decomp: Decomposition of Effects

In multicon: Multivariate Constructs

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

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.

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

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)

Example output

Loading required package: psych
Loading required package: abind
Loading required package: foreach
$GrandMeanX
[1] 4.275

$RowEffectX
      Duty  Intellect  Adversity     Mating pOsitivity Negativity  Deception 
     0.225      0.425     -1.175      0.125      0.225     -0.375     -1.175 
 Sociality 
     1.725 

$ColEffectX
     A      B      C      D      E      F      G      H      I      J 
-0.525 -0.150  0.600  0.350 -1.900  0.850  0.725  0.600 -0.525 -0.025 

$DecompositionX
                A     B    C     D    E     F      G    H      I      J
Duty        1.025  2.65 -0.1 -1.85 -1.6  1.65  1.775 -1.1  0.025 -2.475
Intellect   1.825  2.45 -1.3 -2.05 -1.8  1.45  1.575 -0.3  0.825 -2.675
Adversity  -0.575 -1.95  3.3  0.55 -0.2  3.05 -2.825 -0.7  0.425 -1.075
Mating     -2.875  0.75  2.0  0.25  0.5  1.75 -0.125  0.0 -2.875  0.625
pOsitivity  1.025 -1.35 -4.1  2.15  4.4 -4.35 -2.225 -0.1  3.025  1.525
Negativity -0.375  1.25  2.5 -0.25 -1.0 -3.75  0.375  0.5 -1.375  2.125
Deception  -1.575 -1.95  0.3  0.55 -0.2  0.05  2.175  1.3 -1.575  0.925
Sociality   1.525 -1.85 -2.6  0.65 -0.1  0.15 -0.725  0.4  1.525  1.025

$VarComp
                           Var    VarPerc NumDF DenDF        F          p
Row Variance         0.4694444 0.09825581     7    63 2.137500 0.05222172
Column Variance      0.1813492 0.03795681     9    63 1.351538 0.22943864
Interaction Variance 4.1269841 0.86378738    NA    NA       NA         NA

$GrandMeanX
[1] 4.275

$GrandMeanY
[1] 3.625

$RowEffectX
      Duty  Intellect  Adversity     Mating pOsitivity Negativity  Deception 
     0.225      0.425     -1.175      0.125      0.225     -0.375     -1.175 
 Sociality 
     1.725 

$RowEffectY
      Duty  Intellect  Adversity     Mating pOsitivity Negativity  Deception 
    -0.425     -0.325     -1.025     -0.825      1.475      0.675     -1.525 
 Sociality 
     1.975 

$ColEffectX
     A      B      C      D      E      F      G      H      I      J 
-0.525 -0.150  0.600  0.350 -1.900  0.850  0.725  0.600 -0.525 -0.025 

$ColEffectY
     A      B      C      D      E      F      G      H      I      J 
 0.000  0.375  1.500  0.375 -1.875 -0.375  1.375 -1.125 -0.250  0.000 

$DecompositionX
                A     B    C     D    E     F      G    H      I      J
Duty        1.025  2.65 -0.1 -1.85 -1.6  1.65  1.775 -1.1  0.025 -2.475
Intellect   1.825  2.45 -1.3 -2.05 -1.8  1.45  1.575 -0.3  0.825 -2.675
Adversity  -0.575 -1.95  3.3  0.55 -0.2  3.05 -2.825 -0.7  0.425 -1.075
Mating     -2.875  0.75  2.0  0.25  0.5  1.75 -0.125  0.0 -2.875  0.625
pOsitivity  1.025 -1.35 -4.1  2.15  4.4 -4.35 -2.225 -0.1  3.025  1.525
Negativity -0.375  1.25  2.5 -0.25 -1.0 -3.75  0.375  0.5 -1.375  2.125
Deception  -1.575 -1.95  0.3  0.55 -0.2  0.05  2.175  1.3 -1.575  0.925
Sociality   1.525 -1.85 -2.6  0.65 -0.1  0.15 -0.725  0.4  1.525  1.025

$DecompositionY
              A      B    C      D      E      F      G      H     I    J
Duty        3.8  0.425  2.3 -1.575 -0.325 -1.825  1.425 -1.075 -1.95 -1.2
Intellect  -1.3  3.325  0.2  1.325 -0.425 -1.925 -0.675 -1.175 -0.05  0.7
Adversity  -1.6 -1.975  2.9 -1.975  0.275  4.775  1.025 -0.475 -1.35 -1.6
Mating     -1.8  1.825 -3.3  3.825  0.075 -1.425 -2.175 -0.675  1.45  2.2
pOsitivity -1.1 -0.475 -5.6  1.525  3.775 -3.725 -1.475  3.025  2.15  1.9
Negativity  1.7  0.325  1.2 -2.675 -1.425  3.075  0.325 -2.175  1.95 -2.3
Deception  -1.1 -1.475  2.4 -1.475  0.775 -0.725  3.525  0.025 -0.85 -1.1
Sociality   1.4 -1.975 -0.1  1.025 -2.725  1.775 -1.975  2.525 -1.35  1.4

$RowUniqueCor
          A           B           C           D           E           F 
 0.41293714  0.83626086  0.54269729  0.17749959  0.75944741  0.20546405 
          G           H           I           J 
 0.44694178  0.15885778 -0.08005207  0.11664565 

$ColUniqueCor
       Duty   Intellect   Adversity      Mating  pOsitivity  Negativity 
 0.38757122 -0.07308439  0.65240565 -0.12022472  0.87704012 -0.45723700 
  Deception   Sociality 
 0.58752494  0.39139097 

$VarComp
                           Var    VarPerc NumDF DenDF        F          p
Row Variance         0.4694444 0.09825581     7    63 2.137500 0.05222172
Column Variance      0.1813492 0.03795681     9    63 1.351538 0.22943864
Interaction Variance 4.1269841 0.86378738    NA    NA       NA         NA

$Stats
                         Results
Elevation              0.6500000
Stereotype Accuracy    0.7498748
Differential Elevation 0.6081015
Differential Accuracy  0.3754240

multicon documentation built on May 2, 2019, 3:18 a.m.