A non-iterative alternative to ordinal Log-Linear models

Log-linear modeling is a popular statistical tool for analysing a contingency table. This presentation focuses on an alternative approach to modeling ordinal categorical data. The technique, based on orthogonal polynomials, provides a much simpler method of model fitting than the conventional approach of maximum likelihood estimation, as it does not require iterative calculations nor the fitting and re-fitting to search for the best model. Another advantage is that quadratic and higher order effects can readily be included, in contrast to conventional log-linear models which incorporate linear terms only.

[1]  Shizuhiko Nishisato,et al.  Nonlinear programming approach to optimal scaling of partially ordered categories , 1975 .

[2]  Eric J. Beh,et al.  Theory & Methods: Partitioning Pearson's Chi‐squared Statistic for Singly Ordered Two‐way Contingency Tables , 2001 .

[3]  Eric J. Beh,et al.  Theory & Methods: Partitioning Pearson’s Chi‐Squared Statistic for a Completely Ordered Three‐Way Contingency Table , 1998 .

[4]  Eric J. Beh,et al.  A Comparative Study of Scores for Correspondence Analysis with Ordered Categories , 1998 .

[5]  Clifford C. Clogg,et al.  Some Models for the Analysis of Association in Multiway Cross-Classifications Having Ordered Categories , 1982 .

[6]  B. Macmahon.  MENTAL HEALTH IN THE METROPOLIS: THE MIDTOWN MANHATTAN STUDY , 1963 .

[7]  L. A. Goodman.  Simple Models for the Analysis of Association in Cross-Classifications Having Ordered Categories , 1979 .

[8]  Z. Gilula,et al.  Inferential Ordinal Correspondence Analysis: Motivation, Derivation and Limitations , 1990 .

[9]  Phillip L. Emerson,et al.  Numerical Construction of Orthogonal Polynomials from a General Recurrence Formula , 1968 .

[10]  John C. W. Rayner,et al.  NONPARAMETRIC ANALYSIS FOR DOUBLY ORDERED TWO-WAY CONTINGENCY TABLES , 1996 .

[11]  E. Beh,et al.  Theory & Methods: Partitioning Pearson’s chi‐squared statistic for a partially ordered three‐way contingency table , 1999 .

[12]  M. Kendall,et al.  The advanced theory of statistics , 1945 .

[13]  Stephen E. Fienberg,et al.  The analysis of cross-classified categorical data , 1980 .

[14]  Pieter M. Kroonenberg,et al.  Singular value decompositions of interactions in three-way contingency tables , 1989 .

[15]  Shelby J. Haberman,et al.  The analysis of multivariate contingency tables by restricted canonical and restricted association models , 1988 .

[16]  A. Romney,et al.  Metric Scaling: Correspondence Analysis , 1990 .

[17]  Zvi Gilula,et al.  Grouping and Association in Contingency Tables: An Exploratory Canonical Correlation Approach , 1986 .

[18]  M PETERG..  CORRESPONDENCE ANALYSIS USED COMPLEMENTARY TO LOGLINEAR ANALYSIS , .

[19]  Shelby J. Haberman,et al.  Log-Linear Models for Frequency Tables with Ordered Classifications , 1974 .

[20]  John C. W. Rayner,et al.  Smooth extensions of Pearsons's product moment correlation and Spearman's rho , 1996 .

[21]  Suzanne Winsberg,et al.  Metric scaling correspondence analysis , 1992 .

[22]  S. Haberman,et al.  Canonical Analysis of Contingency Tables by Maximum Likelihood , 1986 .

[23]  P.G.M. Van der Heijden,et al.  A Combined Approach to Contingency Table Analysis Using Correspondence Analysis and Log-Linear Analysis , 1989 .

[24]  P. McCullagh.  Analysis of Ordinal Categorical Data , 1985 .

[25]  John C. W. Rayner,et al.  Analysis of singly ordered two-way contingency tables , 2000, Adv. Decis. Sci..

[26]  R. Cranley,et al.  Multivariate Analysis—Methods and Applications , 1985 .

[27]  J. V. Rosenhead,et al.  The Advanced Theory of Statistics: Volume 2: Inference and Relationship , 1963 .

[28]  Eric J. Beh,et al.  Simple Correspondence Analysis of Ordinal Cross‐Classifications Using Orthogonal Polynomials , 1997 .