# cpc.test: Likelihood ratio test of common principal components in the... In tpepler/cpc: Common principal component (CPC) analysis and applications

## Description

Calculates the likelihood ratio statistic and its degrees of freedom for the hypothesis of common eigenvectors in the k groups against the alternative of unrelated covariance matrices.

## Usage

 `1` ```cpc.test(covmats, nvec, B = cpc::FG(covmats = covmats, nvec = nvec)\$B) ```

## Arguments

 `covmats ` Array of covariance matrices. `nvec ` Vector of sample sizes of the k groups. `B ` Modal matrix simultaneously diagonalising the covariance matrices, estimated under the assumption of common eigenvectors in the k groups. Can be estimated using simultaneous diagonalisation algorithms such as the Flury-Gautschi (implemented in `FG` or the stepwise CPC (implemented in `stepwisecpc`) algorithms.

## Value

Returns a list with the following:

 `chi.square ` The likelihood ratio test statistic. `df ` Degrees of freedom of the test statistic under the null hypothesis. `covmats.cpc ` Estimated covariance matrices under the null hypothesis model.

## Note

This test is based on the assumption that the populations from which the data originated are distributed multivariate normal.

Theo Pepler

## References

Flury, B. (1988). Common Principal Components and Related Multivariate Models. Wiley.

`FG`, `flury.test`, `equal.test`, `prop.test` and `cpcq.test`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```# Versicolor and virginica groups of the Iris data data(iris) versicolor <- iris[51:100, 1:4] virginica <- iris[101:150, 1:4] # Create array containing the two covariance matrices S <- array(NA, c(4, 4, 2)) S[, , 1] <- cov(versicolor) S[, , 2] <- cov(virginica) nvec <- c(nrow(versicolor), nrow(virginica)) cpc.test(covmats = S, nvec = nvec) ```