Full Contingency Tables, Logits, and Split Contingency Tables

Three methods of fitting log-linear models to multivariate contingency-table data with one dichotomous variable are discussed. Logit analysis is commonly used when a full contingency table of s dimensions is regarded as a table of rates of dimension s -1. The split-table method treats the same data as two separate tables each of dimension s -1. We show that the full contingency-table method can be regarded as a generalized approach: models which can be fitted by it include both the mutually exclusive subsets that can be fitted by the other two methods. Even when the logit method permits the model of choice to be fitted, the full contingency-table method of iterative proportional fitting to the set of sufficient configurations has the advantage of requiring neither matrix inversion nor substitution of an arbitrary value in empty elementary cells.

[1]  F. Mosteller,et al.  The National Halothane Study , 1970 .

[2]  S. Kullback,et al.  Contingency tables with given marginals. , 1968, Biometrika.

[3]  J. Berkson,et al.  Application of minimum logit chi square estimate to a problem of Grizzle with a notation on the problem of 'no interaction'. , 1968, Biometrics.

[4]  Hugh E. Bradley.  Multiple Classification Analysis for Arbitrary Experimental Arrangements , 1968 .

[5]  Gary G. Koch,et al.  Hypotheses Of ‘No Interaction’ In Multi-dimensional Contingency Tables , 1968 .

[6]  B. Bhat,et al.  Lamp Tests of Linear and Loglinear Hypotheses in Multinomial Experiments , 1966 .

[7]  W. Hoeffding.  Asymptotically Optimal Tests for Multinomial Distributions , 1965 .

[8]  D. Lindley.  The Bayesian Analysis of Contingency Tables , 1964 .

[9]  M. W. Birch.  The Detection of Partial Association, I: The 2 × 2 Case , 1964 .

[10]  Leo A. Goodman,et al.  Simple Methods for Analyzing Three-Factor Interaction in Contingency Tables , 1964 .

[11]  M. Wise.  Multinomial Probabilities and the χ 2 and X 2 Distributions , 1963 .

[12]  Leo A. Goodman,et al.  On Plackett's Test for Contingency Table Interactions , 1963 .

[13]  Leo A. Goodman,et al.  On Methods for Comparing Contingency Tables , 1963 .

[14]  M. W. Birch.  Maximum Likelihood in Three-Way Contingency Tables , 1963 .

[15]  S. Kullback,et al.  Tests for Contingency Tables and Marltov Chains , 1962 .

[16]  R. Plackett.  A Note on Interactions in Contingency Tables , 1962 .

[17]  J. Grizzle.  A NEW METHOD OF TESTING HYPOTHESES AND ESTIMATING PARAMETERS FOR THE LOGISTIC MODEL , 1961 .

[18]  F. Yates.  Marginal percentages in multiway tables of quantal data with disproportionate frequencies , 1961 .

[19]  V. P. Bhapkar.  Some Tests for Categorical Data , 1961 .

[20]  D. Friedlander.  A Technique for Estimating a Contingency Table, Given the Marginal Totals and Some Supplementary Data , 1961 .

[21]  David T. Brown,et al.  A Note on Approximations to Discrete Probability Distributions , 1959, Inf. Control..

[22]  W. Haenszel,et al.  Statistical aspects of the analysis of data from retrospective studies of disease. , 1959, Journal of the National Cancer Institute.

[23]  D. E. Lamphiear,et al.  CALCULATION OF CHI-SQUARE TO TEST THE NO THREE-FACTOR INTERACTION HYPOTHESIS , 1959 .

[24]  W. G. Cochran.  The $\chi^2$ Test of Goodness of Fit , 1952 .

[25]  H. D. Patterson,et al.  Analysis of Factorial Arrangements when the Data are Proportions , 1952 .

[26]  H. W. Norton.  Calculation of Chi-Square for Complex Contingency Tables , 1945 .

[27]  W. Deming,et al.  On a Least Squares Adjustment of a Sampled Frequency Table When the Expected Marginal Totals are Known , 1940 .

[28]  M. Bartlett.  Contingency Table Interactions , 1935 .

[29]  R. Fisher.  019: On the Interpretation of x2 from Contingency Tables, and the Calculation of P. , 1922 .