A model for contingency tables having an ordered response classification

Research output: Contribution to journalArticle

35 Citations (Scopus)

Abstract

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 the first example, the original and new analyses give the same substantive interpretation, but whereas the former requires interpreting interactions, the latter requires interpreting main effects 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-off points 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-off point may be pooled and that the same information can therefore be obtained from the collapsed dichotomous classification.

Original languageEnglish
Pages (from-to)403-415
Number of pages13
JournalBiometrics
Volume35
Issue number2
DOIs
Publication statusPublished - 1 Jan 1979

Fingerprint

Ordered Categories
Contingency Table
Linear Response
Main Effect
Linear Models
Continuum
Integer
Dependent
Interaction
Model
Object
Interpretation
Relationships
Datasets

Cite this

@article{155bd7fc684449fa8480966a96a940a9,
title = "A model for contingency tables having an ordered response classification",
abstract = "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 the first example, the original and new analyses give the same substantive interpretation, but whereas the former requires interpreting interactions, the latter requires interpreting main effects 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-off points 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-off point may be pooled and that the same information can therefore be obtained from the collapsed dichotomous classification.",
author = "D. Andrich",
year = "1979",
month = "1",
day = "1",
doi = "10.2307/2530343",
language = "English",
volume = "35",
pages = "403--415",
journal = "Biometrics",
issn = "0006-341X",
publisher = "Wiley Blackwell",
number = "2",

}

A model for contingency tables having an ordered response classification. / Andrich, D.

In: Biometrics, Vol. 35, No. 2, 01.01.1979, p. 403-415.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A model for contingency tables having an ordered response classification

AU - Andrich, D.

PY - 1979/1/1

Y1 - 1979/1/1

N2 - 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 the first example, the original and new analyses give the same substantive interpretation, but whereas the former requires interpreting interactions, the latter requires interpreting main effects 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-off points 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-off point may be pooled and that the same information can therefore be obtained from the collapsed dichotomous classification.

AB - 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 the first example, the original and new analyses give the same substantive interpretation, but whereas the former requires interpreting interactions, the latter requires interpreting main effects 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-off points 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-off point may be pooled and that the same information can therefore be obtained from the collapsed dichotomous classification.

UR - http://www.scopus.com/inward/record.url?scp=0018332107&partnerID=8YFLogxK

U2 - 10.2307/2530343

DO - 10.2307/2530343

M3 - Article

VL - 35

SP - 403

EP - 415

JO - Biometrics

JF - Biometrics

SN - 0006-341X

IS - 2

ER -