7.10 Limited information statistics (Cont’d)

The \(M_2\) statistic compares whether the observed and model-predicted first two maginals equal or not.

The \(M_2\) statistic is also \(\chi^2\) distributed, with \(df\) being the number of elements in \(\mathbf{p}_1\) and \(\mathbf{p}_2\) minus the number of parameters.

• \(H_0\): The model fits data well
• \(H_1\): The model does not fit data well