Kaiser-Meyer-Olkin criterion

In the factor analysis, the anti-image correlation matrix forms the basis for checking whether a data set with indicators (variables) can be represented by factors. The test parameters are derived from this ${\displaystyle m}$

• Measure of sampling adequacy (also MSA ) which indicates whether a certain indicator should be included in the factor analysis and
• Kaiser-Meyer-Olkin criterion (also KMK or KMO ), which indicates whether a data set is suitable for a factor analysis.

If the data are approximately multivariate normally distributed , the Bartlett test for sphericity can also be used to check whether a data set is suitable for the factor analysis.

Anti-Image Correlation Matrix

The anti-image correlation matrix contains the negative partial correlations between two indicators outside the diagonal . These indicate how great the correlation between two indicators is if one eliminates the influence of all other indicators. ${\displaystyle p_{jk}}$

If there are common factors behind the data set and each factor loads at least three indicators, then the partial correlations should be close to zero.

The measure of sampling adequacy is on the diagonal of the anti-image correlation matrix in SPSS.

Measure of sampling adequacy

The measure of sampling adequacy is calculated for each indicator as

${\displaystyle MSA_{j}={\frac {\displaystyle \sum _{k\neq j}r_{jk}^{2}}{\displaystyle \sum _{k\neq j}r_{jk}^{2}+\sum _{k\neq j}p_{jk}^{2}}}}$

and indicates to what extent an indicator is suitable for a factor analysis. Here is the correlation between the variable in question and another, and the partial correlation. It can have values ​​between zero and one. If all partial correlations are zero, then is . If that is the case , then this indicator is considered unsuitable, from 0.6 as useful and from values ​​above 0.8 as good. ${\displaystyle r_{jk}}$ ${\displaystyle p_{jk}}$ ${\displaystyle MSA_{j}=1}$ ${\displaystyle MSA_{j}<0{,}5}$

Kaiser-Meyer-Olkin criterion

The Kaiser-Meyer-Olkin criterion is calculated as

${\displaystyle KMO={\frac {\displaystyle {\underset {j\neq k}{\sum \sum }}r_{jk}^{2}}{\displaystyle {\underset {j\neq k}{\sum \sum }}r_{jk}^{2}+{\underset {j\neq k}{\sum \sum }}p_{jk}^{2}}}}$

The criterion can have values ​​between zero and one. Kaiser, Meyer and Olkin are of the opinion that a value below 0.5 on this main diagonal is not acceptable.

example

The 2002 microcensus surveyed how often the respondents were allowed to work on Saturdays (EF147), Sunday / public holidays (EF148), evening work (EF149), night work (EF150), night hours (EF151), shift work (EF152) or work in the period from February to April Home (EF163).

The Kaiser-Meyer-Olkin criterion (red) results in 0.600 and these seven indicators are therefore just about suitable for a factor analysis. The measure of adequacy (yellow) shows that the indicators working on Saturdays and Sundays / public holidays are just about acceptable. Removing these two indicators would increase the Kaiser-Meyer-Olkin criterion. The highest value in the anti-image correlation for a partial correlation (green) with 0.515 is also found between these two indicators.

See also

The criterion must be distinguished from the Kaiser criterion , which is also used in the factor analysis.

Individual evidence

1. ^ W. Ludwig-Mayerhofer: Factor analysis. ILMES - Internet Lexicon of Methods in Empirical Social Research, June 5, 2004, accessed January 30, 2011 . 
2. ^ Cureton, EE / D'Agostino, RB 1983: Factor analysis: an applied approach. Hillside, NJ: Lawrence Erlbaum Associates, pp. 389 f.

literature

• Bernd Rönz: Script: Computer- Aided Statistics II . Humboldt University of Berlin, Chair of Statistics, Berlin 2000.