mvIC_fit: Evaluate multivariate BIC

In GabrielHoffman/mvIC: Multivariate Information Criteria to identify important predictors in high dimensional multivariate regression

Evaluate multivariate BIC

Description

Evaluate multivariate BIC while considering correlation between response variables. For n samples, p responses and m parameters for each model, evaluate the multivariate BIC as

n * logDet(Σ) + log(n) * (p*m + 0.5*p*(p+1))

where Σ is the residual covariance matrix. This formula extends the standard univariate BIC to the multivariate case. For one response the standard penalty is log(n)*m, this just adds a log(n) to that value, but only the differences between two models is important. Estimating the p x p covariance matrix requires 0.5*p*(p+1) parameters. When p > m the residual covariance matrix Sigma is not full rank. In this case the psudo-determinant is used instead.

Usage

mvIC_fit(
  exprObj,
  formula,
  data,
  criterion = c("BIC", "sum BIC", "AIC", "AICC", "CAIC", "sum AIC"),
  shrink.method = c("EB", "none", "var_equal", "var_unequal"),
  nparamsMethod = c("edf", "countLevels", "lme4"),
  pca = TRUE,
  verbose = FALSE,
  ...
)

Arguments

exprObj	matrix of expression data (g genes x n samples), or ExpressionSet, or EList returned by voom() from the limma package
formula	specifies variables for the linear (mixed) model. Must only specify covariates, since the rows of exprObj are automatically used as a response. e.g.: ~ a + b + (1|c) Formulas with only fixed effects also work, and lmFit() followed by contrasts.fit() are run.
data	data.frame with columns corresponding to formula
criterion	multivariate criterion ('AIC', 'BIC') or summing score assuming independence of reponses ('sum AIC', 'sum BIC')
shrink.method	Shrink covariance estimates to be positive definite. Using "var_equal" assumes all variance on the diagonal are equal. This method is the fastest because it is linear time. Using "var_unequal" allows each response to have its own variance term, however this method is quadratic time. Using "none" does not apply shrinkge, but is only valid when there are very few responses
nparamsMethod	"edf": effective degrees of freedom. "countLevels" count number of levels in each random effect. "lme4" number of variance compinents, as used by lme4. See description in nparam
pca	use PCA to transform variables
verbose	Default TRUE. Print messages
...	additional arguements passed to logDet

Details

Evaluate multivariate BIC on matrix of response variables. Smaller is better.

Value

multivariate BIC value

References

\insertRef

pauler1998schwarzmvIC

\insertRef

bedrick1994modelmvIC

\insertRef

wu2013weightedmvIC

Examples

# create matrix of responses
Y = with(iris, rbind(Sepal.Width, Sepal.Length))

# Evaluate model 1
mvIC_fit( Y, ~ Species, data=iris)

# Evaluate model 2
# smaller mvIC means better model
mvIC_fit( Y, ~ Petal.Width + Petal.Length + Species, data=iris)

GabrielHoffman/mvIC documentation built on Aug. 30, 2022, 7:58 p.m.