# mlpca_d: Maximum likelihood principal component analysis for mode D... In RMLPCA: Maximum Likelihood Principal Component Analysis

## Description

Performs maximum likelihood principal components analysis for mode D error conditions (commom row covariance matrices). Employs rotation and scaling of the original data.

## Usage

 `1` ```mlpca_d(X, Cov, p) ```

## Arguments

 `X` IxJ matrix of measurements `Cov` JxJ matrix of measurement error covariance, which is commom to all rows `p` Rank of the model's subspace

## 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.

## Value

The parameters returned are the results of SVD on the estimated subspace. The quantity Ssq represents the sum of squares of weighted residuals.

## References

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

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18``` ``` library(RMLPCA) data(data_clean) data(data_error_d) # covariance matrix data(cov_d) data(data_cleaned_mlpca_d) # data that you will usually have on hands data_noisy <- data_clean + data_error_d # run mlpca_c with rank p = 5 results <- RMLPCA::mlpca_d( X = data_noisy, Cov = cov_d, p = 2 ) # estimated clean dataset data_cleaned_mlpca <- results\$U %*% results\$S %*% t(results\$V) ```

RMLPCA documentation built on Jan. 13, 2021, 9:40 a.m.