A SAS analyst fits PROC GENMOD to count data representing hospital readmissions per patient. The output shows significant overdispersion (deviance/DF = 3.2). Which distribution family should replace Poisson to better handle overdispersion?
Select an answer to reveal the explanation.
Short Explanation
You need the negative binomial distribution because the Poisson model assumes the mean equals the variance, and a deviance/DF of 3.2 shows overdispersion. The negative binomial adds a dispersion parameter so the variance can exceed the mean, which fits overdispersed count data.
Full Explanation
The negative binomial distribution is correct because Poisson regression assumes mean = variance, but deviance/DF = 3.2 indicates overdispersion, where variance exceeds mean. The negative binomial adds a dispersion parameter allowing variance to exceed the mean, making it appropriate for overdispersed count data. In PROC GENMOD, specify DIST=NEGBIN. The binomial distribution is wrong because it is for proportion or count-out-of-total data, not open-ended counts. The gamma distribution is wrong because it models continuous positive values, such as time between readmissions, not counts. The normal distribution with the LOG link is wrong because it is a log-linear model that does not constrain predictions to integer counts.