I am trying to do model simplification looking at how different factors may affect distance. So I have snails kept in several habitats and I wanted to see if that affects how closely another snail may follow that snail. So I start off with this model:

```
model1 <- lmer(sqrt(dist+6)~ (1|snail)+food+stress+food:stress+
weight+OriginalL+FollowedL)
summary(model1)
```

and the summary is this:

```
Linear mixed model fit by REML ['lmerMod']
Formula: sqrt(dist + 6) ~ (1 | snail) + food + stress + food:stress +
weight + OriginalL + FollowedL
REML criterion at convergence: 561.1
Scaled residuals:
Min 1Q Median 3Q Max
-2.2941 -0.7698 -0.3347 0.7515 1.9564
Random effects:
Groups Name Variance Std.Dev.
snail (Intercept) 0.000 0.000
Residual 2.334 1.528
Number of obs: 148, groups: snail, 37
Fixed effects:
Estimate Std. Error t value
(Intercept) 4.960927 0.662947 7.483
foodSweetPotato -0.219039 0.357768 -0.612
stressshelter -0.246649 0.355999 -0.693
weight 0.002520 0.063259 0.040
OriginalL 0.015549 0.013072 1.189
FollowedL -0.008044 0.005972 -1.347
foodSweetPotato:stressshelter -0.300143 0.503215 -0.596
Correlation of Fixed Effects:
(Intr) fdSwtP strsss weight OrgnlL FllwdL
foodSwetPtt -0.309
stressshltr -0.315 0.502
weight -0.615 0.008 0.009
OriginalL -0.617 -0.021 0.032 0.123
FollowedL -0.470 0.118 0.059 0.087 -0.004
fdSwtPtt:st 0.230 -0.707 -0.708 -0.008 -0.024 -0.055
```

Should I remove the least significant factor or remove the interactions first?

And after this is it a simple anova between my first model and most simplified model?

## Best Answer

A very short answer:

at allabout inference, or selection of, main effects when there are interactions involving those main effects in the model; this is called the principle of marginality (sorry, that Wikipedia page is a mess, but it gives you alittlemore information ...), so the narrow-sense answer to your question would be toalwaysconsider removing interactions first, and as a corollary toneverconsider removing main effects if an interaction that involves them is retained in the model.reallywant to drop terms from your model or not ... see e.g.Regression Modeling Strategies(Springer), or see the Stata FAQ for an abbreviated versionI'm not sure what you mean by "is it a simple anova between my first model and most simplified model"? If you want to do inference on the terms in the model, you can use a likelihood ratio test (implemented via

`anova()`

in R), or an F test, or ...