A Non-Iterative Alternative to Ordinal Log-Linear Models

Beh, Eric J.; Davy, Pamela J.

doi:10.1207/s15327612jamd0802_1

Cited by 9 publications

(23 citation statements)

References 22 publications

(54 reference statements)

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“…Note the squaring of σ I and σ J . Similarly, the MNI estimate (eqn 26) should be while the BDNI estimate (eqn 25) is and coincides exactly with the original non‐iterative parameter estimate derived by Beh & Davy (2004). In the original paper, the R code used to calculate the estimates of this parameter using Newton's method and the three non‐iterative procedures reflects the corrected versions of the estimates stated here and is therefore true and correct.…”

supporting

confidence: 53%

Corrigendum: AN EVALUATION OF NON‐ITERATIVE METHODS FOR ESTIMATING THE LINEAR‐BY‐LINEAR PARAMETER OF ORDINAL LOG‐LINEAR MODELS

Beh¹,

Farver²

2010

Aus NZ J of Statistics

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Beh & Farver (2009) presented a description of non-iterative parameter estimation methods for ordinal log-linear models. Using the notation considered in our paper, the logarithm of the expected value of the (i, j)th cell frequency from the ordinal log-linear model iswhere φ is the common log-odds ratio of the contingency table. We demonstrated the use of Newton's method to calculate the MLE of the parameter. As an alternative, we also presented three direct, or non-iterative, methods to estimate the parameter. Central to the exposition was that the (i, j)th cell in the contingency table can be alternatively modelled byWhen u = 1 and v = 1, φ 11 is the measure of linear-by-linear association and has a similar interpretation to φ in (1). It was correctly stated that φ 11 from (2) may be calculated by

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supporting

confidence: 53%

Corrigendum: AN EVALUATION OF NON‐ITERATIVE METHODS FOR ESTIMATING THE LINEAR‐BY‐LINEAR PARAMETER OF ORDINAL LOG‐LINEAR MODELS

Beh¹,

Farver²

2010

Aus NZ J of Statistics

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show abstract

“…It failed because of the two zero cell values, although this problem was easily overcome by adding 0.05 to each cell. Beh & Davy (1998, 1999, 2004) indicated that BDNI estimation provides a satisfactory means of estimating the parameter φ. The findings discussed in confirm these initial results.…”

Section: Discussionmentioning

confidence: 99%

“…An alternative approach to parameter estimation for ordinal log‐linear models is to consider the non‐iterative, or direct, estimation procedure described by Beh & Davy (1998, 1999, 2004). These authors introduced a non‐iterative method of estimating the parameter φ and demonstrated, by way of applications, that the procedure produces very similar results obtained using Newton's method.…”

Section: The Basics Of Log‐linear Modelsmentioning

confidence: 99%

“…By considering , the linear‐by‐linear association can be quantified by which is the non‐iterative estimate that Beh & Davy (2004) described, designated here as the BD non‐iterative estimate (BDNI) of φ. These authors showed by way of an example that this expression works very well when compared with the iterative algorithms of Agresti (1984) and Haberman (1974).…”

Section: The Non‐iterative Estimation Proceduresmentioning

confidence: 99%

“…Recently, Beh & Davy (2004) proposed a method of estimating parameters from ordinal log‐linear models that is non‐iterative. They concluded by way of examples that their technique works as well as the iterative procedures of Agresti (1984) and Haberman (1974), but with the computational advantages that direct estimation methods have.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An Evaluation of Non‐iterative Methods for Estimating the Linear‐by‐linear Parameter of Ordinal Log‐linear Models

Beh¹,

Farver

2009

Aus NZ J of Statistics

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Parameter estimation for association and log-linear models is an important aspect of the analysis of cross-classified categorical data. Classically, iterative procedures, including Newton's method and iterative scaling, have typically been used to calculate the maximum likelihood estimates of these parameters. An important special case occurs when the categorical variables are ordinal and this has received a considerable amount of attention for more than 20 years. This is because models for such cases involve the estimation of a parameter that quantifies the linear-by-linear association and is directly linked with the natural logarithm of the common odds ratio. The past five years has seen the development of non-iterative procedures for estimating the linear-by-linear parameter for ordinal log-linear models. Such procedures have been shown to lead to numerically equivalent estimates when compared with iterative, maximum likelihood estimates. Such procedures also enable the researcher to avoid some of the computational difficulties that commonly arise with iterative algorithms. This paper investigates and evaluates the performance of three non-iterative procedures for estimating this parameter by considering 14 contingency tables that have appeared in the statistical and allied literature. The estimation of the standard error of the association parameter is also considered.

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The analysis of dependence for three ways contingency tables with ordinal variables: A case study of patient satisfaction data

Simonetti

Beh

D’Ambra

2009

Journal of Applied Statistics

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For many questionnaires and surveys in the marketing, business, and health disciplines, items often involve ordinal scales (such as the Likert scale and rating scale) that are associated in sometimes complex ways. Techniques such as classical correspondence analysis provide a simple graphical means of describing the nature of the association. However, the procedure does not allow the researcher to specify how one item may be associated with another, nor does the analysis allow for the ordinal structure of the scales to be reflected. This article presents a graphical approach that can help the researcher to study in depth the complex association of the items and reflect the structure of the items. We will demonstrate the applicability of this approach using data collected from a study that involves identifying major factors that influence the level of patient satisfaction in a Neapolitan hospital

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A Non-Iterative Alternative to Ordinal Log-Linear Models

Cited by 9 publications

References 22 publications

Corrigendum: AN EVALUATION OF NON‐ITERATIVE METHODS FOR ESTIMATING THE LINEAR‐BY‐LINEAR PARAMETER OF ORDINAL LOG‐LINEAR MODELS

Corrigendum: AN EVALUATION OF NON‐ITERATIVE METHODS FOR ESTIMATING THE LINEAR‐BY‐LINEAR PARAMETER OF ORDINAL LOG‐LINEAR MODELS

An Evaluation of Non‐iterative Methods for Estimating the Linear‐by‐linear Parameter of Ordinal Log‐linear Models

The analysis of dependence for three ways contingency tables with ordinal variables: A case study of patient satisfaction data

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