Row–column interaction models, with an R implementation

Thomas Yee () and Alfian Hadi ()

Computational Statistics, 2014, vol. 29, issue 6, 1427-1445

Abstract: We propose a family of models called row–column interaction models (RCIMs) for two-way table responses. RCIMs apply some link function to a parameter (such as the cell mean) to equal a row effect plus a column effect plus an optional interaction modelled as a reduced-rank regression. What sets this work apart from others is that our framework incorporates a very wide range of statistical models, e.g., (1) log-link with Poisson counts is Goodman’s RC model, (2) identity-link with a double exponential distribution is median polish, (3) logit-link with Bernoulli responses is a Rasch model, (4) identity-link with normal errors is two-way ANOVA with one observation per cell but allowing semi-complex modelling of interactions of the form $$\mathbf{A}\mathbf{C}^T$$ A C T , (5) exponential-link with normal responses are quasi-variances. Proposed here also is a least significant difference plot augmentation of quasi-variances. Being a special case of RCIMs, quasi-variances are naturally extended from the $$M=1$$ M = 1 linear/additive predictor $$\eta $$ η case (within the exponential family) to the $$M>1$$ M > 1 case (vector generalized linear model families). A rank-1 Goodman’s RC model is also shown to estimate the site scores and optimums of an equal-tolerances Poisson unconstrained quadratic ordination. New functions within the VGAM R package are described with examples. Altogether, RCIMs facilitate the analysis of matrix responses of many data types, therefore are potentially useful to many areas of applied statistics. Copyright Springer-Verlag Berlin Heidelberg 2014

Keywords: Goodman’s row–column association model; Quasi-variances; Reduced-rank vector generalized linear models; Two-way table responses; Unconstrained quadratic ordination; VGAM R package (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:compst:v:29:y:2014:i:6:p:1427-1445

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DOI: 10.1007/s00180-014-0499-9

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