VIF (#26)

* VIF and GVIF

Author: palday

Project.toml

@@ -1,7 +1,7 @@
 name = "StatsAPI"
 uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
 authors = ["Milan Bouchet-Valat <[email protected]"]
-version = "1.6.0"
+version = "1.7.0"
 
 [deps]
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"

src/regressionmodel.jl

@@ -132,3 +132,50 @@ function linearpredictor end
 In-place version of [`linearpredictor`](@ref), storing the result in `storage`.
 """
 function linearpredictor! end
+
+"""
+    vif(m::RegressionModel)
+
+Compute the variance inflation factor (VIF).
+
+The [VIF](https://en.wikipedia.org/wiki/Variance_inflation_factor) measures
+the increase in the variance of a parameter's estimate in a model with multiple parameters relative to
+the variance of a parameter's estimate in a model containing only that parameter.
+
+See also [`gvif`](@ref).
+
+!!! warning
+    This method will fail if there is (numerically) perfect multicollinearity,
+    i.e. rank deficiency. In that case though, the VIF
+    is not particularly informative anyway.
+"""
+function vif end
+# This generic function is owned by StatsModels.jl, which is the sole provider
+# of the default definition.
+
+"""
+    gvif(m::RegressionModel; scale=false)
+
+Compute the generalized variance inflation factor (GVIF).
+
+If `scale=true`, then each GVIF is scaled by the degrees of freedom
+for (number of coefficients associated with) the predictor: ``GVIF^(1 / (2*df))``.
+
+The [GVIF](https://doi.org/10.2307/2290467)
+measures the increase in the variance of a (group of) parameter's estimate in a model
+with multiple parameters relative to the variance of a parameter's estimate in a
+model containing only that parameter. For continuous, numerical predictors, the GVIF
+is the same as the VIF, but for categorical predictors, the GVIF provides a single
+number for the entire group of contrast-coded coefficients associated with a categorical
+predictor.
+
+See also [`vif`](@ref).
+
+## References
+
+Fox, J., & Monette, G. (1992). Generalized Collinearity Diagnostics.
+Journal of the American Statistical Association, 87(417), 178. doi:10.2307/2290467
+"""
+function gvif end
+# This generic function is owned by StatsModels.jl, which is the sole provider
+# of the default definition.