Homework Assignment 6

1) Define a count outcome for the dataset of your choosing, the Area Resource File used in class provides many options here

1. State a research question about your outcome

I will use the BRFSS data and my research question is: Does health affect the number of hours a person sleeps in a 24-hour period?

2. Is an offset term necessary? why or why not? If an offset term is need, what is the appropriate offset?

Yes, an offset term is necessary to account for the unequal population sizes in the “genhealth” variable.

2) Consider a Poisson regression model for the outcome

1. Evaluate the level of dispersion in the outcome

The level of dispersion in the outcome is 1.33. While it is over 1, it is not too much off of 1 so while there is overdispersion, it is not too great.

2. Is the Poisson model a good choice?

The Poisson model is not a good fit because the residual deviance is 0 which shows the model does not fit for this data.

library(gtsummary)
library(gt)

brfss2020$genhealth <- as.numeric(brfss2020$genhealth)

glmpos<-glm(sleptim1 ~ offset(log(genhealth)) + checkup1 + educa, data = brfss2020, family = poisson)


glmpos %>%
  tbl_regression(exp=TRUE)

Characteristic	IRR1	95% CI1	p-value
checkup1
0last2yrs	—	—
1last5yrs	1.06	1.05, 1.06	<0.001
2never	1.05	1.02, 1.07	<0.001
educa
1noschool	—	—
2elementary	0.96	0.92, 1.01	0.15
3somehs	0.99	0.94, 1.04	0.7
4hsgrad	1.14	1.08, 1.19	<0.001
5somecol	1.19	1.14, 1.25	<0.001
6baorhigher	1.39	1.32, 1.46	<0.001
1 IRR = Incidence Rate Ratio, CI = Confidence Interval

scale <- sqrt(glmpos$deviance/glmpos$df.residual)

scale

## [1] 1.331512

1-pchisq(glmpos$deviance, df = glmpos$df.residual)

## [1] 0

3) Consider a Negative binomial model

library(MASS)

## 
## Attaching package: 'MASS'

## The following object is masked from 'package:gtsummary':
## 
##     select

## The following object is masked from 'package:dplyr':
## 
##     select

glmnb <- glm.nb(sleptim1 ~ offset(log(genhealth)) + checkup1 + educa, data = brfss2020)

glmnb %>%
  tbl_regression()

Characteristic	log(IRR)1	95% CI1	p-value
checkup1
0last2yrs	—	—
1last5yrs	0.06	0.05, 0.07	<0.001
2never	0.06	0.03, 0.09	<0.001
educa
1noschool	—	—
2elementary	-0.07	-0.14, 0.00	0.034
3somehs	-0.04	-0.11, 0.02	0.2
4hsgrad	0.10	0.04, 0.17	0.002
5somecol	0.15	0.09, 0.22	<0.001
6baorhigher	0.31	0.24, 0.37	<0.001
1 IRR = Incidence Rate Ratio, CI = Confidence Interval

4) Compare the model fits of the alternative models using AIC

The negavite binomal model fits better then the Poisson model according to the AIC.

AIC(glmpos, glmnb)