# Response variable: percentage and too many zeros (zero inflated Poisson?)

I am analysing the effect of density (categorical), gonad mass (continuous) and temperature (continuous) on the percentage of acini spawning in a gonad. My replicate unit is a scallop.

As my response variable is a percentage, and I have many zeros, I was wondering if a zero inflated Poisson regression would be adequate. I know this is used for count data - but as my data is percentage I am wondering if it would be all right to use this model.

• do you have a value for the denominator? That is, can you say how many total individuals might have spawned? If so, you can treat this as binomial (or zero-inflated binomial if necessary). Many zeros doesn't necessarily mean you need a zero-inflated model, if the mean spawning proportion is low enough. – Ben Bolker Jan 6 '14 at 14:08
• Yes, basically it is a random point count in the gonad, where either 30 or 50 acini where assessed for spawning or not. so my data in each gonad is yes/no/no/yes... 30 or 50 times. From this I calculated the percentage. Below the first few rows of my data. Each row is one scallop density percent gonad temperature 1.455 0 3.1 11.35558 1.455 0 4.7 11.35558 0.59 0 12.44 11.35558 0.59 4 1.72 11.35558 0.59 0 4.28 11.35558 0.59 0 5.39 11.35558 – Tania Mendo Jan 6 '14 at 22:01
• in R, I would suggest m1 <- glm(pct_spawned ~ density+mass+temperature, weights=tot_acini, family=binomial); ss <- simulate(m1,1000); zeroDist <- colSums(ss=0); hist(zeroDist) and see if your actual number of zeros falls within the distribution (I set up an additive model, I don't know whether you want or need to consider interactions) – Ben Bolker Jan 7 '14 at 2:32

• I would put the emphasis differently. The Gaussian is a limiting case of the Poisson, suggesting that discreteness is not the most fundamental property of the latter. Poisson models have been found useful for continuous responses so long as $\exp(Xb)$ is a reasonable functional form. But percentages are bounded, so unless the mean of your variable is very near zero and large percentages extremely rare, I agree that the Poisson is unlikely to be a good fit. Zero-inflated beta might be another candidate. We don't have enough information on the data to make a really good recommendation. – Nick Cox Jan 6 '14 at 10:20