mvIC

Evaluate information criteria for multivariate model selection

mvIC extends the standard the standard Akaike or Bayesian Information Criterion (AIC, BIC) to the case of multivariate regression. The model fit across many response variables is evaluated and the criterion explicitly considers correlation between reponses. mvIC is applicable to linear and linear mixed models.

Forward stepwise regression with the mvIC criterion enables automated variable selection for high dimensional datasets.

Installation

devtools::install_github("GabrielHoffman/mvIC", repos=BiocManager::repositories())

This automatically installs dependencies from Bioconductor

Examples

Multivariate linear model

# Predict Sepal width and Length given Species
# Evaluate model fit
fit1 = lm( cbind(Sepal.Width, Sepal.Length) ~ Species, data=iris)
score = mvIC( fit1 )

# add Petal width and length
# smaller mvIC means better model
fit2 = lm( cbind(Sepal.Width, Sepal.Length) ~ Petal.Width + Petal.Length + Species, data=iris)
mvIC( fit2 )

Multivariate linear mixed model

library(lme4)
# Predict Sepal width and Length given Species
# Evaluate model fits separately
fit1 = lmer( Sepal.Width ~ (1|Species), data=iris, REML=FALSE)
fit2 = lmer( Sepal.Length ~ (1|Species), data=iris, REML=FALSE)
score = mvIC( list(fit1,fit2) )

# Use mvIC_fit() to fit multivariate regression
# Combine responses on *rows*
Y = with(iris, rbind(Sepal.Width, Sepal.Length))
 
# Evaluate multiple responses
# Can specify any formula of fixed or random effects
mvIC_fit( Y, ~ (1|Species), data=iris)

Forward stepwise regression

# Combine responses on *rows*
Y = with(iris, rbind(Sepal.Width, Sepal.Length))

# variables to consider in the model
variables = c("Petal.Length", "Petal.Width", "(1|Species)")

# fit forward stepwise regression starting with model: ~1. 
bestModel = mvForwardStepwise( Y, ~ 1, data=iris, variables=variables)

Categorical variables can be modeled as random effects using the (1|x) syntax. If a random effect is specified, a linear mixed model is fit and the number of parameter equal to the effective degrees of freedom of the model fit. Note that using a linear mixed model is more computationally demanding, but

prevents over-correction with variables with many categories
regularizes the effect of estimate for each category
gracefully handles colinearity between categorical variables