Computation of MallowsCp

Mallow's Cp is one of the very useful metrics and selection criteria for machine learning algorithms (models). It is used to estimate the closest number to the number of predictors and the intercept (approximate number of explanatory variables) of linear and non-linear based models. The function inherits residuals from the estimated model. The uniqueness of this function compared to other procedures for computing Mallow's Cp is that it does not require nested models for computation and it is not limited to lm based models only.

Usage

MallowsCp(model2, y, x, type, Nlevels = 0)

Arguments

model2

The estimated model from which the Mallows Cp would be computed

y

The vector of the LHS variable of the estimated model

x

The matrix of the RHS variable of the estimated model. Note that if the model adds additional factor variables into the output, then the number of additional factors Nlevels is required otherwise the computed Cp would be biased.

type

The type of model (LM, ALM, GLM,N-LM, nls, ARDL, SMOOTH, SPLINE, ARIMA, plm) for which Cp would be computed broadly divided in to linear (LM, ALM, GLM, ARDL, SMOOTH, SPLINE, ARIMA, plm) and non-linear (GLM,N-LM, nls). The type of model must be specified as indicated. Supported models are LM, ALM, GLM (for binary based models), N-LM (not linear for models not clearly defined as linear or non-linear especially some of the essemble models that are merely computed not estimated) or nls for other non linear models, ARDL, SMOOTH for smooth.spline, SPLINE for bs spline models, ARIMA and plm.

Nlevels

Optional number of additional variables created if the model has categorical variables that generates additional dummy variables during estimation or the number of additional variables created if the model involves interaction terms.

Value

A list with the following components

MallowsCp

of the Model.

Examples

library(Dyn4cast)
ctl <- c(4.17, 5.58, 5.18, 6.11, 4.50, 4.61, 5.17, 4.53, 5.33, 5.14)
trt <- c(4.81, 4.17, 4.41, 3.59, 5.87, 3.83, 6.03, 4.89, 4.32, 4.69)
x <- gl(2, 10, 20, labels = c("Ctl", "Trt"))
y <- c(ctl, trt)
Model <- lm(y ~ x)
Type <- "LM"
MallowsCp(model2 = Model, y = y, x = x, type = Type, Nlevels = 0)
#> [1] 2