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I am comparing mixed models in R using anova. My model m5 has one of the variables from model m4 omitted and I want to compare the 2 models to see if the dropped variable was significant.

Comparing the 2 models - the difference in AIC values is less than 3, so does this mean the variable isn't really significant? Using anova the AIC values in the output are different - what does this mean?

Thanks.:)

> m4 <- lmer(fr_per_fl ~ ele+prox+sl+veg+h+trunk+can+gap+th+(1|orc), DataT)
> AIC(m4)

[1] 43.0984

> m5 <- lmer(fr_per_fl ~ ele+prox+sl+veg+h+trunk+can+gap+(1|orc), DataT)
> AIC(m5)

[1] 40.54589

> anova(m5,m4)

refitting model(s) with ML (instead of REML)

Data: DataT

Models:

m5: fr_per_fl ~ ele + prox + sl + veg + h + trunk + can + gap + (1 | orc)
m4: fr_per_fl ~ ele + prox + sl + veg + h + trunk + can + gap + th + (1 | orc)

Df     AIC      BIC logLik deviance  Chisq Chi Df Pr(>Chisq)   

m5 20 -26.007  -5.1163 33.003  -66.007                            
m4 21 -47.716 -25.7809 44.858  -89.716 23.709      1  1.121e-06 ***

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Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
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    $\begingroup$ Zoe, you can indent each row of R output by 4 spaces so that the output is formatted properly in your post. I've done this for you here but in the future you can do it yourself - it's handy to know how. $\endgroup$ Mar 21, 2019 at 3:04

1 Answer 1

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The link https://www.ssc.wisc.edu/sscc/pubs/MM/MM_TestEffects.html has a nice discussion on how you can perform tests involving fixed effects in a linear mixed model.

The first such test is a so-called Wald test, which you can obtain directly from the summary of your m4 model, presuming you fitted this model to the data using the maximum likelihood (ML) method. Just look for the p-value associated with the predictor th in your model summary. This test is usually not recommended, for reasons explained in the above link.

The second such test is the likelihood ratio test. For this test, which will compare the model excluding the predictor th against the model including the predictor th (presuming both models are fitted with the ML method), the syntax is:

anova(m5,m4,test="Chisq")

It seems that this is what you have above, suggesting that the predictor th has a significant (linear) effect in your model.

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