A model for contingency tables having an ordered response classification

A common case of ordered categories in contingency tables is where objects are classified according to a rating procedure with respect to some dependent variable. A rating mechanism for such ordered categories, resulting in a log-linear response model in which successive categories are scored with successive integers, is proposed. Two sets of data which have been analysed with other models are reanalysed. In thefirst example, the original and new analyses give the same substantive interpretation, but whereas the former requires interpreting interactions, the latter requires interpreting main effiects only. Consequently, the latter analysis is considered simpler. In the second example, the relationship between the variables of interest is again found to be the same as in the original analysis, but in addition, a new insight into the operation of the rating mechanism is suggested. Specifically, it is suggested that one of the cut-offpoints on the rating continuum is not discriminating. Because the original classification was trichotomous, the implication is that the categories on either side of the non-discriminating cut-ofJ point may be pooled and that the same information can therefore be obtained from the collapsed dichotomous classification.

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

[2]  J. R. Ashford,et al.  An Approach to the Analysis of Data for Semi-Quantal Responses in Biological Assay , 1959 .

[3]  J. Ashford,et al.  The Study of Observer Variation in the Radiological Classification of Pneumoconiosis , 1960, British journal of industrial medicine.

[4]  G. Rasch On General Laws and the Meaning of Measurement in Psychology , 1961 .

[5]  H. A. David,et al.  The method of paired comparisons , 1966 .

[6]  R. A. Bradley,et al.  Rank Analysis of Incomplete Block Designs: I. The Method of Paired Comparisons , 1952 .

[7]  G. Koch,et al.  Estimating the Total Number of Events with Data from Multiple-Record Systems: A Review of Methodological Strategies , 1977 .

[8]  Joseph Berkson,et al.  Tables for the Maximum Likelihood Estimate of the Logistic Function , 1957 .

[9]  D. J. Finney Probit analysis; a statistical treatment of the sigmoid response curve. , 1947 .

[10]  R. Plackett,et al.  The Relation between Quantal and Graded Responses to Drugs , 1956 .

[11]  P. Armitage Tests for Linear Trends in Proportions and Frequencies , 1955 .

[12]  Erling B. Andersen,et al.  Sufficient statistics and latent trait models , 1977 .

[13]  G. Rasch,et al.  A MATHEMATICAL THEORY OF OBJECTIVITY AND ITS CONSEQUENCES FOR MODEL CONSTRUCTION , 1968 .

[14]  C. L. Mallows,et al.  Individual Choice Behaviour. , 1961 .

[15]  Robin Plackett The analysis of categorical data , 1974 .

[16]  R. A. Bradley,et al.  RANK ANALYSIS OF INCOMPLETE BLOCK DESIGNS , 1952 .

[17]  D. Andrich A rating formulation for ordered response categories , 1978 .