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UNIDIMENSIONALITY – MULTIDIMENSIONALITY (An example)

UNIDIMENSIONALITY – MULTIDIMENSIONALITY (An example). Panayiotis Panayides. Rules of thumb for the existence of a second dimension. In the unexplained variance a secondary dimension must have the strength of at least 3 items.

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UNIDIMENSIONALITY – MULTIDIMENSIONALITY (An example)

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  1. UNIDIMENSIONALITY – MULTIDIMENSIONALITY (An example) Panayiotis Panayides

  2. Rules of thumb for the existence of a second dimension • In the unexplained variance a secondary dimension must have the • strength of at least 3 items. • Eigenvalue < 3 (in a reasonable length test) then the test is probably • unidimensional. (Linacre, 2005) • 2. The first factor must explain a significant % of the unexplained variance • (more than 20%) • A significant % of the total variance in the data • (Linacre, 2005, eigenvalue 2.7, N = 14, 0.2% of total variance) Example: Maths (27) and Language (28) diagnostic tests

  3. PCA of raw scores

  4. x + x = ……….. x.x = ……..

  5. PCA of standardised residuals(Linacre, 1998)

  6. Test – 51 items Test – 55 items Person Reliability : 0.90 Person separation: 3.05 Strata : 4.4 Person Reliability : 0.92 Person separation: 3.38 Strata : 4.84

  7. Given • the small % of unexplained variance (7.5%) explained by the first contrast • the small % of Total variance (3.7%) explained by the first contrast • the variance explained by the second dimension is about 14 times smaller • than the variance explained by the dimension measured by the test • the closeness of the points to a straight line passing through the origin • the extremely high correlation (r = 0.994) between the person measures • the fact that the two tests were on different subjects but were very easy Unidimensional

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