I have a fisheries dataset for which I have calculated value for each grid cell on a map. The value is the proportion of the total fishing sets in that cell for each month/year. So, I have values between 0-1, but not including 0 and 1 (the range is actually very skewed and is: 0.0005347594 to 0.1933216169). I am interested in whether the proportion of fishing sets is higher close to a specific location over time.
I have read that there are two ways to do this - either a GLM with a binomial family and logit link, or a beta regression.
I have tried both of these methods in R:
m1 <- glm(PercentTotalSets ~ factor(SetYear) + DayLength + DistTZCF + DistNWHI, family = binomial(link='logit'), data = Totals_CellId)
BetaGLM <- betareg(PercentTotalSets ~ factor(SetYear) + DayLength + DistTZCF + DistNWHI, data = Totals_CellId )
With the binomial GLM, I get very different results than I would if I ran a GLM with a gamma distribution (e.g.,
DistNWHI is not significant with a p-value of .9 whereas before it was significant). With the beta regression, I get very similar results to a GLM with a gamma distribution (e.g.,
DistNWHI is significant with similar p-value).
I think that the beta regression is the correct method, because I do not have 0s or 1s and I need to set bounds, but I am not sure if this is correct.
I'd appreciate any and all advice.