Count Model Data Using the AHRF

For this short report, I use counts from the 2019-20 Area Health Resource Files and focus on the count outcome of percentage of food stamp/SNAP recipients in Texas counties based on urban/rural county status. I apply an offset term (i.e. log(Population))in the model to account for unequal population sizes across Texas county regions.

First, I consider a Poisson regression model for rate of county recipients utilizing SNAP/food stamp subsidies using a Poisson rate model for rate of occurrence. The Poisson model does not seem to be a good choice for the model as the outcome variable in the model has non integer responses. I evaluate the level of dispersion in the outcome variable by comparing the residual deviance to the residual degrees of freedom. The dispersion ratio is 352.756, which is way larger than 1 indicating a very poor model fit to the data. There is a high level of dispersion in the Poisson model.

Characteristic Beta 95% CI1 p-value
rucc
01 — —
01 — —
02 64 37, 92 <0.001
03 24 -4.4, 53 0.10
04 69 35, 103 <0.001
05 92 46, 139 <0.001
06 55 33, 77 <0.001
07 37 12, 61 0.004
08 15 -15, 44 0.3
09 15 -11, 42 0.3

1 CI = Confidence Interval

Characteristic IRR1 95% CI1 p-value
factor(rucc)
01 — —
02 4.79 4.58, 5.01 <0.001
03 8.09 7.70, 8.51 <0.001
04 17.9 17.0, 18.9 <0.001
05 17.5 16.4, 18.7 <0.001
06 40.2 38.7, 41.8 <0.001
07 53.6 51.3, 55.9 <0.001
08 87.0 82.5, 91.6 <0.001
09 251 240, 264 <0.001

1 IRR = Incidence Rate Ratio, CI = Confidence Interval 

## # Overdispersion test
## 
##        dispersion ratio =   352.756
##   Pearson's Chi-Squared = 86425.262
##                 p-value =   < 0.001
## Overdispersion detected.
## 
## Attaching package: 'MASS'
## The following object is masked from 'package:gtsummary':
## 
##     select
## The following object is masked from 'package:dplyr':
## 
##     select
Characteristic IRR1 95% CI1 p-value
factor(rucc)
01 — —
02 7.04 4.35, 11.5 <0.001
03 4.25 2.58, 7.13 <0.001
04 2.65 1.49, 4.97 0.001
05 2.53 1.20, 6.24 0.024
06 8.27 5.56, 12.1 <0.001
07 10.4 6.74, 16.0 <0.001
08 21.0 12.6, 35.7 <0.001
09 60.0 37.7, 96.0 <0.001

1 IRR = Incidence Rate Ratio, CI = Confidence Interval