multicon (version 1.6)

decomp: Decomposition of Effects

Description

A function for decomposing a matrix into its grand mean, row effects, column effects, and unique effects and examining the association of these effects with corresponding effects in another matrix

Usage

decomp(x, y=NULL, na.rm=TRUE, use="pair")

Arguments

x

A matrix of data to decompose

y

An optional criterion matrix of data to examine for componential similarity to x

na.rm

A logicial indicating if missing values should be removed

use

A character indicating how to handle missing data for correlations

Value

A list containing the following

GrandMeanX

The grand mean of the x matrix

GrandMeanY

The grand mean of the y matrix

RowEffectX

The mean of the rows for the x matrix

RowEffectY

The mean of the rows for the y matrix

ColEffectX

The mean of the columns for the x matrix

ColEffectY

The mean of the columns for the y matrix

DecompositionX

The unique effects in the X matrix after decomposition

DecompositionY

The unique effects in the Y matrix after decomposition

RowUniqueCor

A vector containing the correlations between the corresponding rows of the decomposed matrices

ColUniqueCor

A vector containing the correaltions between the corresponding columns of the decomposed matrices

VarComp

A data.frame containing the variance components for rows, columns, and interactions

Stats

A 4 x 1 matrix containing 4 similarity components (only returned if a criterion matrix y is provided) Elevation Accuracy: The grand mean of x minus the grand mean of y Differential Eleveation: The correlation between the row effects Stereotype Accuracy: The correlation between the column effects Differential Accuracy: The correlation between the uniquenesses

Details

Following Cronbach (1955) this function deomposes the data matrices in x and y and returns a number of characerisicts about these matrices including four measures of their similarity. See value section.

References

Cronbach, L. J. (1955). Processes affecting scores on "understanding of others" and "assumed similarity." Psychological Bulletin, 52, 177-193.

Examples

data(exsitu)
data(insitu)
  # Decomposition of the column and row effects of a single data matrix
decomp(exsitu)
  # Decomposition of the column and row effects of two data matrices including
  # the similarities (correlations) between the row, column, and unqiue effects. 
decomp(exsitu, insitu)