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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!

merv
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user2096647
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    If you need help with interpretation of statistical model results, you should be asking over at [stats.se], where statistical questions are on-topic. This is not a specific programming question and therefore is not appropriate for Stack Overflow. – MrFlick Jun 09 '16 at 20:35
  • Thanks, I'll move my question over there. – user2096647 Jun 09 '16 at 20:58

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