# 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

 `1` ```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

 ```1 2 3 4 5 6 7``` ```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
\$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.