Table 1.
Hierarchical random regression linear mixed models of clutch size as a function of laying date of increasing polynomial order and their significance, as specified by Equation (1). Reported in the upper part of the table are the REML variances (covariances are reported in the text). The significance of higher order random regression is tested by a likelihood ratio test comparing the likelihood of each model to the hierarchical lower one. Residual variance is denoted for each model, and the coefficients of the random regression (Equation [1]) are listed in increasing order such that ind1 is the first-order (linear) coefficient, ind2 the second order. For each test, the degrees of freedom (df) are given by the number of additional variances and covariances that are estimated. The most parsimonious model is presented in bold. The lower part of the table presents the fixed effects and their standard error of the most parsimonious model, with their significance tested using F-tests.
| Random regression variances |
Test between models |
|||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Model | Residuals | Year | ind0 | ind1 | ind2 | ind3 | LogL | χ2 | df | P |
| 1 | 0.735 | – | – | – | – | – | –397.2 | |||
| 2 | 0.575 | 0.179 | – | – | – | – | –295.2 | 204.0 | 1 | <0.001 |
| 3 | 0.452 | 0.165 | 0.126 | – | – | – | –264.8 | 60.8 | 1 | <0.001 |
| 4 | 0.413 | 0.161 | 0.122 | 0.417 | – | – | –256.7 | 16.2 | 2 | 0.003 |
| 5 | 0.397 | 0.156 | 0.141 | 0.240 | 0.975 | – | –251.7 | 10.0 | 3 | 0.019 |
| 6 | 0.391 | 0.156 | 0.146 | 0.234 | 1.083 | 0.487 | –249.3 | 4.8 | 4 | 0.31 |
| Fixed effect | Estimate | df (nom) | df(den) | F | P | |||||
| μ | 3.38 ± 0.080 | |||||||||
| Laying date | –0.062 ± 0.0032 | 1 | 382.3 | 377.3 | <.001 | |||||
| Age | 1: –0.22 ± 0.14 | |||||||||
| 2: 0.032 ± 0.10 | 2 | 983.6 | 1.3 | 0.285 | ||||||