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Row–column interaction models, with an R implementation

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  • Thomas Yee
  • Alfian 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 $$\mathbf{A}\mathbf{C}^T$$ 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

Suggested Citation

  • Thomas Yee & Alfian Hadi, 2014. "Row–column interaction models, with an R implementation," Computational Statistics, Springer, vol. 29(6), pages 1427-1445, December.
  • Handle: RePEc:spr:compst:v:29:y:2014:i:6:p:1427-1445
    DOI: 10.1007/s00180-014-0499-9
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    References listed on IDEAS

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    1. Schenker N. & Gentleman J. F., 2001. "On Judging the Significance of Differences by Examining the Overlap Between Confidence Intervals," The American Statistician, American Statistical Association, vol. 55, pages 182-186, August.
    2. Yee, Thomas W., 2014. "Reduced-rank vector generalized linear models with two linear predictors," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 889-902.
    3. Yee, Thomas W., 2010. "The VGAM Package for Categorical Data Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i10).
    4. Firth, David, 2000. "Quasi-variances in Xlisp-Stat and on the web," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 5(i04).
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