Table 3 Summary of the backward stepwise variables selection process according to the Akaike’s Information Criterion (AIC). In bold, the selected model
From: Modeling sapling distribution over time using a functional predictor in a generalized additive model
Variables included in the alternative models during backward stepwise selection process | AIC |
|---|---|
Intermediate stage of the regeneration period | |
(1) \( \alpha +\beta \cdot \frac{N{\mathrm{small}}_{ij}}{\mathrm{AreaIn}{10}_i}+\sum \limits_{n=1}^N\left({f}_1\left({\mathrm{Dist}}_{\mathrm{in}}\right)\cdot \frac{N{\mathrm{small}}_{ij}}{\mathrm{AreaIn}{10}_i}\right)+{f}_2\left({X}_i,{Y}_i\right)+{\mathrm{Time}}_j \) | 1 3120.98 |
(2) \( \alpha +\sum \limits_{n=1}^N\left({f}_1\left({\mathrm{Dist}}_{\mathrm{in}}\right)\cdot \frac{dbh_{jn}}{\mathrm{AreaIn}{30}_i}\right)+{f}_2\left({X}_i,{Y}_i\right)+{\mathrm{Time}}_j \) | 1 3126.06 |
(3) \( \alpha +\beta \cdot \frac{N{\mathrm{small}}_{ij}}{\mathrm{AreaIn}{10}_i}+{f}_2\left({X}_i,{Y}_i\right)+{\mathrm{Time}}_j \) | 1 3125.11 |
(4) \( \alpha +\beta \cdot \frac{N{\mathrm{small}}_{ij}}{\mathrm{AreaIn}{10}_i}+\sum \limits_{n=1}^N\left({f}_1\left({\mathrm{Dist}}_{\mathrm{in}}\right)\cdot \frac{N{\mathrm{small}}_{ij}}{\mathrm{AreaIn}{10}_i}\right) \) | 1500.13 |
(5) \( \alpha +\beta \cdot \frac{N{\mathrm{small}}_{ij}}{\mathrm{AreaIn}{10}_i}+\sum \limits_{n=1}^N\left({f}_1\left({\mathrm{Dist}}_{\mathrm{in}}\right)\cdot \frac{N{\mathrm{small}}_{ij}}{\mathrm{AreaIn}{10}_i}\right)+{f}_2^j\left({X}_i,{Y}_i\right) \) | 1 3432.74 |
End of the regeneration period | |
(1) \( \alpha +\beta \cdot \frac{N{\mathrm{small}}_{ij}}{\mathrm{AreaIn}{10}_i}+\sum \limits_{n=1}^N\left({f}_1\left({\mathrm{Dist}}_{\mathrm{in}}\right)\cdot \frac{N{\mathrm{small}}_{ij}}{\mathrm{AreaIn}{10}_i}\right)+{f}_2\left({X}_i,{Y}_i\right)+{\mathrm{Time}}_j \) | 5083.94 |
(2) \( \alpha +\sum \limits_{n=1}^N\left({f}_1\left({\mathrm{Dist}}_{\mathrm{in}}\right)\cdot \frac{dbh_{jn}}{\mathrm{AreaIn}{30}_i}\right)+{f}_2\left({X}_i,{Y}_i\right)+{\mathrm{Time}}_j \) | 5083.48 |
(3) α + f2(X i , Y i ) + Time j | 5120.71 |
(4) \( \alpha +\sum \limits_{n=1}^N\left({f}_1\left({\mathrm{Dist}}_{\mathrm{in}}\right)\cdot \frac{dbh_{jn}}{\mathrm{AreaIn}{30}_i}\right) \) | 5387.18 |
(5) \( \alpha +\beta \cdot \frac{N{\mathrm{small}}_{ij}}{\mathrm{AreaIn}{10}_i}+\sum \limits_{n=1}^N\left({f}_1\left({\mathrm{Dist}}_{\mathrm{in}}\right)\cdot \frac{N{\mathrm{small}}_{ij}}{\mathrm{AreaIn}{10}_i}\right)+{f}_2^j\left({X}_i,{Y}_i\right) \) | 5184.80 |