# SHAP Values – Can SHAP Be Used for Linear Mixed Models?

importancemixed modelrshapley-value

Can SHAP importance be used for linear mixed models? I've seen it used for a variety of different modeling methods and was curious if it was possible to use it for linear mixed models? I am using the lme4 package in R.

Any help at all is greatly appreciated!

Shapley values are associated with the word explainability. The correct interpretation of the word explainability has nothing to do with describing the relationship of $$x \rightarrow y$$, but $$d(x) \rightarrow y$$, where $$x$$ is the covariates and $$y$$ is the outcome and $$d(x)$$ is a set of rules on $$x$$ that make $$y$$ predictions.
With a linear mixed model you have everything you could ever want. You have both $$x \rightarrow y$$ and $$d(x) \rightarrow y$$, but now $$d(x)$$ is a smooth function $$f(x)$$. Shapley values would give you coefficient estimates based off of $$d(x)$$ that have no lower variance than your linear mixed model $$f(x)$$. If you don't believe me then do a bootstrap sample of your data. Fit models to 1K replication and pull out your coefficients and compare them to your shapley values you will see (on average) that $$var(coef_{shap}) \geq var(coef_{lm})$$
The reason people use shapley values is because they do not care about $$x \rightarrow y$$. They just want to know why the model (set of rules) predicted what it did $$d(x) \rightarrow y$$. This is helpful with diagnosing a random forest predictions, for example.