7.11 Limited information statistics (Cont’d)

An effect size measure that is usually used in conjunction with the \(M_2\) statistic is the root mean square error of approximation (RMSEA\(_2\)):

\[\text{RMSEA}_2=\sqrt{\max(\frac{M_2-df}{N\times df},0)}\]

Simulation study showed that \(\text{RMSEA}_2<.03\) indicates excellent fit, \(.03\leq \text{RMSEA}_2<.045\) a good fit and \(\text{RMSEA}_2\geq .045\) poor fit(Liu et al., 2016).

References

Liu, Y., Tian, W., & Xin, T. (2016). An application of m 2 statistic to evaluate the fit of cognitive diagnostic models. Journal of Educational and Behavioral Statistics, 41(1), 3–26.