pcovr_est {PCovR}

Estimation of Principal Covariates Regression parameters, given a prespecified weighting value and number of components

Description

Analyzing regression data with many and/or highly collinear predictor variables, by simultaneously reducing the predictor variables to a given number of components and regressing the criterion variables on these components. A weighting parameter value is specified that determines the extent to which both aspects influence the solution. Cross-validation (Hastie, Tibshirani & Friedman, 2001) options are included.

Usage

pcovr_est(X, Y, r, a, cross = FALSE, fold = "LeaveOneOut")

Arguments

X

Matrix containing predictor scores (observations x predictors)

Y

Matrix containing criterion scores (observations x criteria)

r

The desired number of components

a

The desired weighting parameter value

cross

Logical. If TRUE cross-validation is performed

fold

Value of k when performing k-fold cross-validation. By default, leave-one-out cross-validation is performed.

Value

W

Component weights matrix (predictors x components)

B

Regression weights for predictors (predictors x criteria)

Rx2

Proportion of explained variance in X

Ry2

Proportion of explained variance in Y

Te

Component score matrix (observations x components)

Px

Loading matrix of components (components x predictors)

Py

Regression weights matrix (components x criteria)

Qy2

Cross-validation fit

Author(s)

Marlies Vervloet ([e-mail])

References

De Jong, S., & Kiers, H. A. (1992). Principal covariates regression: Part I. Theory. Chemometrics and Intelligent Laboratory Systems , 155-164.

Hastie, T., Tibshirani, R., & Friedman, J. (2001). The elements of statistical learning: Data mining, inference and prediction. New York: Springer.

Marlies Vervloet, Henk A. Kiers, Wim Van den Noortgate, Eva Ceulemans (2015). PCovR: An R Package for Principal Covariates Regression. Journal of Statistical Software, 65(8), 1-14. URL http://www.jstatsoft.org/v65/i08/.

Examples

data(alexithymia)
X <- data.matrix(alexithymia$X)
Y <- data.matrix(alexithymia$Y)
results <- pcovr_est(X, Y, r=2, a=.90)
str(results)