KMO: Kaiser-Meyer-Olkin Statistics

In REdaS: Companion Package to the Book 'R: Einführung durch angewandte Statistik'

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 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 A (for details see Kaiser & Rice, 1974) that contains all bivariate partial correlations given all other items in the a_ij = r_ij | X \ {i, j} which is:

A = [diag(R⁻¹)]^(-1 ∕ 2) R⁻¹ [diag(R⁻¹)]^(-1 ∕ 2)

where R is the correlation matrix, based on the data 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):

KMO = (∑∑ r²_ij) ∕ (∑∑ r²_ij + a²_ij), i ≠ j

MSA_i = (∑_j r²_ij) ∕ (∑_j r²_ij + a²_ij), j ≠ i

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

≥ .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")

REdaS documentation built on June 13, 2022, 9:05 a.m.