Hi!
I have data on captures per year (n=13) and I want to analyze the relation with years (is it increasing, decreasing or staying the same with time).
Total captures ~ year
Because it is number of individuals in a period of time, first I fitted a GLM with Poisson distribution, however, the overdispersion was very high, so I changed to Negative binomial. With this, I eliminated the overdispersion but the model fitting doesn't look great (see photo), and the explained deviance is %36.
On the other side I fitted an lm, following the normal distribution, and the model fitting looks better (see photo), and the R2 is 0.46.
PD: Also when fitting the distribution of the dependent variable using the function fitdist (from fitdistrplus package) the normal distribution seems to be the best fitted (see photo).
Mu question is, should I choose the best model (LM), or should I choose the GLM because of the type of data I have?
Thank you!
Hi Itaxso, with 13 points it will be hard to get a good fit.
Is there any reason you are fixed with lm/glm?
Try gam (package mgcv) with tweedie family distribution ....
https://fromthebottomoftheheap.net/2011/06/12/additive-modelling-and-the-hadcrut3v-global-mean-temperature-series/
https://fromthebottomoftheheap.net/2011/07/21/smoothing-temporally-correlated-data/
https://fromthebottomoftheheap.net/2014/05/15/identifying-periods-of-change-with-gams/
Good luck ......
EITHER EXPAND SAMPLE SIZE or just dump the data or just use it for learning. A sample of n = 13 is consider small to make a study that would provide predictive model leading to a generalizability. secondly, if the highest adjust R squared you could obtain is 0.46 it means that you proposed model could explain only 46% of the data. you cannot explain the remaining 54%----in the field we say be unable to explain the majority of the data is not much of a forecast model. A guessing game may be at best 50/50 and if a research produces less than a guess, it is not worth considering. Look for a different kind of modeling and expand sample size.
From a theoretical point of view, the NB model is the correct one. If the normal looks better for your residuals, that's just a fluke.
The values you counted are rather large (about 1000 - 6000). That makes differences between the NB and the gaussian model quite irrelevant. But still, due to the log-link of the NB model you estimate a relative change, whereas the gaussian model (using the identity link) estimates an absolute change. I think that changes should be proportional, another theoretical justification of the NB model over the gaussian model.
Regarding the R²: there is no r² for the NB model. The one you reported can only be one of the 1001 pseud-R² measures. You cannot compare R² values between these models. You should rather compare the maximum likelihood, AIC or BIC (since both models have one nuisance parameter and the same number of coefficients, it does not matter which of these measures you use) -- if you want to compare anything.
In my opinion, NB is theoretically justified, and you should have considerable evidence that the theory does not apply to your case (what still might not neccesarily mean that you should the use a gaussian model!). I don't see that evidence.
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