scholarly journals On Estimating the Linear-by-Linear Parameter for Ordinal Log-Linear Models: A Computational Study

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Eric J. Beh ◽  
Thomas B. Farver
Keyword(s):  
Linear Models ◽  
Computational Study ◽  
Contingency Tables ◽  
Linear Parameter ◽  
Iterative Techniques ◽  
Ordinal Variables ◽  
Linear Association ◽  
Iterative Procedures ◽  
Log Linear

Estimating linear-by-linear association has long been an important topic in the analysis of contingency tables. For ordinal variables, log-linear models may be used to detect the strength and magnitude of the association between such variables, and iterative procedures are traditionally used. Recently, studies have shown, by way of example, three non-iterative techniques can be used to quickly and accurately estimate the parameter. This paper provides a computational study of these procedures, and the results show that they are extremely accurate when compared with estimates obtained using Newton’s unidimensional method.

scholarly journals A Computational Study Assessing Maximum Likelihood and Noniterative Methods for Estimating the Linear-by-Linear Parameter for Ordinal Log-Linear Models

2012 ◽  
Vol 2012 ◽  
pp. 1-8
Author(s):  
Eric J. Beh ◽  
Thomas B. Farver
Keyword(s):  
Maximum Likelihood ◽  
Newton’S Method ◽  
Newton's Method ◽  
Linear Models ◽  
Computational Study ◽  
Linear Measure ◽  
Iterative Procedures ◽  
Measure Of Association ◽  
Log Linear ◽  
The Impact

For ordinal log-linear models, the estimation of the parameter reflecting the linear-by-linear measure of association has long been a topic for the analysis of dependence for contingency tables. Typically, iterative procedures (including Newton’s method) are used to determine the maximum likelihood estimate of the parameter. Recently Beh and Farver (2009, ANZJS, 51, 335–352) show by way of example three reliable and accurate noniterative techniques that can be used to estimate the parameter and extended this study by examining their reliability computationally. This paper further investigates the reliability of the non-iterative procedures when compared with Newton’s method for estimating this association parameter and considers the impact of the sample size on the estimate.

scholarly journals Ordinal Log-Linear Models for Contingency Tables

2016 ◽  
Vol 16 (1) ◽  
pp. 264-273
Author(s):  
Justyna Brzezińska
Keyword(s):  
Contingency Table ◽  
Linear Models ◽  
Contingency Tables ◽  
Linear Analysis ◽  
Categorical Variables ◽  
Ordinal Variables ◽  
Advantages And Disadvantages ◽  
Effect Model ◽  
Log Linear ◽  
Model Algorithm

Abstract A log-linear analysis is a method providing a comprehensive scheme to describe the association for categorical variables in a contingency table. The log-linear model specifies how the expected counts depend on the levels of the categorical variables for these cells and provide detailed information on the associations. The aim of this paper is to present theoretical, as well as empirical, aspects of ordinal log-linear models used for contingency tables with ordinal variables. We introduce log-linear models for ordinal variables: linear-by-linear association, row effect model, column effect model and RC Goodman’s model. Algorithm, advantages and disadvantages will be discussed in the paper. An empirical analysis will be conducted with the use of R.

scholarly journals The Application of Log-Linear Model to Selected Poison Patients

2020 ◽  
pp. 1-7
Author(s):  
Fatin N.S.A. ◽  
Norlida M.N. ◽  
Siti Z.M.J.
Keyword(s):  
Linear Model ◽  
Linear Models ◽  
Demographic Data ◽  
Contingency Tables ◽  
Categorical Variables ◽  
State Variables ◽  
Exposure Route ◽  
Higher Dimensional ◽  
Route Of Exposure ◽  
Log Linear

Log-linear model is a technique used to analyze the cross-classification categorical data or the contingency table. It is used to obtain the parsimony models that describe the interaction between the categorical variables in contingency tables. Log-linear models are commonly used in evaluating higher dimensional contingency tables that involves more than two categorical variables. This study focuses on analyzing data of poisoned patients from 2012 to 2014 using log-linear model. There are two model analyzed; model for demographic data of patients and model of poisoning information. For the first model, the variables involved are gender, age, race and state. Variables for the second model are circumstance of exposure, type of exposure, location of exposure, route of exposure and types of poison. Both log-linear models are developed to investigate the association between variables in the model. As a result of this study, the best model for demographic data and poisoning information are the model with three-ways interaction. For the best model of demographic data, there is an association between gender, age and race, race, gender and state as well as age, race and state. Meanwhile, the best model for poisoning information reveals that there is relationship between circumstance of exposure, route of exposure and type of poison, location of exposure, route of exposure and type of poison, circumstance of exposure, type of exposure and route of exposure, circumstance of exposure, location of exposure and route of exposure, circumstance of exposure, type of exposure and type of poison and also type of exposure, location of exposure and type of poison. Keywords: log-linear; demographic; gender; age; race; state; circumstance of exposure; type of exposure; location of exposure; route of exposure; types of poison

Log Linear Models and Tests of Independence for Contingency Tables

Biometrics ◽  
1972 ◽  
Vol 28 (1) ◽  
pp. 137 ◽  
Author(s):  
James E. Grizzle ◽  
O. Dale Williams
Keyword(s):  
Linear Models ◽  
Contingency Tables ◽  
Log Linear ◽  
Tests Of Independence

scholarly journals Analysing Sensitive Data from Dynamically-Generated Overlapping Contingency Tables

2020 ◽  
Vol 36 (2) ◽  
pp. 275-296
Author(s):  
Joshua J. Bon ◽  
Bernard Baffour ◽  
Melanie Spallek ◽  
Michele Haynes
Keyword(s):  
Linear Models ◽  
Contingency Tables ◽  
Sensitive Data ◽  
Data Set ◽  
Administrative Records ◽  
Cell Counts ◽  
Wide Range ◽  
Australian Census ◽  
Australian Bureau Of Statistics ◽  
Log Linear

AbstractContingency tables provide a convenient format to publish summary data from confidential survey and administrative records that capture a wide range of social and economic information. By their nature, contingency tables enable aggregation of potentially sensitive data, limiting disclosure of identifying information. Furthermore, censoring or perturbation can be used to desensitise low cell counts when they arise. However, access to detailed cross-classified tables for research is often restricted by data custodians when too many censored or perturbed cells are required to preserve privacy. In this article, we describe a framework for selecting and combining log-linear models when accessible data is restricted to overlapping marginal contingency tables. The approach is demonstrated through application to housing transition data from the Australian Census Longitudinal Data set provided by the Australian Bureau of Statistics.

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