# KMO: Kaiser-Meyer-Olkin Statistics In REdaS: Companion Package to the Book 'R: Einführung durch angewandte Statistik'

description

## Usage

 ```1 2 3 4 5 6``` ```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

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.

`cor`, `bart_spher`

## Examples

 ```1 2 3 4 5``` ```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") ```

### Example output

```Loading required package: grid
A           B           C           D           E
A  1.00000000  0.12027233  0.05888807 -0.03727014 -0.10461185
B  0.12027233  1.00000000  0.06291143  0.05417371 -0.08279073
C  0.05888807  0.06291143  1.00000000  0.08570349 -0.00189880
D -0.03727014  0.05417371  0.08570349  1.00000000 -0.04973146
E -0.10461185 -0.08279073 -0.00189880 -0.04973146  1.00000000

Kaiser-Meyer-Olkin Statistics

Call: KMOS(x = daten, use = "pairwise.complete.obs")