I'm not sure if I am getting your question, but if you are using multiple regression with a pile of predictors it is probably best to use either best subsets regression or stepwise regression to evaluate the predictors. If you use best subsets regression, you can examine Cp, PRESS, s, and VIF to get the best predictor combinations. Then, run your multiple regression at this point. I much prefer best subsets to stepwise regression. HEre is the procedure for you:
1) run a best subsets regression with all of your selected predictors. 2) Examine the Valence Inflation Factors (VIF). If any VIF > 5 then eliminate the predictor with the highest VIF and then re-run the regression. Keep doing this until all VIF is less than or equal to 5. 3) List all models that have Cp less than or equal to (p+1) where p = # of variables in the model. 4) Among the models in 3 above, choose the best model using the best subset criteria 5) analyze the chosen model including residual analysis and influence analysis. 6) revise model if analysis requires revision. Reasons for revision include: adding curvilinear terms, transforming variables, deleting individual observations. 7) use the selected model for prediction and confidence intervals. Malcolm On Thu, Dec 2, 2010 at 5:02 PM, Alexandre F. Souza <[email protected]> wrote: > Dear friends, > > It has been recently suggested by Legendre and co-authors that we > include quadratic and product terms of our environmental variables in > constrained ordinations. For instance, to include not only latitude but > also latitude^2 and latitude*longitude, the same with physical and > biotic variables aimed at being correlated with ordination axis in some > way. > > I am following McCune and Grace's book (2002) suggestion of > correlating environmental variables with NMDS axes. However common > correlations of multiple variables x each nmds axis are not the best > options because at each correlation they do not control for the other > variables in the dataset. Those authors also state that multiple > regression use partial correlation coefficients and thus would be a > better methos for correlating several environmental variables with > ordination axes. > > However, multiple regression suffers from multicolinearity, which is > greatly enhanced when we use product or quadratic terms of the > environmental variables. > > What do you think about that? > > Best whishes, > > Alexandre > > Dr. Alexandre F. Souza > Programa de Pós-Graduação em Biologia: Diversidade e Manejo da Vida > Silvestre > Universidade do Vale do Rio dos Sinos (UNISINOS) > Av. UNISINOS 950 - C.P. 275, São Leopoldo 93022-000, RS - Brasil > Telefone: (051)3590-8477 ramal 1263 > Skype: alexfadigas > [email protected] > http://www.unisinos.br/laboratorios/lecopop > -- Malcolm L. McCallum Managing Editor, Herpetological Conservation and Biology "Peer pressure is designed to contain anyone with a sense of drive" - Allan Nation 1880's: "There's lots of good fish in the sea" W.S. Gilbert 1990's: Many fish stocks depleted due to overfishing, habitat loss, and pollution. 2000: Marine reserves, ecosystem restoration, and pollution reduction MAY help restore populations. 2022: Soylent Green is People! Confidentiality Notice: This e-mail message, including any attachments, is for the sole use of the intended recipient(s) and may contain confidential and privileged information. Any unauthorized review, use, disclosure or distribution is prohibited. If you are not the intended recipient, please contact the sender by reply e-mail and destroy all copies of the original message.
