# Solved – ANOVA table (and its interpretation) for a single GAM model

I am not really confident in interpreting the ANOVA table of a GAM model. I understand how it can be used to compare models (see for instance this question), but I am interested in interpreting it for a single model.

For concreteness:

``library( mgcv ) set.seed( 1 ) RawData <- data.frame( y = rbinom( 1000, 1, 0.5 ), x1 = rnorm( 1000 ), x2 = as.factor( rbinom( 1000, 1, 0.5 ) ), x3 = rnorm( 1000 ), x4 = as.factor( rbinom( 1000, 1, 0.5 ) ) ) fit <- gam( y ~ s( x1 ) + x2 + s( x3, by = x2 ) + x4, data = RawData, family = nb( link = log ) ) anova( fit )  Family: Negative Binomial(251657.167)  Link function: log  Formula: y ~ s(x1) + x2 + s(x3, by = x2) + x4  Parametric Terms:    df Chi.sq p-value x2  1  1.775   0.183 x4  1  0.796   0.372  Approximate significance of smooth terms:             edf Ref.df Chi.sq p-value s(x1)     1.000  1.000  0.047   0.828 s(x3):x20 1.000  1.000  0.078   0.779 s(x3):x21 1.000  1.001  0.188   0.665 ``

In particular, I'd be interested in the following:

1. Can chi.sq values be given an "explained variance" interpretation (or similar), i.e. can they be used to measure variable importance, just like for a usual linear model?
2. Can the chi.sq values of the smooth and parametric terms handled similarly?
3. What to do with interactions? (As `x2` and `x3` in the example: `x3` appears on two lines, `x2` appears in those, and as a parametric term in addition.)
Contents

It's probably best to take a look at the mgcv help file ?anova.gam in R, but in answer to the specific questions:

1. The parametric chi.sq test statistics are just like their linear model equivalents, but the test statistic used for the smooths is different, and doesn't have an explained variance interpretation. I would not try to use them directly to measure variable importance. For details see http://opus.bath.ac.uk/32382/1/spv3.pdf.

2. No, as explained above.

3. I would fit the model with and without the interaction and compare (but probably by AIC).

Simon Wood

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