Online Resource 1: Results of Alternative Model Selection Methods

Online Resource 1: Results of alternative model selection methods

In the main article, inference was made from a weighted averaging of eighteen a priori candidate models, closely following the advice for multi-model inference made by Burnham and Anderson (2002). This way, uncertainty of the model selection is incorporated in the final parameter estimates. For comparison, we here provide the results of two alternative selection procedures: a classic stepwise backward model selection procedures based on p-values (critical p-value of 0.10) and one based on AIC-values (e.g. Zuur et al. 2009). Although this approach is antithetical to the multi-model inference theory of Burnham and Anderson (2002) and may result in data overfitting, it reduces the concern that not all possible model combinations were considered. The initial (full) model includes much more factors than the most parameterised models from the set of candidate models. These factors are ecologically explainable, but they were a priori considered as unrealistic interaction terms, and were therefore not included in the set of eighteen candidate models. The initial model is as follows:

Survival/Trials ~ Distance_to_edge + Fragment + Distance_to_edge x Fragment + Concealment + Concealment x Fragment + Clutch_Initation_Day + Nest_Age + Nest_Age² + Season +

[Distance_to_edge + Fragment + Distance_to_edge x Fragment + Concealment + Concealment x Fragment + Clutch_Initation_Day + Nest_Age + Nest_Age²] x Season

Table 3.1 Parameter estimates of a logistic exposure model of nest predation on Cabanis’s Greenbul nests obtained after model averaging of eighteen candidate models, a backward model selection based on AIC values, and a backward model selection based on p-values.

Model averaged- full method / Model averaged - subset method / AIC-based / p-value based
Intercept / 3,31 / 3,31 / (0,77)*** / 3,79 / (0,73)*** / 4,27 / (0,87)***
Distance_to_edge / -0,01 / -0,01 / (0,01)* / 0,00 / (0) ns / -0,01 / (0)*
Fragment(Ngangao) / -1,99 / -1,99 / (0,8)* / -1,76 / (0,45)*** / -2,98 / (0,76)***
Concealment / -0,01 / -0,01 / -0,01 ns / na / -0,01 / (0,01) ns
CIDa / 0,02 / 0,02 / (0,01)** / 0,03 / (0,01)*** / 0,03 / (0,01)***
Year (2008/2009) / 0,56 / 0,60 / (0,64) / -1,39 / (0,89) ns / -1,01 / (0,91) ns
Year (2009/2010) / 1,61 / 1,74 / (0,69)* / -0,56 / (0,94) ns / -0,33 / (0,96) ns
Nest_Age / -0,01 / -0,02 / (0,06) ns / -0,06 / (0,03)* / -0,06 / (0,03)*
Nest_Age² / 0,00 / 0,00 / (0) ns / na / na
Distance x Frag(Ngangao) / 0,01 / 0,01 / (0,01) ns / na / 0,01 / (0,01) ns
Concealment x Frag(Ngangao) / 0,01 / 0,02 / (0,01)* / na / 0,02 / (0,01) ns
CIDa x Year(2008/2009) / 0,00 / -0,01 / (0,01) ns / -0,01 / (0,01) ns / -0,01 / (0,01) ns
CIDa x Year(2009/2010) / -0,02 / -0,02 / (0,01)* / -0,03 / (0,01)** / -0,03 / (0,01)**
Nest_Age x Year(2008/2009) / na / na / 0,09 / (0,03)** / 0,09 / (0,04)*
Nest_Age x Year(2009/2010) / na / na / 0,11 / (0,04)** / 0,10 / (0,04)**
Frag(Ngangao) x Year(2008/2009) / na / na / 0,78 / (0,58) ns / 0,85 / (0,59) ns
Frag(Ngangao) x Year(2009/2010) / na / na / 1,36 / (0,56)* / 1,32 / (0,58)*

ns not significant (p>0.05); * p < 0.05; ** p < 0.01; ***:p < 0.001

a CID = Clutch Initiation Day

na: parameter not present in the model

In terms of factors in the model, both the AIC-based and the p-value based selected models are rather similar to the weighted averaged model, but these additionally including the Nest_Age x Year and/or Fragment x Year interactions that were not present in any candidate model. With the exception of the parameters that are affected by these interactions (especially the Intercept and Year terms), all three models yielded rather comparable parameter estimates and significance values for most parameters. This confirms that the described patterns are based on a robust statistical model, irrespective the exact model selection tool.

References

Burnham KP, Anderson DR (2002) Model selection and multimodel inference. A practical information-theoretic approach. 2nd ed. Springer-Verlag, New York

Zuur AF, Ieno EN, Walker NJ, Saveliev AA, Smith GM (2009) Mixed Effects Models and Extensions in Ecology with R. Springer, New York