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I have a large multivariate abundance data and I am interested in comparing multiple models that fit different combinations of three categorical predictor variables to my species matrix response variable. I have been using anova() to compare my different models, but I am having difficulty interpreting the output. Below, I have given my code as well as the corresponding R output.
invert.mvabund <- mvabund(mva.dat) null<-manyglm(mva.dat~1, family='negative.binomial') m1 <- manyglm(mva.dat~Habitat+Detritus, family='negative.binomial') m2 <- manyglm(mva.dat~Habitat*Detritus, family='negative.binomial') m3 <- manyglm(mva.dat~Habitat*Detritus+Block, family='negative.binomial') anova(null,m1,m2,m3) Analysis of Deviance Table null: mva.dat ~ 1 m1: mva.dat ~ Habitat + Detritus m2: mva.dat ~ Habitat * Detritus m3: mva.dat ~ Habitat * Detritus + Block Multivariate test: Res.Df Df.diff Dev Pr(>Dev) null 99 m1 94 5 257.2 0.001 *** m2 90 4 87.7 0.003 ** m3 81 9 173.5 0.003 ** Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
How do I interpret these results? Is m2 the best-fitting model because it has the lowest deviance, even though it has a higher p-value than m1? Is this because the p-value is suggesting that there is a significant level of deviance, so the optimal model will have a higher p-value? Any suggestions on how to interpret these results would be much appreciated- I haven't been able to find a clear answer in my Google searches. Thanks!