array_bic_aic: Calculate the AIC and BIC.

In tensr: Covariance Inference and Decompositions for Tensor Datasets

Description

Calculate the AIC and BIC for Kronecker structured covariance models, assuming the array normal distribution.

Usage

array_bic_aic(sig_squared, p, mode_ident = NULL, mode_diag = NULL,
  mode_unstructured = NULL)

Arguments

sig_squared	A numeric. The MLE of sigma^2 in the array normal model (the 'variance' form of the total variation parameter).
p	A vector of integers. The dimension of the data array (including replication modes).
mode_ident	A vector of integers. The modes assumed to have identity covariances.
mode_diag	A vector of integers. The modes assumed to have diagional covariances.
mode_unstructured	A vector of integers. The modes of assumed to have unstructured covariances.

Details

The AIC and BIC depend only on the data through the MLE of the total variation parameter. Given this, the dimension of the array, and a specification of which modes are the identity and which are unstructured, this function will calculate the AIC and BIC.

Value

AIC A numeric. The AIC of the model.

BIC A numeric. The BIC of the model.

Author(s)

David Gerard.

See Also

holq for obtaining sig_squared.

Examples

# Generate random array data with first mode having unstructured covariance
#  second having diagonal covariance structure and third mode having identity
#  covariance structure.
set.seed(857)
p <- c(4, 4, 4)
Z <- array(stats::rnorm(prod(p)), dim = p)
Y <- atrans(Z, list(tensr:::rwish(diag(p[1])), diag(1:p[2]), diag(p[3])))

# Use holq() to fit various models.
false_fit1 <- holq(Y, mode_rep = 1:3) ## identity for all modes
false_fit2 <- holq(Y, mode_rep = 2:3) ## unstructured first mode
true_fit <- holq(Y, mode_rep = 3, mode_diag = 2) ## correct model

# Get AIC and BIC values.
false_aic1 <- array_bic_aic(false_fit1$sig ^ 2, p, mode_ident = 1:length(p))
false_aic2 <- array_bic_aic(false_fit2$sig ^ 2, p, mode_ident = 2:length(p),
                            mode_unstructured = 1)
true_aic <- array_bic_aic(true_fit$sig ^ 2, p, mode_ident = 2:length(p), mode_diag = 1)

# Plot the results.
plot(c(false_aic1$AIC, false_aic2$AIC, true_aic$AIC), type = "l",
     xaxt = "n", xlab = "Model", ylab = "AIC", main = "AIC")
axis(side = 1, at = 1:3, labels = c("Wrong Model 1", "Wrong Model 2", "Right Model"))

plot(c(false_aic1$BIC, false_aic2$BIC, true_aic$BIC), type = "l", xaxt = "n",
     xlab = "Model", ylab = "BIC", main = "BIC")
axis(side = 1, at = 1:3, labels = c("Wrong Model 1", "Wrong Model 2", "Right Model"))

Example output

Scale Diff =  0 
     Scale =  154.2977 

Scale Diff =  0.9474794 
     Scale =  79.22942 

Scale Diff =  0 
     Scale =  79.22942 

Scale Diff =  1.399258 
     Scale =  64.31057 

Scale Diff =  0.03221078 
     Scale =  62.30372 

Scale Diff =  0.002281847 
     Scale =  62.16187 

Scale Diff =  0.0003964936 
     Scale =  62.13723 

Scale Diff =  8.992577e-05 
     Scale =  62.13165 

Scale Diff =  2.163337e-05 
     Scale =  62.1303 

Scale Diff =  5.288946e-06 
     Scale =  62.12997 

Scale Diff =  1.299368e-06 
     Scale =  62.12989 

Scale Diff =  3.196904e-07 
     Scale =  62.12987 

Scale Diff =  7.868683e-08 
     Scale =  62.12987 

Scale Diff =  1.936925e-08 
     Scale =  62.12987 

Scale Diff =  4.767876e-09 
     Scale =  62.12987 

Scale Diff =  1.173631e-09 
     Scale =  62.12987 

Scale Diff =  2.888905e-10 
     Scale =  62.12987 

tensr documentation built on May 2, 2019, 2:32 p.m.