{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:47:49Z","timestamp":1760244469480,"version":"build-2065373602"},"reference-count":62,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,11,24]],"date-time":"2022-11-24T00:00:00Z","timestamp":1669248000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>Over the past decade, a series of procedures has been introduced to estimate, using a non-iterative method, the linear-by-linear association parameter of an ordinal log-linear model. This paper will examine the two key non-iteratively determined estimates of the parameter for the analysis of the association between the two categorical variables that form a contingency table; these are the log and the Beh-Davy non-iterative estimates, referred to simply as the LogNI and the BDNI estimates, respectively. Such an examination will focus on determining their asymptotic characteristics. To do so, a computational study was undertaken for tables of varying sizes to show that these two estimates are asymptotically unbiased. It is also shown that both estimates are asymptotically normally distributed. On the basis of the standard errors, their relative efficiency was established for the 13 commonly analysed contingency tables that appear throughout the literature.<\/jats:p>","DOI":"10.3390\/computation10120206","type":"journal-article","created":{"date-parts":[[2022,11,25]],"date-time":"2022-11-25T02:29:23Z","timestamp":1669343363000},"page":"206","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Asymptotic Characteristics of the Non-Iterative Estimates of the Linear-by-Linear Association Parameter for Ordinal Log-Linear Models"],"prefix":"10.3390","volume":"10","author":[{"given":"Sidra","family":"Zafar","sequence":"first","affiliation":[{"name":"The Advancement Portfolio, University of Sydney, Camperdown, NSW 2006, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Salman A.","family":"Cheema","sequence":"additional","affiliation":[{"name":"Department of Applied Sciences, National Textile University, Faisalabad 37610, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eric J.","family":"Beh","sequence":"additional","affiliation":[{"name":"National Institute for Applied Statistics Research Australia (NIASRA), University of Wollongong, Wollongong, NSW 2522, Australia"},{"name":"Centre for Multi-Dimensional Data Visualisation (MuViSu), Stellenbosch University, Stellenbosch 7602, South Africa"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9000-9556","authenticated-orcid":false,"given":"Irene L.","family":"Hudson","sequence":"additional","affiliation":[{"name":"Mathematical Sciences, School of Science, Royal Melbourne Institute of Technology (RMIT), Melbourne, VIC 3000, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,24]]},"reference":[{"key":"ref_1","unstructured":"Christensen, R. 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