Log-Linear Models for Frequency Tables with Ordered Classifications

Haberman, Shelby J.

doi:10.2307/2529224

Cited by 197 publications

(138 citation statements)

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“…Another popular iterative approach, and one adopted in this paper, is Newton's unidimensional method. Refer to Goodman [3], Haberman [4,10], and Agresti [5] for further details on the method. Here a brief description of Newton's method will be provided although a more detailed account on the algorithm used in this paper is provided in Beh and Farver [9].…”

Section: Mle (Newton's Unidimensional Method)mentioning

confidence: 99%

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

Beh

Farver

2012

ISRN Computational Mathematics

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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.

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Section: Mle (Newton's Unidimensional Method)mentioning

confidence: 99%

“…These include, but are not limited to, the contributions of Goodman [3], Haberman [4], Agresti [5, Appendix B], Nelder and Wedderburn [6], Galindo-Garre and Vermunt [7], and Aït-Sidi-Allal et al [8].…”

Section: The Ordinal Log-linear Modelmentioning

confidence: 99%

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

Beh

Farver

2012

ISRN Computational Mathematics

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“…Models of this kind have a long history in the literature on log-linear models (Haberman, 1974b) and variations have begun to appear with general diagnostic models (Xu & von Davier, 2007).…”

Section: The Polytomous Casementioning

confidence: 99%

Comparison of Multidimensional Item Response Models: Multivariate Normal Ability Distributions Versus Multivariate Polytomous Ability Distributions

Haberman

Davier

Lee

2008

ETS Research Report Series

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ETS, the ETS logo, and LISTENING. LEARNING. LEADING. are registered trademarks of Educational Testing Service (ETS). PRAXIS is a trademark of ETS.As part of its nonprofit mission, ETS conducts and disseminates the results of research to advance quality and equity in education and assessment for the benefit of ETS' constituents and the field. ETS Research Reports provide preliminary and limited dissemination of ETS research prior topublication. To obtain a PDF or a print copy of a report, please visit:http://www.ets.org/research/contact.html AbstractMultidimensional item response models can be based on multivariate normal ability distributions or on multivariate polytomous ability distributions. For the case of simple structure in which each item corresponds to a unique dimension of the ability vector, some applications of the two-parameter logistic model to empirical data are employed to illustrate how, at least for the example under study, comparable results can be achieved with either approach. Comparability involves quality of model fit as well as similarity in terms of parameter estimates and computational time required. In both cases, numerical work can be performed quite efficiently. In the case of the multivariate normal ability distribution, multivariate adaptive Gauss-Hermite quadrature can be employed to greatly reduce computational labor. In the case of a polytomous ability distribution, use of log-linear models permits efficient computations.

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“…This model differs from our baseline specification in equation (3) because Tj, refers to a priori values rather than freely estimated ones.30 We thus end up with a hybrid specification that stands somewhere between the association models of Haberman (1974) and those of Hout (1984). As indicated in equation (14), the row categories in our data are scaled with the standard unit scores of a linear-by-linear interaction model (see Haberman 1974;Duncan 1979;Goodman 1979a), whereas the column categories are scaled with external scores of the kind deployed by Hout (1984Hout ( , 1988, Hauser (1984), and others (Hout and Jackson 1986;SzelCnyi 1988).…”

Section: American Journal Of Sociologymentioning

confidence: 99%

Models for Describing the Underlying Structure of Sex Segregation

Charles¹,

Grusky²

1995

American Journal of Sociology

146

110

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This article introduces a structural approach to analyzing sex segregation data that rests on margin-free measures of the underlying association in sex-by-occupation arrays. The starting point for the analyses is a log-multiplicative model that is formally consistent with the conventional practice of summarizing cross-national variability in a single parameter pertaining to the overall strength of sex segregation. Under this baseline specification, the segregation regime is forced to take on the same basic shape in each country, with the only form of permissible variability being a uniform compression or expansion of the peaks and valleys characterizing the shared segregation profile. Although the latter model does not account for the cross-national variability in our illustrative data, it can be readily generalized in ways that both improve the fit and yield new insights into the structure and sources of sex segregation. These elaborated models can be used to examine the hierarchical structure of segregation, to identify the dominant "segregation profiles" in industrial countries, and to parse out the net residue of segregation at multiple levels of analysis.The study of occupational sex segregation appears to be entering its takeoff period. This can be seen, for example, in the recent resurgence of interest in describing how the structure of sex segregation varies across Earlier versions of this paper were presented to the American

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Log-Linear Models for Frequency Tables with Ordered Classifications

Cited by 197 publications

References 0 publications

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

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

Comparison of Multidimensional Item Response Models: Multivariate Normal Ability Distributions Versus Multivariate Polytomous Ability Distributions

Models for Describing the Underlying Structure of Sex Segregation

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