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(Y. 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.