Hi all,
I have a data set made of 12 years each one with a number of males and a number of females. I tested the relationship between the sex ratio (proportion of males over the total) weighted for the number of individuals of each year. In R: glm.1<-glm(cbind(males,females)~predictor,binomial,data=data) With this aim I prepared a set of candidate models each one representing a specific biological hypothesis. I work with two data sets because I used two sexing methods and in one data set I have some extra individuals sexed each year with another method. Hence data sets have different sample sizes (min=14 and 43, max=880 and 950, mean=244 and 324, respectively). One identical set and analysis for each data set. I considered four predictors but each model contained at most two predictors (one categorical predictor plus one of the other three that, instead, are continuous). The categorical predictor has a clear effect on the sex ratio as resulting from simple plotting of data and by logic beyond the hypothesis it depicts. I know both analyses are at risk of being overparameterized but I trust that QAICc (Akaike Information Criterion corrected for small samples and overdispersion) had ride of this problem. In fact, for the smaller data set I don't find any clear pattern and, as a result, the null (only intercept) model performs as well as the one considering the categorical predictor. I report the QAICc (c-hat=1.2) ranking and as a measure of the effect size, the Nagelkerkes Pseudo-R2, that in this case, for the best ranked non-null model (the categorical predictor) is about 0.3. For the bigger data set I find very clear results and the model accounting for the categorical predictor plus another (continuous) predictor is ranked first at more than six deltaAICc (c-hat=1) from the next one (the one with only the categorical predictor). In this case, the Nagelkerkes Pseudo-R2 is about 0.95 and I feel somehow uncomfortable with that high optimistic estimate. In R the Nagelkerkes Pseudo-R2 was computed following Faraway (2006) as: R2.nagelkerke<-(1-exp((glm.1$dev - glm.1$null)/nrow(data)))/(1-exp(-glm.1$null/nrow(data))) Any opinion/suggestion on this case? Faraway, J. J. (2006). Extending the Linear Model with R. Boca Raton. FL: Chapman & Hall/CRC. [[alternative HTML version deleted]]
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