefficients:
##               Estimate Std. Error z value Pr(>|z|)   
## (Intercept) -0.5102693  0.9053301  -0.564  0.57301   
## oligarchy    0.0730814  0.0345958   2.112  0.03465 * 
## pollib      -0.7129779  0.2725635  -2.616  0.00890 **
## parties      0.0307739  0.0111873   2.751  0.00595 **
## pctvote      0.0138722  0.0097526   1.422  0.15491   
## popn         0.0093429  0.0065950   1.417  0.15658   
## size        -0.0001900  0.0002485  -0.765  0.44447   
## numelec     -0.0160783  0.0654842  -0.246  0.80605   
## numregim     0.1917349  0.2292890   0.836  0.40303   
## ---
## 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: 28.668  on 27  degrees of freedom
## AIC: 111.48
## 
## Number of Fisher Scoring iterations: 6

# Fit model Stepwise AIC
lm_pois2 <- stepAIC(lm_pois, trace=TRUE)

## Start:  AIC=111.48
## miltcoup ~ oligarchy + pollib + parties + pctvote + popn + size + 
##     numelec + numregim
## 
##             Df Deviance    AIC
## - numelec    1   28.728 109.54
## - size       1   29.281 110.09
## - numregim   1   29.363 110.17
## - popn       1   30.628 111.44
## - pctvote    1   30.668 111.48
## <none>           28.668 111.48
## - oligarchy  1   33.032 113.84
## - parties    1   35.501 116.31
## - pollib     1   35.581 116.39
## 
## Step:  AIC=109.54
## miltcoup ~ oligarchy + pollib + parties + pctvote + popn + size + 
##     numregim
## 
##             Df Deviance    AIC
## - numregim   1   29.363 108.17
## - size       1   29.455 108.26
## - popn       1   30.639 109.45
## - pctvote    1   30.716 109.53
## <none>           28.728 109.54
## - parties    1   36.243 115.05
## - oligarchy  1   36.645 115.45
## - pollib     1   36.872 115.68
## 
## Step:  AIC=108.17
## miltcoup ~ oligarchy + pollib + parties + pctvote + popn + size
## 
##             Df Deviance    AIC
## - size       1   30.044 106.85
## - popn       1   30.653 107.46
## <none>           29.363 108.17
## - pctvote    1   31.705 108.51
## - parties    1   36.778 113.59
## - pollib     1   37.830 114.64
## - oligarchy  1   40.300 117.11
## 
## Step:  AIC=106.85
## miltcoup ~ oligarchy + pollib + parties + pctvote + popn
## 
##             Df Deviance    AIC
## - popn       1   31.081 105.89
## <none>           30.044 106.85
## - pctvote    1   32.247 107.06
## - parties    1   37.597 112.41
## - pollib     1   38.022 112.83
## - oligarchy  1   40.589 115.40
## 
## Step:  AIC=105.89
## miltcoup ~ oligarchy + pollib + parties + pctvote
## 
##             Df Deviance    AIC
## - pctvote    1   32.856 105.67
## <none>           31.081 105.89
## - parties    1   37.599 110.41
## - pollib     1   39.762 112.57
## - oligarchy  1   48.950 121.76
## 
## Step:  AIC=105.66
## miltcoup ~ oligarchy + pollib + parties
## 
##             Df Deviance    AIC
## <none>           32.856 105.67
## - parties    1   38.204 109.01
## - pollib     1   40.025 110.83
## - oligarchy  1   50.446 121.25

summary(lm_pois2)

## 
## Call:
## glm(formula = miltcoup ~ oligarchy + pollib + parties, family = "poisson", 
##     data = na.omit(africa))
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -1.3583  -1.0424  -0.2863   0.6278   1.7517  
## 
## Coefficients:
##              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  0.251377   0.372689   0.674  0.50000    
## oligarchy    0.092622   0.021779   4.253 2.11e-05 ***
## pollib      -0.574103   0.204383  -2.809  0.00497 ** 
## parties      0.022059   0.008955   2.463  0.01377 *  
## ---
## 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: 32.856  on 32  degrees of freedom
## AIC: 105.66
## 
## Number of Fisher Scoring iterations: 5

plot(lm_pois2$fitted.values, lm_pois2$residuals)
abline(h=0, col="blue")

qqnorm(lm_pois2$residuals)
qqline(lm_pois2$residuals)

exp(lm_pois2$coefficients)

## (Intercept)   oligarchy      pollib     parties 
##   1.2857949   1.0970473   0.5632097   1.0223037