dimReduct: Strip uninformative measurements

In splits: SPecies' LImits by Threshold Statistics

Description

This function is essentially a wrapper around nScree and paran, taking a matrix of measurements and returning the predictions from a Principal Components Analysis PCA. The number of axes in the PCA predictions is determined from either the Kaiser-Guttman criterion KG or Horn's Parallel Analysis PA depending on which is specified.

Usage

dimReduct(XX, how = "PA", scale = TRUE, iterations=0, centile=0)

Arguments

XX	A matrix of measurements. Each row corresponds to one observation.
how	PA or KG. defaults to PA
scale	Scale variances, defaults to TRUE
iterations	The number of iterations used for PA.
centile	The centile

Details

PA is implemented using the excellent paran with default settings, but can be adapted as required, e.g. to apply the revisions to address Glorfeld's claims of over-retention of variables. See paran. KG is implemented from the standard deviations of the PCA model output.

prcomp is used to fit the PCA model, which assumes linear measurements. Transformation may be required prior to the PCA.

Multiple measurements on a focal individual are often highly correlated. Similarities along one axis might mask differences along another and thus generate inflated estimates of similarity between individuals unless prior weighting is given to certain axes. Rather than arbitrary assignment of a, say, 0.05 threshold, the number of axes that adequately describe each individual retained can be determined using PA or KG. Both too many or too few axes of variation can generate bias.

Value

sS	A matrix of predicted values from the PCA, with observations as rows and model predictions as columns.

Author(s)

Thomas H.G. Ezard tomezard [at] gmail [dot] com, but the hard work for PA by Alexis Dinno (see paran)

References

Dinno, A. in press. Implementing Horns Parallel Analysis for Principal Components Analysis and Factor Analysis. The Stata Journal.

Ezard, T.H.G., Pearson, P.N. & Purvis, A. 2010. Algorithmic Approaches to Delimit Species in Multidimensional Morphospace. BMC Evol. Biol. 10: 175, doi:10.1186/1471-2148-10-175.

Glorfeld, L. W. 1995. An Improvement on Horn's Parallel Analysis Methodology for Selecting the Correct Number of Factors to Retain. Ed. Psych.Meas. 55, 377-393

Guttman, L. 1954. Some necessary conditions for common factor analysis. Psychometrika 19, 149-162.

Horn, J. L. 1965. A rationale and a test for the number of factors in factor analysis. Psychometrika 30, 179-185.

Kaiser, H. F. 1960. The application of electronic computer to factor analysis. Ed. Pysch. Meas. 20, 141-151.

See Also

prcomp and princomp,paran

Examples

data(iris)
dimReduct(iris[,-5])

splits documentation built on July 16, 2021, 3 p.m.