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dc.contributor.authorYEE, Thomas W.
dc.contributor.authorHADI, Alfian F.
dc.date.accessioned2023-03-27T03:20:13Z
dc.date.available2023-03-27T03:20:13Z
dc.date.issued2014-03-27
dc.identifier.urihttps://repository.unej.ac.id/xmlui/handle/123456789/113541
dc.description.abstractWe propose a family of models called row–column interaction models (RCIMs) for two-way table responses. RCIMs apply some link function to a para meter (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 mod els, 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. Pro posed 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 (vec tor 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.en_US
dc.language.isoenen_US
dc.publisherComputational Statisticsen_US
dc.subjectGoodman’s row–column association modelen_US
dc.subjectQuasi-variancesen_US
dc.subjectReduced rank vector generalized linear modelsen_US
dc.subjectTwo-way table responsesen_US
dc.subjectUnconstrained quadratic ordinationen_US
dc.subjectVGAM R packageen_US
dc.titleRow–column interaction models, with an R implementationen_US
dc.typeArticleen_US


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