Uses the stepwise procedure described in Section 13.1.4 to find a pattern for a set of observed eigenvalues with good BIC value.
pcbic.stepwise(eigenvals, n)The \(Q\)-vector of eigenvalues of the covariance matrix, in order from largest to smallest.
The degrees of freedom in the covariance matrix.
A list with the following components:
A list of patterns, one for each value of length \(K\).
A vector of the BIC's for the above patterns.
The best (smallest) value among the BIC's in BICs.
The pattern with the best BIC.
A \(Q\)-vector containing the MLE's for the eigenvalues for the pattern with the best BIC.
pcbic, pcbic.unite,
and pcbic.subpatterns.
# Build cars1
require("mclust")
mcars <- Mclust(cars)
cars1 <- cars[mcars$classification == 1, ]
xcars <- scale(cars1)
eg <- eigen(var(xcars))
pcbic.stepwise(eg$values, 95)
#> $Patterns
#> $Patterns[[1]]
#> [1] 1 1 1 1 1 1 1 1 1 1 1
#>
#> $Patterns[[2]]
#> [1] 1 1 1 1 1 2 1 1 1 1
#>
#> $Patterns[[3]]
#> [1] 1 1 1 2 2 1 1 1 1
#>
#> $Patterns[[4]]
#> [1] 1 1 3 2 1 1 1 1
#>
#> $Patterns[[5]]
#> [1] 1 1 3 2 1 2 1
#>
#> $Patterns[[6]]
#> [1] 1 1 3 3 2 1
#>
#> $Patterns[[7]]
#> [1] 1 1 3 3 3
#>
#> $Patterns[[8]]
#> [1] 1 4 3 3
#>
#> $Patterns[[9]]
#> [1] 1 4 6
#>
#> $Patterns[[10]]
#> [1] 5 6
#>
#> $Patterns[[11]]
#> p1
#> 11
#>
#>
#> $BICs
#> [1] -861.196176 -869.009931 -876.649946 -885.088665 -892.222896 -895.488524
#> [7] -888.501861 -870.823946 -801.384858 -657.561496 4.553877
#>
#> $BestBIC
#> [1] -895.4885
#>
#> $BestPattern
#> [1] 1 1 3 3 2 1
#>
#> $LambdaHat
#> [1] 6.20990339 1.83332778 0.71561848 0.71561848 0.71561848 0.21276067
#> [7] 0.21276067 0.21276067 0.07077652 0.07077652 0.03007833
#>