I'm novice with respect to AIC model selection so I'm wondering what are the hypotheses that model selection addresses and ANCOVA does not? To provide an example, imagine we've got y (response variable), x (continuous predictor), and group (discrete predictor). I could see fitting three models:
(1) y as a function of group (2) y as a function of group + x (3) y as a function of group + x + group*x And depending on which model is best supported we conclude different things: model 1 supported = no support for considering x, model 2 = no support for considering multiplicative term, model 3 = there is reason to believe all terms are worthy of inclusion. Wouldn't an ANCOVA do a similar thing? We get an ANOVA table that tells us the sum of squares for each term, and the resultant hypothesis test. So depending on the p-values (I know nobody likes to depend on p-values), we could reach any conclusion roughly equivalent to those I (perhaps wrongly) supposed for the model selection case. Equivalent results would be something like: group significant, OR group & x significant, OR group & x & group*x significant. Am I missing something with model selection? Thanks for your thoughts and insights, Andy On Thu, Apr 1, 2010 at 2:26 PM, David Hewitt <[email protected]> wrote: > I certainly agree with Gareth that the ANCOVA approach should be > simple. But it won't address all hypotheses posed by the "slopes > and/or intercepts" framework. What you need is a model selection > approach. Fit the various linear models of interest (some of which may > be ANCOVA-type models), calculate AICc, and see which model(s) are > best supported by the data. Oh, and check all the assumptions. This is > a piece of cake in R; see e.g. the packages 'lm' and 'AICcmodavg'. > > Dave Hewitt > Research Fishery Biologist > USGS Western Fisheries Research Center > Klamath Falls Field Station, Oregon > http://profile.usgs.gov/dhewitt > > > From: Gareth Russell > Subject: Re: Comparing slopes and intercepts in linear regressions > > I'm afraid ANCOVA is the way to go. It shouldn't be cumbersome though, > not in any up-to-date software. If you have three columns of data (two > continuous, one categorical), and specify one of the continuous as the > dependent and the other two as predictors, then almost all software > packages will do an ANCOVA. > > Gareth Russell > > ----- > On Wed, 31 Mar 2010 11:02:07 -0400, Howie Neufeld wrote: > Dear All - > > I have a stats question concerning comparing linear regressions. If > you have two or more regressions, and want to know if their slopes > and/or intercepts are significantly different, what procedure would > you use? I am familiar with SAS mainly. Zar has a two-sample t-test > equivalent for comparing two slopes, but the procedure for intercepts > is extremely cumbersome, as is the multiple slope comparison, which > involves ANOCOVA. > Thanks! > Howie Neufeld >
