10.3 Fitting a Quasi-Poisson Model

We will now fit a Quasi-Poisson regression model to the Ferraro et al. (2016) data. As described previously the Quasi-Poisson model is a generalization of the Poisson regression and is used when modeling an overdispersed count variable.

ferraro2016 <- read.csv("data/ferraro2016.csv")

ferraro2016$female <- as.factor(ferraro2016$female)
ferraro2016$obese  <- as.factor(ferraro2016$obese)
ferraro2016$abuse_rare <- as.factor(ferraro2016$abuse_rare)
ferraro2016$abuse_freq1 <- as.factor(ferraro2016$abuse_freq1)
ferraro2016$abuse_freq2 <- as.factor(ferraro2016$abuse_freq2)

model4 <- glm(
  formula = morbidityw1 ~ 1 + female + health + age + smoke_dose + heavydr2 + obese + fampos + friendpos + abuse_rare + abuse_freq1 + abuse_freq2, 
  family = quasipoisson(link=log), 
  data = ferraro2016,
  na.action = na.exclude
)

summary(model4)

## 
## Call:
## glm(formula = morbidityw1 ~ 1 + female + health + age + smoke_dose + 
##     heavydr2 + obese + fampos + friendpos + abuse_rare + abuse_freq1 + 
##     abuse_freq2, family = quasipoisson(link = log), data = ferraro2016, 
##     na.action = na.exclude)
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.2792560  0.1439042   1.941  0.05241 .  
## female1       0.3284639  0.0384021   8.553  < 2e-16 ***
## health        0.1665501  0.0419736   3.968 7.43e-05 ***
## age           0.0153301  0.0015396   9.957  < 2e-16 ***
## smoke_dose    0.0055588  0.0008907   6.241 5.02e-10 ***
## heavydr2      0.1136408  0.0440990   2.577  0.01002 *  
## obese1        0.2639706  0.0394117   6.698 2.56e-11 ***
## fampos       -0.0885551  0.0314942  -2.812  0.00496 ** 
## friendpos    -0.0711315  0.0282620  -2.517  0.01190 *  
## abuse_rare1  -0.0118142  0.0503028  -0.235  0.81433    
## abuse_freq11  0.0903667  0.0557820   1.620  0.10535    
## abuse_freq21  0.2731073  0.0519243   5.260 1.55e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for quasipoisson family taken to be 2.443076)
## 
##     Null deviance: 7403.7  on 2754  degrees of freedom
## Residual deviance: 6414.4  on 2743  degrees of freedom
##   (267 observations deleted due to missingness)
## AIC: NA
## 
## Number of Fisher Scoring iterations: 5

Remember, we can interpret these coefficients just as we would regression coefficients, however, we would be speaking in terms of the log of the mean count.

Broadly, we may be interested in (1) predictions, (2) slopes and (3) hypothesis tests. Let’s briefly review functionality for each of these areas.