Negative binomial regression
Predict an over-dispersed count with an extra dispersion parameter.
When to use it
Use negative binomial regression for counts when the variance is larger than a Poisson model allows. The table still reports an incidence rate ratio. The extra piece is the dispersion parameter α.
Assumptions
The outcome is a non-negative count. Rows are independent. Tensr estimates α from the counts and refits the coefficients at that value. The report prints α, its standard error, and a likelihood-ratio comparison with a Poisson model. When the counts are not over-dispersed, α can collapse and the standard error stays blank.
Running it in Tensr
Options
Prop
Type
Reading the output
Visit counts with extra-Poisson scatter, predicted from anxiety. Dispersion was built in, so α should be estimated rather than collapsing to zero.
| Term | Estimate | SE | 95% CI | IRR | p-value |
|---|---|---|---|---|---|
| const | -1.213 | 0.692 | [-2.571, 0.144] | 0.297 | .080 |
| anxiety | 0.281 | 0.131 | [0.025, 0.537] | 1.324 | .032 |
Negative binomial regression for visits with 1 predictor(s), n = 96. The primary result is significant (p = < .001). This is large enough, in this sample, to treat the comparison this page is about as a real association rather than noise. Metrics: Dispersion α = 2.19; α SE = 0.599; LR vs Poisson χ² = 75.168; LR vs Poisson p = < .001; AIC = 292.213; Deviance = 84.712.
Reporting (APA 7)
Negative binomial regression for visits with 1 predictor(s), n = 96. This result is significant (p = < .001). The effect is moderate, so report its size with the p-value.
When α collapses, use Poisson
The same 96 people, with absences as a Poisson count of missed sessions and anxiety as the predictor. Negative binomial still runs, but α is 0.004 (SE = 0.071) and the likelihood-ratio test against Poisson is χ² = 0.004, p = .948. Poisson AIC is 333.110; negative binomial AIC is 335.105. The extra dispersion parameter is not doing any work.
| Term | Estimate | SE | IRR | p-value |
|---|---|---|---|---|
| const | 0.026 | 0.281 | 1.026 | .926 |
| anxiety | 0.136 | 0.052 | 1.145 | .009 |
Use Poisson regression for this table. Keep negative binomial when α is estimated with a usable standard error, as in the visits example above.
Coming from SPSS
Analyze → Regression → Negative Binomial.
SPSS negative binomial estimates the dispersion. Tensr estimates α as well, and prints it with a standard error.
Related
A Poisson model of a count is Poisson regression.