1) If you want a likelihood (AIC, etc), you can use a Poisson of negative binomial model with an offset (the offset should be the log of the number of eggs).

2) if you want to compare something against "GroupC.ricrodii-B", you can relevel "Group" to have "GroupC.ricrodii-B" as the reference level. Another option is to use multcomp::glht() that allows you to specify arbitrary linear contrasts, but in this case the simplest solustion is to refit the model with the releveled Group factor.

Your GLM model looks correct. To compare Group (A) to Group (B) for instance, one way is to change the reference variable. This is fairly simple to do using the relevel() function. Here is a tutorial with an example of how to change your reference variable when doing contrasts. In this case, you could make either "GroupC.ricordii-A" or "GroupC.ricordii-B" the reference group - it doesn't matter which.

https://rstudio-pubs-static.s3.amazonaws.com/65059_586f394d8eb84f84b1baaf56ffb6b47f.html

Jochen Wilhelm thanks again for your answer (you really answered every question I posted on this forum XD!!)! If I use a Poisson of negative binomial model with an offset (log(N_eggs)), how would my formula then look like?

MASS::glm.nb(NumSuccess ~ Group + offset(log(numEggs)), data=dd)

where "NumSuccess" and "numEggs" are counts. Your variable "Success" mentiones in your original post is likely NumSuccess/NumEggs. The actual variable names in your data.frame "dd" might be different, for sure.

glm.nb() is defined in the package MASS. Since it is only for the negative binomial family, there is no "family" argument to be specified. Just like for Poisson, log() is the default link function.

http://statmath.wu.ac.at/courses/heather_turner/glmCourse_003.pdf

https://towardsdatascience.com/offsetting-the-model-logic-to-implementation-7e333bc25798

https://www.cscu.cornell.edu/news/statnews/94_offsets.pdf

An entirely different approach to get likelihood values using your relative success variable would be using a beta-model (https://www.ime.usp.br/~sferrari/beta.pdf). But I think in your case modelling counts (+offsets) is more direct and more appropriate (and possibly more robust and more powerful).

Jochen Wilhelm , so then my number of hatchlings would be equal to the suggested NumSuccess, right? Then it looks promising!

One more question (if I may):

When I include the variable 'average nest temperature', the AIC reduces a lot (which means a better fit of the model). Then I get this output:

Call:

glm.nb(formula = `Total hatchlings` ~ Location + (relevel(dd$Species,

ref = "Ricordii")) + `Average temperature` + offset(log(Eggs...23)),

data = dd, init.theta = 13.78459852, link = log)

Deviance Residuals:

Min 1Q Median 3Q Max

-3.2045 -0.8098 0.3388 0.6144 1.0381

Coefficients:

Estimate Std. Error z value Pr(>|z|)

(Intercept) -2.31366 5.11994 -0.452 0.651

LocationPuente Arriba 0.11286 0.25485 0.443 0.658

LocationTierra 0.08780 0.20066 0.438 0.662

Cornuta -0.14199 0.18168 -0.782 0.434

`Average temperature` 0.02240 0.05686 0.394 0.694

(Dispersion parameter for Negative Binomial(13.7846) family taken to be 1)

Null deviance: 51.655 on 46 degrees of freedom

Residual deviance: 50.550 on 42 degrees of freedom

(143 observations deleted due to missingness)

AIC: 272.75

Number of Fisher Scoring iterations: 1

Theta: 13.78

Std. Err.: 7.47

2 x log-likelihood: -260.753

Assuming this would be the best fitting model, what can I conclude from this (how can I report this in my paper) when trying to answer the question if Species, Location and Average Temperature are predictors of Success (also taking in mind that the species Ricordii and Location Malaguenta is used as reference)?

;)

Hmmm, what makes me wonder: 46 degrees of freedom and 143 observations missing! Do you really have such a lot of missing values? If yes, why? And can you resonably assume that these are "missing at random" (that missingness is not related somehow to any of the predictors)?

The coefficients table does not look very convincing. The standar errors of all the estimates are rther large (and the p-values are high, indicating that the data are not very surprising even if one of the coefficients would be restricted to be zero).

As far as I understand it, these data are not conclusive regarding any coefficient in your model. This may be related to the large amount of missing data, maybe there is something going wrong. If not, then there is nothing much to report; you might have a look at the confidence intervals and check if they are fully within some range of negligible effects, in which case you may conclude that the data are incompatible with hypotheses about relevant effects.

The estimate for the nest temp. is 0.02, with a standard error of 0.06, so your data are actually compatible with anything between 0.02-2*0.06 = -1 to 0.02+2*0.06 = +1.4. The p-value of 0.694 gives a quick hint that this interval includes zero, so the data are conpatible with positive as well as with negative temperature effects.

The estimate (and the interval limits) are log ratios, so lthe lower limit for the temperature effect, -1, sais that the ratio of total hatchings per unit temperature increase (I assume it's 1K) is exp(-1) = 0.37, so the number of total hatchings drops to 37% when the temperature is 1K higher. The other limit, +1.4, indicates that the total hatchings increase to exp(1.4) = 4.1 or 410% per 1K higher temperature. Both values (37% and 410%) and everything inbetween are compatible with your data! This is a huge interval, what allows you actually nothing to conclude for the effect of the temperature.

All this is the average effect across all species and all locations. If you think that the temperature effect depends on the species, the model must include the corresponding interaction (species:temperature).

Thanks again Jochen Wilhelm for your clear explanation! Indeed I miss a lot of data, because only from a limited number of nests, the temperature was measured (still it gives me enough data to use) so I'm aware of that ;). I agree that we cannot conclude much from the model, but how do you think I should mention this in the paper?