F. Guillaume Blanchet, Pierre Legendre, and Daniel Borcard. 2008. Forward selection of explanatory variables. Ecology 89:2623–2632.

Appendix D. Forward selection simulations carried out in the multivariate situation: using one or two stopping criteria.

FIG. D1. Comparison of forward selection done on positively autocorrelated BEMs using both the and the alpha-level as stopping criteria (a-b, e-f, i-j), to the same procedure where the alpha-level was the only stopping criterion (c-d, g-h, k-l). Three different situations are presented: (1) the standard deviation of the deterministic portion of the response variable is the same as the standard deviation of the error (a-d), (2) the standard deviation of the error is 0.25 times the standard deviation of the deterministic portion (e-h), and (3) the standard deviation of the error is 0.001 times the standard deviation of the deterministic portion (i-l). The left-hand column presents the number of variables selected among the five used to create the response variable (correct selections). The right-hand column shows the bad selections, i.e., the number of variables selected among those that were not used to create the response variable. 5000 simulations were run for each magnitude of error. This set of figures presents results for the univariate situation.

FIG. D2. Comparison of forward selection done on negatively autocorrelated BEMs using both the and the alpha-level as stopping criteria (a-b, e-f, i-j), to the same procedure where the alpha-level was the only stopping criterion (c-d, g-h, k-l). Three different situations are presented: (1) the standard deviation of the deterministic portion of the response variable is the same as the standard deviation of the error (a-d), (2) the standard deviation of the error is 0.25 times the standard deviation of the deterministic portion (e-h), and (3) the standard deviation of the error is 0.001 times the standard deviation of the deterministic portion (i-l). The left-hand column presents the number of variables selected among the five used to create the response variable (correct selections). The right-hand column shows the bad selections, i.e., the number of variables selected among those that were not used to create the response variable. 5000 simulations were run for each magnitude of error. This set of figures presents results for the univariate situation.

FIG. D3. Comparison of forward selection done on variables randomly selected from a normal distribution using both the and the alpha-level as stopping criteria (a-b, e-f, i-j), to the same procedure where the alpha-level was the only stopping criterion (c-d, g-h, k-l). Three different situations are presented: (1) the standard deviation of the deterministic portion of the response variable is the same as the standard deviation of the error (a-d), (2) the standard deviation of the error is 0.25 times the standard deviation of the deterministic portion (e-h), and (3) the standard deviation of the error is 0.001 times the standard deviation of the deterministic portion (i-l). The left-hand column presents the number of variables selected among the five used to create the response variable (correct selections). The right-hand column shows the bad selections, i.e., the number of variables selected among those that were not used to create the response variable. 5000 simulations were run for each magnitude of error. This set of figures presents results for the univariate situation.

FIG. D4. Comparison of forward selection done on variables randomly selected from a uniform distribution using both the and the alpha-level as stopping criteria (a-b, e-f, i-j), to the same procedure where the alpha-level was the only stopping criterion (c-d, g-h, k-l). Three different situations are presented: (1) the standard deviation of the deterministic portion of the response variable is the same as the standard deviation of the error (a-d), (2) the standard deviation of the error is 0.25 times the standard deviation of the deterministic portion (e-h), and (3) the standard deviation of the error is 0.001 times the standard deviation of the deterministic portion (i-l). The left-hand column presents the number of variables selected among the five used to create the response variable (correct selections). The right-hand column shows the bad selections, i.e., the number of variables selected among those that were not used to create the response variable. 5000 simulations were run for each magnitude of error. This set of figures presents results for the univariate situation.

FIG. D5. Comparison of forward selection done on PCNMs using both the and the alpha-level as stopping criteria (a-b, e-f, i-j), to the same procedure where the alpha-level was the only stopping criterion (c-d, g-h, k-l). Three different situations are presented: (1) the standard deviation of the deterministic portion of the response variable is the same as the standard deviation of the error (a-d), (2) the standard deviation of the error is 0.25 times the standard deviation of the deterministic portion (e-h), and (3) the standard deviation of the error is 0.001 times the standard deviation of the deterministic portion (i-l). The left-hand column presents the number of variables selected among the five used to create the response variable (correct selections). The right-hand column shows the bad selections, i.e., the number of variables selected among those that were not used to create the response variable. 5000 simulations were run for each magnitude of error. This set of figures presents results for the multivariate situation.

FIG. D6. Comparison of forward selection done on positively autocorrelated BEMs using both the and the alpha-level as stopping criteria (a-b, e-f, i-j), to the same procedure where the alpha-level was the only stopping criterion (c-d, g-h, k-l). Three different situations are presented: (1) the standard deviation of the deterministic portion of the response variable is the same as the standard deviation of the error (a-d), (2) the standard deviation of the error is 0.25 times the standard deviation of the deterministic portion (e-h), and (3) the standard deviation of the error is 0.001 times the standard deviation of the deterministic portion (i-l). The left-hand column presents the number of variables selected among the five used to create the response variable (correct selections). The right-hand column shows the bad selections, i.e., the number of variables selected among those that were not used to create the response variable. 5000 simulations were run for each magnitude of error. This set of figures presents results for the multivariate situation.

FIG. D7. Comparison of forward selection done on negatively autocorrelated BEMs using both the and the alpha-level as stopping criteria (a-b, e-f, i-j), to the same procedure where the alpha-level was the only stopping criterion (c-d, g-h, k-l). Three different situations are presented: (1) the standard deviation of the deterministic portion of the response variable is the same as the standard deviation of the error (a-d), (2) the standard deviation of the error is 0.25 times the standard deviation of the deterministic portion (e-h), and (3) the standard deviation of the error is 0.001 times the standard deviation of the deterministic portion (i-l). The left-hand column presents the number of variables selected among the five used to create the response variable (correct selections). The right-hand column shows the bad selections, i.e., the number of variables selected among those that were not used to create the response variable. 5000 simulations were run for each magnitude of error. This set of figures presents results for the multivariate situation.

FIG. D8. Comparison of forward selection done on variables randomly selected from a normal distribution using both the and the alpha-level as stopping criteria (a-b, e-f, i-j), to the same procedure where the alpha-level was the only stopping criterion (c-d, g-h, k-l). Three different situations are presented: (1) the standard deviation of the deterministic portion of the response variable is the same as the standard deviation of the error (a-d), (2) the standard deviation of the error is 0.25 times the standard deviation of the deterministic portion (e-h), and (3) the standard deviation of the error is 0.001 times the standard deviation of the deterministic portion (i-l). The left-hand column presents the number of variables selected among the five used to create the response variable (correct selections). The right-hand column shows the bad selections, i.e., the number of variables selected among those that were not used to create the response variable. 5000 simulations were run for each magnitude of error. This set of figures presents results for the multivariate situation.

FIG. D9. Comparison of forward selection done on variables randomly selected from a uniform distribution using both the and the alpha-level as stopping criteria (a-b, e-f, i-j), to the same procedure where the alpha-level was the only stopping criterion (c-d, g-h, k-l). Three different situations are presented: (1) the standard deviation of the deterministic portion of the response variable is the same as the standard deviation of the error (a-d), (2) the standard deviation of the error is 0.25 times the standard deviation of the deterministic portion (e-h), and (3) the standard deviation of the error is 0.001 times the standard deviation of the deterministic portion (i-l). The left-hand column presents the number of variables selected among the five used to create the response variable (correct selections). The right-hand column shows the bad selections, i.e., the number of variables selected among those that were not used to create the response variable. 5000 simulations were run for each magnitude of error. This set of figures presents results for the multivariate situation.