RMLPCA (version 0.0.1)

mlpca_b: Maximum likelihood principal component analysis for mode B error conditions

Description

Performs maximum likelihood principal components analysis for mode B error conditions (independent errors, homoscedastic within a column). Equivalent to perfoming PCA on data scaled by the error SD, but results are rescaled to the original space.

Usage

mlpca_b(X, Xsd, p)

Arguments

X

MxN matrix of measurements.

Xsd

MxN matrix of measurements error standard deviations.

p

Rank of the model's subspace, p must be than the minimum of M and N.

Value

The parameters returned are the results of SVD on the estimated subspace. The quantity Ssq represents the sum of squares of weighted residuals. All the results are nested in a list format.

Details

The returned parameters, U, S and V, are analogs to the truncated SVD solution, but have somewhat different properties since they represent the MLPCA solution. In particular, the solutions for different values of p are not necessarily nested (the rank 1 solution may not be in the space of the rank 2 solution) and the eigenvectors do not necessarily account for decreasing amounts of variance, since MLPCA is a subspace modeling technique and not a variance modeling technique.

References

Wentzell, P. D. "Other topics in soft-modeling: maximum likelihood-based soft-modeling methods." (2009): 507-558.

Examples

# NOT RUN {
library(RMLPCA)
data(data_clean)
data(data_error_b)
data(sds_b)

# data that you will usually have on hands
data_noisy <- data_clean + data_error_b

# run mlpca_b with rank p = 2
results <- RMLPCA::mlpca_b(
  X = data_noisy,
  Xsd = sds_b,
  p = 2
)

# estimated clean dataset
data_cleaned_mlpca <- results$U %*% results$S %*% t(results$V)
# }