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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 standard ANOVA models with random effects for multi-indexed arrays of random variables with an arbitrary nesting structure on the indices are considered from the viewpoint of symmetry. It is found that the covariance matrix of such an array has sufficient symmetry to permit viewing the usual components of variance as a generalised spectrum and the linear models of random effects as a generalised spectral decomposition.

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A Widely Applicable Extension of the Random Effects Two-Way Layout: Its Definition and Statistical Analysis Based on Group Invariance

ANOVA models with random effects: an approach via symmetry

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2 results

A Widely Applicable Extension of the Random Effects Two-Way Layout: Its Definition and Statistical Analysis Based on Group Invariance

ANOVA models with random effects: an approach via symmetry