Row–column interaction models, with an R implementation View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2014-12

AUTHORS

Thomas W. Yee, Alfian F. Hadi

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 ACT, (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 linear/additive predictor η case (within the exponential family) to the 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. More... »

PAGES

1427-1445

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00180-014-0499-9

DOI

http://dx.doi.org/10.1007/s00180-014-0499-9

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1006140235


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