Measure of deviancy from marginal mean equality based on cumulative marginal probabilities in square contingency tables

Shuji Ando ()
Additional contact information
Shuji Ando: Tokyo University of Science

Metrika: International Journal for Theoretical and Applied Statistics, 2024, vol. 87, issue 8, No 5, 1037-1048

Abstract: Abstract This study proposes a measure that can concurrently evaluate the degree and direction of deviancy from the marginal mean equality (ME) model in square contingency tables with ordered categories. The proposed measure is constructed as the function of the row and column cumulative marginal probabilities. When the ME model does not fit data, we are interested in measuring the degree of deviancy from the ME model, because the model having weaker restrictions than the ME model is only the saturated model. This existing measure, which represents the degree of deviancy from the ME model, does not depend on the probabilities that observations will fall in the main diagonal cells of the table. For the data in which observations are concentrated in the main diagonal cells, the existing measure may overestimate the degree of deviancy from the ME model. The proposed measure can address this issue. This study derives an estimator and an approximate confidence interval for the proposed measure using the delta method. The proposed measure would be utility for comparing degrees of deviancy from the ME model in two datasets. The proposed measure is evaluated the usefulness with the application to real data of clinical trials.

Keywords: Comparing; Delta method; Direction; Main diagonal cells; Ordinal catagorical data; 62H17 (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s00184-023-00945-x Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:metrik:v:87:y:2024:i:8:d:10.1007_s00184-023-00945-x

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/184/PS2

DOI: 10.1007/s00184-023-00945-x

Access Statistics for this article

Metrika: International Journal for Theoretical and Applied Statistics is currently edited by U. Kamps and Norbert Henze

More articles in Metrika: International Journal for Theoretical and Applied Statistics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().