A Study of Bias for Non-Iterative Estimates of the Linear-by-Linear Association Parameter from the Ordinal Log-Linear Model Sidra Zafar, Salman A. Cheema, Eric J. Beh, Irene L. Hudson Abstract Ordinal log-linear models (OLLM) are commonly used to analyse the association in a contingency table with ordered categorical variables. Recently, a non- iterative procedure was introduced to estimate the linear-by-linear association parameter of the OLLM. This paper will consider two of these non-iterative estimates and show that they are unbiased. 1 Introduction Log-linear models (LLM) are one of the most commonly used techniques to analyse the association between categorical variables in a contingency table. One may refer to, for example, Christensen (1997) and Agresti (2002) for a detailed discussion of many of the issues. Much of this work has focused on the study of variables consisting of nominally structured categories. However, there are many practical situations where variables consist of ordered categories and it is important to reflect the structure of these variables. Hence, LLM’s for these cases are therefore commonly referred to as ordinal log-linear models, or OLLMs. An important aspect of LLMs, and OLLMs, is the estimation of the parameters from these models. ____________________________ Sidra Zafar, School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, 2308, NSW, Australia; email: sidra.zafar@uon.edu.au Salman A. Cheema, School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, 2308, NSW, Australia; email: salman.cheema@uon.edu.au Eric J. Beh, School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, 2308, NSW, Australia; email: eric.beh@newcastle.edu.au Irene L. Hudson, School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, 2308, NSW, Australia; email: irenelena.hudson@gmail.com