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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.

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  • $\begingroup$ 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. $\endgroup$ – Ben Bolker Jan 6 '14 at 14:08
  • $\begingroup$ 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 $\endgroup$ – Tania Mendo Jan 6 '14 at 22:01
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    $\begingroup$ 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) $\endgroup$ – Ben Bolker Jan 7 '14 at 2:32
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The difficulty with the Poisson is that it is defined on the integers; you're dealing with a fraction between 0 and 1.

If you have percentages, presumably you have the numerator and the denominator of that percentage, in which case you might normally look at something more like logistic regression.

This then suggests that a corresponding zero-inflated model would be zero-inflated binomial.

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  • $\begingroup$ 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. $\endgroup$ – Nick Cox Jan 6 '14 at 10:20
  • $\begingroup$ I've never heard of zero-inflated beta. In beta distribution the probability of zero is zero so you have nothing to inflate. For the same reason you can't say zero-modified beta distribution. The appropriate terminology here could be zero-added beta distribution or beta with point mass at zero. Hence the extra tag I added. $\endgroup$ – Hibernating Jan 6 '14 at 13:02
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    $\begingroup$ stata-journal.com/sjpdf.html?articlenum=st0147 is just one source for the terminology zero-inflated beta. I don't see a case for disturbing previous terminology here: zero inflation to me means that the probability of zeros is (possibly) increased over the default model. $\endgroup$ – Nick Cox Jan 6 '14 at 14:36
  • $\begingroup$ My preference is to use "zero-inflated" when I can use any of these: "zero-inflated","zero-deflated" and "zero-modified". Zero is not part of the standard beta's support, so it does sound abusive you can decrease the probability of zero (so it becomes negative). It is also my preference to use "stopped-sum" distribution rather than "compound" distribution to avoid confusion in the literature that sometimes defines compound distribution as mixed distribution. I like and seek consistency in everything, but thanks for the reference anyway. $\endgroup$ – Hibernating Jan 7 '14 at 4:36
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Try Tweedie Generalized Linear Models or something similar. See this discussion for more detail. Here is another one, with partial support of the Tweedie, and also suggesting it might be easier to deal with raw counts.

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