Lecture 05 AE: Poisson Regression

Goodness-of-fit and overdispersion

library(tidyverse)
library(broom)
library(knitr)
# add other packages as needed

hh_data <- read_csv("data/fHH1.csv")

Household vs. age, age^2, and location

hh_age_loc <- glm(total ~ age + I(age^2) + location, 
                  data = hh_data, family = poisson)

tidy(hh_age_loc, conf.int = T) |> 
  kable(digits = 4)

term	estimate	std.error	statistic	p.value	conf.low	conf.high
(Intercept)	-0.3843	0.1821	-2.1107	0.0348	-0.7444	-0.0306
age	0.0704	0.0069	10.1900	0.0000	0.0569	0.0840
I(age^2)	-0.0007	0.0001	-10.9437	0.0000	-0.0008	-0.0006
locationDavaoRegion	-0.0194	0.0538	-0.3605	0.7185	-0.1250	0.0859
locationIlocosRegion	0.0610	0.0527	1.1580	0.2468	-0.0423	0.1641
locationMetroManila	0.0545	0.0472	1.1542	0.2484	-0.0378	0.1473
locationVisayas	0.1121	0.0417	2.6853	0.0072	0.0308	0.1945

Calculating residuals in R

You can get the residuals in two ways:

1. residuals function with type = "pearson" or type = "deviance".

2. augment function with type.residuals = "pearson" or type.residuals = deviance.

Calculate model deviance & Goodness-of-fit

Ex 1

Use the deviance residuals to calculate the model deviance.

# Calculate model deviance

Ex 2

Check your work above using the glance function.

# Get deviance using glance function

Ex 3

Conduct a goodness-of-fit test

# Conduct goodness-of-fit test

Quasi-Poisson

hh_age_loc_q <- glm(total ~ age + I(age^2) + location, 
                    data = hh_data, family = quasipoisson)

Ex 4

What do we expect the dispersion parameter to be if there is no overdispersion?

Ex 5

Use the Pearson residuals to calculate the dispersion parameter.

# Calculate dispersion parameter 

Ex 6

View the dispersion parameter in the model output

#summary(hh_age_loc_q)

Negative binomial regression model

hh_age_loc_nb <- MASS::glm.nb(total ~ age + I(age^2) + location, data = hh_data)
tidy(hh_age_loc_nb) |> 
  kable(digits = 4)

term	estimate	std.error	statistic	p.value
(Intercept)	-0.3753	0.2076	-1.8081	0.0706
age	0.0699	0.0079	8.8981	0.0000
I(age^2)	-0.0007	0.0001	-9.5756	0.0000
locationDavaoRegion	-0.0219	0.0625	-0.3501	0.7262
locationIlocosRegion	0.0577	0.0615	0.9391	0.3477
locationMetroManila	0.0562	0.0551	1.0213	0.3071
locationVisayas	0.1104	0.0487	2.2654	0.0235