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

poisson-regressionzero inflation

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.

Best Answer

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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Zero-Inflated Poisson Model – Comprehensive Understanding

Criterion is based upon (informed) model comparisons. You are trying to account for over-dispersion.

Poisson var(x) ~ mu

Neg Binomial var(x) > mu

"Extra" zeros

ZIP var(x) ~ mu

ZIPB var(x) > mu
One active package that you can use is install.packages("pscl") You can then fit a number of models such as a hurdle model that uses a negative binomial for the counts and a binomial model for modeling the probability of zeros. This would be written something like:
```
fit <- hurdle(Admission ~ Temperature + Humidity), dist="negbin", data = data)

 summary (fit)
```

Note that the output will have two sets of coefficients: one for the hurdle component and one for the count data. This output also provides an estimate of the theta parameter (overdispersion) of the negative binomial

Or you may want to look at the zero-inflation model

fit1<-zeroinfl(Admissions ~ Temperature + Humidity), data = data,dist="negbin",link="logit")

These models can be examined with AIC (also compare these models to your Poisson model...) AIC(fit,fit1)

Solved – Approaches to regression with zero inflated response

In this case, where your data is simply overwhelmed by the number of zeros, IMO it makes the most sense to split this into a frequency model and a severity model. I.e. something like a logistic regression (or whatever such model you prefer) for whether the data is non-zero, and then a separate model on the severity conditioned on the weight being non-zero.

(Edit: removed my misunderstanding of the problem).

What exactly are you trying to do?

Best Answer

Related Solutions

Zero-Inflated Poisson Model – Comprehensive Understanding

Solved – Approaches to regression with zero inflated response

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