Description Usage Arguments Details Value Author(s) References See Also Examples
description
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x |
The data X for |
use |
defines the method to use if missing values are present (for a detailed explanation see |
stats |
determines if |
vars |
can be |
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. |
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 |
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
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.
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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")
Measures of Sampling Adequacy (MSA):
A B C D E
0.5173978 0.5563367 0.5240787 0.4796702 0.5416592
KMO-Criterion: 0.5269849
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