Incomplete Tests of Conditional Association for the Assessment of Model Assumptions

Many of the models that have been proposed for response data share the assumptions that define the monotone homogeneity (MH) model. Observable properties that are implied by the MH model allow for these assumptions to be tested. For binary response data, the most restrictive of these properties is c...

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Bibliographic Details
Published in:Psychometrika 2022-12, Vol.87 (4), p.1214-1237
Main Author: Ligtvoet, Rudy
Format: Article
Language:English
Subjects:
Assessment
Behavioral Science and Psychology
Humanities
Inferences
Law
Psychology
Psychometrics
Rasch model
Statistical Theory and Methods
Statistics for Social Sciences
Testing and Evaluation
Theory and Methods
Variables
Violations
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Summary:Many of the models that have been proposed for response data share the assumptions that define the monotone homogeneity (MH) model. Observable properties that are implied by the MH model allow for these assumptions to be tested. For binary response data, the most restrictive of these properties is called conditional association (CA). All the other properties considered can be considered incomplete tests of CA that alleviate the practical limitations encountered when assessing the MH model assumptions using CA. It is found that the assessment of the MH model assumptions with an incomplete test of CA, rather than CA, is generally associated with a substantial loss of information. We also look at the sensitivity of the observable properties to model violation and discuss the implications of the results. It is argued that more research is required about the extent to which the assumptions and the model specifications influence the inferences made from response data.
ISSN:0033-3123
1860-0980
DOI:10.1007/s11336-022-09841-1