As a consequence, both standard errors and p-values are too low, sometimes way too low.Īn effective alternative is negative binomial regression, which generalizes the Poisson regression model by introducing a dispersion parameter. The problem with Poisson regression models is that count data frequently suffer from overdispersion-the conditional variance is larger than the conditional mean. Incidental parameter bias does not occur with Poisson models, however. For logistic models, conditional likelihood eliminates what’s known as “incidental parameters bias,” which can be quite severe when the number of repeated measurements per individual is small. Conditional likelihood can greatly reduce computer time and memory requirements because the individual-specific parameters don’t have to be estimated. Specifically, for each individual, the contribution to the likelihood function is conditioned on the sum of the repeated measures, thereby eliminating the individual-specific parameters from the likelihood function.Ĭonditional likelihood has two advantages: 1. In conditional likelihood, the “incidental parameters” for each individual are conditioned out of the likelihood function. Logistic and Poisson fixed effects models are often estimated by a method known as conditional maximum likelihood. Fixed effects models come in many forms depending on the type of outcome variable: linear models for quantitative outcomes, logistic models for dichotomous outcomes, and Poisson regression models for count data (Allison 2005, 2009). They accomplish this by introducing an additional parameter for each individual in the sample. Here’s the story:įor panel data with repeated measures, fixed effects regression models are attractive for their ability to control for unobserved variables that are constant over time. If you’ve ever considered using Stata or LIMDEP to estimate a fixed effects negative binomial regression model for count data, you may want to think twice.
Beware of Software for Fixed Effects Negative Binomial Regression JBy Paul Allison