Why would someone use lm and ANOVA (anova(lm(x))) instead of AOV (or the other way around)? The mean squares and sum of squares are the same, but the F values and p-values are slightly different. I am modeling a dependent~independent1*independent2. Thanks, Matt Bridgman [[alternative HTML version deleted]]
The underlying least squares arithmetic of aov and lm is identical. In R, the QR algorithm is used. The difference between the two is intent of the analysis and the default presentation of the results. With lm [Linear Model], the focus is on the effect of the individual columns of the predictor matrix. The columns are usually interpreted as values of real-valued observations. The regression coefficients are usually meaningful and interesting. With aov [Analysis Of Variance], the focus is on the effects of factors. These are multi-degree of freedom effects associated with categorical variables. The arithmetic is based on a set of dummy variables constructed from a contrast matrix. The individual regression coefficients themselves are not easily interpretable. You can pursue the details of this summary in any good statistical methods book. Rich
Matthew Bridgman wrote:> Why would someone use lm and ANOVA (anova(lm(x))) instead of AOV (or > the other way around)? > The mean squares and sum of squares are the same, but the F values > and p-values are slightly different. > >Crudely put, aov() is effectively useless on unbalanced designs. On the other hand, it will allow you to handle models with multistratum error structure. I am somewhat at a loss as to how you manage to get the same MS and SS but different F. Presumably, the denominator is different, but if you're not messing with Error() terms, then I believe both aov() and anova(lm()) would use the residual MS. An example might help.> I am modeling a dependent~independent1*independent2. > > Thanks, > Matt Bridgman > [[alternative HTML version deleted]] > > ______________________________________________ > R-help at stat.math.ethz.ch mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. >