Kaiser-Meyer-Olkin-Statistics {REdaS}

Kaiser-Meyer-Olkin Statistics

Description

description

Usage

KMOS(x, use = c("everything", "all.obs", "complete.obs", "na.or.complete",
    "pairwise.complete.obs"))

## S3 method for class 'MSA_KMO'
print(x, stats = c("both", "MSA", "KMO"), vars = "all",
    sort = FALSE, show = "all", digits = getOption("digits"), ...)

Arguments

x

The data \mathbf{X} for KMOS(), an object of class 'MSA_KMO' for the print method.

use

defines the method to use if missing values are present (for a detailed explanation see bart_spher; see also cor).

stats

determines if "MSA", "KMO" or "both" (default) are printed.

vars

can be "all" or a vector of index numbers of variables to print the MSAs for.

sort

sorts the MSAs in increasing order.

show

shows the specified number of variables (from 1 to the number of potentially sorted variables).

digits

the number of decimal places to print.

...

further arguments.

Details

The Measure of Sampling Adequacy (MSA) for individual items and the Kaiser-Meyer-Olkin (KMO) Criterion rely on the Anti-Image-Correlation Matrix \mathbf{A} (for details see Kaiser & Rice, 1974) that contains all bivariate partial correlations given all other items in the a_{ij}=r_{ij\,\vert\,\mathbf{X}\setminus\{i,\,j\}} which is:

\mathbf{A}=\left[\mathrm{diag}(\mathbf{R}^{-1})\right]^{-1/2}\,\mathbf{R}^{-1}\,\left[\mathrm{diag}(\mathbf{R}^{-1})\right]^{-1/2}

where \mathbf{R} is the correlation matrix, based on the data \mathbf{X}.

The KMO and MSAs for individual items are (adapted from Equations (3) and (4) in Kaiser & Rice, 1974; note that a is q in the article):

\mathit{KMO}=\frac{\sum_{i=1}^{k}\sum_{j=1}^{k}r_{ij}^2}{\sum_{i=1}^{k}\sum_{j=1}^{k}r_{ij}^2+a_{ij}^2},\qquad i\neq j

\mathit{MSA}_i=\frac{\sum_{j=1}^{k}r_{ij}^2}{\sum_{j=1}^{k}r_{ij}^2+a_{ij}^2},\qquad j\neq i

Historically, as suggested in Kaiser (1974) and Kaiser & Rice (1974), a rule of thumb for those values is:

\geq{}.9	marvelous
[.8,\,.9)	meritorious
[.7,\,.8)	middling
[.6,\,.7)	mediocre
[.5,\,.6)	miserable
<.5	unacceptable

Value

A list of class 'MSA_KMO'

call

the issued function call

cormat

correlation matrix

pcormat

normalized negative inverse of the correlation matrix (pairwise correlations given all other variables)

n

the number of observations

k

the number of variables/items

MSA

measure of sampling adequacy

KMO

Kaiser-Meyer-Olkin criterion

Author(s)

Marco J. Maier

References

Kaiser, H. F. (1970). A Second Generation Little Jiffy. Psychometrika, 35(4), 401–415.

Kaiser, H. F. (1974). An Index of Factorial Simplicity. Psychometrika, 39(1), 31–36.

Kaiser, H. F., & Rice, J. (1974). Little Jiffy, Mark IV. Educational and Psychological Measurement, 34, 111–117.

See Also

cor, bart_spher

Examples

set.seed(5L)
daten <- data.frame("A"=rnorm(100), "B"=rnorm(100), "C"=rnorm(100),
                    "D"=rnorm(100), "E"=rnorm(100))
cor(daten)
KMOS(daten, use = "pairwise.complete.obs")