A widely applicable extension of the random effects two-way layout: Its definition and statistical analysis based on group invariance

A type of data layout that may be considered as an extension of the two-way random effects analysis of variance is characterized and modeled based on group invariance. The data layout seems to be suitable for several scenarios in psychometrics, including the one in which multiple measurements are taken on each of a set of variables, and the measurements can be divided into exchangeable subsets. The algebraic structure of the model is studied, which leads to results that are applicable to such problems as estimating correlation matrix corrected for attenuation and testing symmetry hypotheses.The author would like to thank NIH for support through grants M01 RR00044 and P01 DE13539, and NSF and ASA Survey Section for a travel grant which allowed him to present this paper as an invited young researcher at the Conference in Celebration of Wayne A. Fuller's 70th birthday.