Chuang, Christy; Gheva, David; Odoroff, Charles Methods for diagnosing multiplicative-interaction models for two-way contingency tables. (English) Zbl 0591.62052 Commun. Stat., Theory Methods 14, 2057-2080 (1985). Summary: An expanded class of multiplicative-interaction models is proposed for two-way contingency tables. These models, a generalization of Goodman’s association models, fill in the gap between the independence and the saturated models. Diagnostic rules based on a transformation of the data are proposed for the detection of such models. These rules, utilizing the singular value decomposition of the transformed data, are very easy to use. Maximum likelihood estimation is considered and the computational algorithms discussed. Two data sets are used to demonstrate the diagnostic rules. Cited in 1 Document MSC: 62H17 Contingency tables 65C99 Probabilistic methods, stochastic differential equations 62-04 Software, source code, etc. for problems pertaining to statistics Keywords:attached score; estimated basis term; fixed basis term; matrix; approximation; unattached score; expanded class of multiplicative- interaction models; two-way contingency tables; generalization of Goodman’s association models; independence; saturated models; Diagnostic rules; transformation of the data; singular value decomposition; Maximum likelihood estimation; computational algorithms Software:BMDP PDFBibTeX XMLCite \textit{C. Chuang} et al., Commun. Stat., Theory Methods 14, 2057--2080 (1985; Zbl 0591.62052) Full Text: DOI References: [1] Agresti A., J. Amer.Statist.Assoc 78 pp 184– (1983) · doi:10.1080/01621459.1983.10477950 [2] Agresti A., Comm.Statist 12 pp 1261– (1983) · doi:10.1080/03610928308828530 [3] Amdersen E.B., Discrete Statistical Models with Social Science Applications (1980) [4] Bishop Y.M.M., Discrete Multivariate Analysis: Theory and Practice (1975) [5] Chaung C., Comm.Statist 11 pp 2977– (1982) · Zbl 0512.62062 · doi:10.1080/03610928208828436 [6] Chaung C., Comm.Statist 12 pp 2871– (1983) · Zbl 0527.62054 · doi:10.1080/03610928308828646 [7] Clogg C.C., J.Amer.Statist.Assoc 77 pp 803– (1982) · doi:10.1080/01621459.1982.10477891 [8] Clogg C.C., Amer.J.Sociol 88 pp 114– (1982) · doi:10.1086/227636 [9] Cox D.R., Analysis of Binary Data (1970) · Zbl 0199.53301 [10] Dixon W.J., BMDP Statistical Software (1981) · Zbl 0549.62004 [11] Fienberg S.E., The Estimation of Cell Probabilities in Two-Way Contingency Tables (1968) [12] The Analysis of Cross-Classified Categorical Data (1983) [13] Freeman G.H., Appl. Statist 24 pp 46– (1975) · doi:10.2307/2346704 [14] Cabriel K.R., Computer Science and Statistics: Proceedings of the Fifteenth Symposium of the interface pp 304– (1983) [15] Gabriel K.R., J.Roy.Statist.Soc 40 pp 186– (1978) [16] Gabriel K.R., Technometrics 21 pp 489– (1979) · doi:10.1080/00401706.1979.10489819 [17] Gilula Z., Comm.Statist 11 pp 1233– (1982) · doi:10.1080/03610928208828307 [18] Goodman L.A., Analysis Qualitative/Categorical Data (1978) · Zbl 0396.92020 [19] Goodman L.A., J.Amer.Statist.Assoc 74 pp 537– (1979) · doi:10.1080/01621459.1979.10481650 [20] Goodman L.A., J.Amer.Statist.Assoc 76 pp 320– (1981) [21] Grizzle J.E., Biometrics 25 pp 489– (1969) · Zbl 1149.62317 · doi:10.2307/2528901 [22] Haberman S.J., Biometrics 30 pp 589– (1974) · Zbl 0294.62026 · doi:10.2307/2529224 [23] Analysis of Qualitatives Data (1979) [24] Haberman S.J., Ann.Statist 9 pp 1178– (1981) · Zbl 0479.62043 · doi:10.1214/aos/1176345635 [25] Householder A.S., Amer.Math.Monthly 45 pp 165– (1938) · Zbl 0019.14701 · doi:10.2307/2302980 [26] Ku H.H., J.Amer.Statist.Assoc 66 pp 55– (1971) · doi:10.1080/01621459.1971.10482219 [27] Mandel J., J.Nat’l.Bur.Stand.Sect.B 72 pp 309– (1969) · Zbl 0195.17404 · doi:10.6028/jres.073B.031 [28] Mandel J., Technometrics 13 pp 1– (1971) · doi:10.1080/00401706.1971.10488751 [29] NAC Frotran Mini Manual - Mark 11 (1984) [30] Nelder J.A., J.Roy.Statist.,Soc 135 pp 370– (1972) · doi:10.2307/2344614 [31] Plackett R.L., The Analysis of Categorical Data (1974) · Zbl 0286.62010 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.