Kaiser-Meyer-Olkin-Statistics: 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

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.

Value

A list of class 'MSA_KMO'
callthe issued function call
cormatcorrelation matrix
pcormatnormalized negative inverse of the correlation matrix (pairwise correlations given all other variables)
nthe number of observations
kthe number of variables/items
MSAmeasure of sampling adequacy
KMOKaiser-Meyer-Olkin criterion

encoding

UTF-8

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: cl{ $\geq{}.9$ marvelous $[.8,\,.9)$ meritorious $[.7,\,.8)$ middling $[.6,\,.7)$ mediocre $[.5,\,.6)$ miserable $

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.

Examples

Run this code

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")

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