10.3 Quasi-Poisson Regression Model

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.