PCovR (version 2.7.2)

ErrorRatio: Error variance ratio

Description

Estimating the ratio of the error variance of the predictor block, versus the error variance of the criterion block.

Usage

ErrorRatio(X, Y, Rmin = 1, Rmax = ncol(X)/3, prepX="stand",prepY="stand")

Value

The returned value is the estimated error variance of X, divided by the estimated error variance of Y.

Arguments

X

Dataframe containing predictor scores

Y

Dataframe containing criterion scores

Rmin

Lowest number of components considered

Rmax

Highest number of components considered

prepX

Preprocessing of predictor scores: standardizing (stand) or centering data (cent)

prepY

Preprocessing of criterion scores: standardizing (stand) or centering data (cent)

Author

Marlies Vervloet

Details

An estimate for the error variance of X can be obtained by applying principal component analysis to X and determining the optimal number of components through a scree test; the estimate equals the associated percentage of unexplained variance. The estimate for the error variance of Y boils down to the percentage of unexplained variance when Y is regressed on X. This approach for estimating and was based on the work of Wilderjans, Ceulemans, Van Mechelen, and Van den Berg (2011).

References

Wilderjans, T. F., Ceulemans, E., Van Mechelen, I., & Van den Berg, R. A. (2011). Simultaneous analysis of coupled data matrices subject to different amounts of noise. British Journal of Mathematical and Statistical Psychology , 64, 277-290.

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(psychiatrists)
ratio <- ErrorRatio(psychiatrists$X,psychiatrists$Y)