Cognitive diagnosis models of students’ skill profiles as a basis for adaptive teaching: an example from introductory accounting classes

Empirical Research in Vocational Education and Training

Table 2 Central test-level and item-level fit indices used in CDM research

Fit measure	Values indicating adequate fit	References
Test-level
MADcor	≤ 0.05	DiBello et al. (2007)
SRMSR	≤ 0.05	Maydeu-Olivares (2013)
MADQ3/MADaQ3	≤ 0.20 or .10	Yen (1984)
max \(\chi\) ² value	≥ 14.87^a	Groß, Robitzsch, and George (2016)
Item-level
RMSEA	≤ 0.10	Oliveri and Davier (2011)
IDI	approx. ≥ 0.35	Lee et al. (2012)
accuracy	≥ 0.70	Nunnally and Bernstein (1994)
consistency	≥ 0.70	Nunnally and Bernstein (1994)

MADcor Average absolute deviation between observed correlations and model predicted correlations, SRMR Standardized root mean square root of squared residuals, MADQ3 = mean of absolute values of Q3 statistic (Yen 1984), MADaQ3 Mean of absolute values of centered Q3 statistic, RMSEA Root mean square error of approximation, IDI = item discrimination index
^aGroß et al. (2015) propose a chi square value with a bonferroni corrected significance level (\(\alpha\) ^a = \(\alpha /((J(J-1))/2)\); \(\alpha\) ^a = bonferroni corrected significance level, \(\alpha\) = original/desired significance level, J number of items) which equals 14.87 for 30 item