My goal is to know the relation of two variables: Density and proportion in diapause. However, the complicated part of my analysis is that the proportion in diapause acts in two different ways, as binomial or continuous. The densities of larvae (ind. var.) tested were: solitary (only 1 larvae per container) and densities from 6 to 400 (each of these densities per container). The response variable is the proportion of larvae that went into diapause. However, this number would be only 0 or 1 for the solitary density or a continuous range from 0-1 for the other densities.
I thought about using logistic regression, but proportion of diapause does not necessarily increase with increased densities: More larvae are in diapause when solitary than when in densities of 6 and 20, after that proportion of diapause increases being higher at 400.
Thanks in advance for any sugestion!
I think that some kind of mixture model is required. It is possible that fairly standard ones such as a zero-inflated Poisson or a zero-inflated negative Binomial regression might work, but a more bespoke model might be preferable.
In a zero-inflated Poisson you would model the diapause probability via the logistic regression and the density via a Poisson distribution. I may have misunderstood the precise details but I'm fairly confident that some kind of mixture model would work.
I think that you would use the logistic regression model . the density via a Poisson distribution as an independent var & the proportion in diapause ( in two different ways) as a response var.
let's suppose that your observations are of the form:
Container1 nb larv : 1 nb diap : 0
Container2 nb larv : 1 nb diap : 1
Container3 nb larv : 455 nb diap : 128
etc
This kind of data are to be treated with a GLM model (probably of the Binomial or the Poisson families).
The fact that in some containers responses are zero or one while in others they are almost continuous and between zero or one is not a problem for the softwares, as long as the total numbers (nb larv in my setting) are known.
The differences of nb larv may be a methodological issue (kind : why such differences?), but any educated software will master it.
Thanks!!! The example shown by. Jean Maccario is exactly how my data looks. I applied the logistic regression to the data. But my data does not fit this distribution. This is probably because my results follow almost a bell curve: For example, in percentages 10% of the individuals diapause at a density of 1, 2% at density 6, 3% at density 20, 15% at 100 and increasing from there. About the methodological issue, I wanted to know the effect of density on diapause and according to the literature diapause is higher in solitary and crowded conditions. Therefore solitary was a necessary treatment.
I will try to use a model from the Poisson family and get back to you. Other solution that comes to my mind is if maybe doing a transformation to the data would work to analyse it with GLM.
Thank you!
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