A Multivariate Logistic Distance Model for the Analysis of Multiple Binary Responses

Worku, Hailemichael M.; Rooij, Mark de

doi:10.1007/s00357-018-9251-4

Cited by 4 publications

(8 citation statements)

References 38 publications

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“…In that case, (v r1m − v r0m ) = 1 for the dimensions to which response variable r pertains. For this constrained model, Worku and De Rooij (2018) showed that the parameters can be estimated using standard software for logistic regression by using a structured design matrix for the predictors. This paper describes them as members of a larger family of models, the MELODIC family.…”

Section: Constrained Modelsmentioning

confidence: 99%

“…Moreover, q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q D0 D1 M0 we lay a dimensional structure on the response space. A standard GEE model would be equal to our one-dimensional model, with the constraint that all responses are equally well discriminated (see Worku and De Rooij, 2018). Ziegler et al (1998) discuss a set-up where the predictor variables have different effects on each of the response variables.…”

Section: Related and Competing Approachesmentioning

confidence: 99%

“…The family extends the recently proposed multivariate logistic distance models (Worku and De Rooij, 2018) which built on earlier logistic distance models (Takane et al, 1987;Takane, 1987;De Rooij, 2009) and can be considered as examples in the "Gifi goes logistic" framework as laid out by De Leeuw (2005) and Evans (2014).…”

Section: Introductionmentioning

confidence: 96%

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The MELODIC family for simultaneous binary logistic regression in a reduced space

Rooij¹,

Groenen²

2021

Preprint

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Logistic regression is a commonly used method for binary classification. Researchers often have more than a single binary response variable and simultaneous analysis is beneficial because it provides insight into the dependencies among response variables as well as between the predictor variables and the responses. Moreover, in such a simultaneous analysis the equations can lend each other strength, which might increase predictive accuracy. In this paper, we propose the MELODIC family for simultaneous binary logistic regression modeling. In this family, the regression models are defined in a Euclidean space of reduced dimension, based on a distance rule. The model may be interpreted in terms of logistic regression coefficients or in terms of a biplot. We discuss a fast iterative majorization (or MM) algorithm for parameter estimation. Two applications are shown in detail: one relating personality characteristics to drug consumption profiles and one relating personality characteristics to depressive and anxiety disorders. We present a thorough comparison of our MELODIC family with alternative approaches for multivariate binary data.

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Section: Constrained Modelsmentioning

confidence: 99%

Section: Related and Competing Approachesmentioning

confidence: 99%

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The MELODIC family for simultaneous binary logistic regression in a reduced space

Rooij¹,

Groenen²

2021

Preprint

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“…The family extends the recently proposed multivariate logistic distance models [69] which built on earlier logistic distance models [20,57,59] and can be considered as examples in the "Gifi goes logistic" framework as laid out by De Leeuw [17] and Evans [24].…”

Section: Introductionmentioning

confidence: 99%

On Likelihood Ratio Tests for Dimensionality Selection

Takane

Heijden

2023

Behaviormetrics: Quantitative Approaches to Human Behavior

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This series covers in their entirety the elements of behaviormetrics, a term that encompasses all quantitative approaches of research to disclose and understand human behavior in the broadest sense. The term includes the concept, theory, model, algorithm, method, and application of quantitative approaches from theoretical or conceptual studies to empirical or practical application studies to comprehend human behavior. The Behaviormetrics series deals with a wide range of topics of data analysis and of developing new models, algorithms, and methods to analyze these data.The characteristics featured in the series have four aspects. The first is the variety of the methods utilized in data analysis and a newly developed method that includes not only standard or general statistical methods or psychometric methods traditionally used in data analysis, but also includes cluster analysis, multidimensional scaling, machine learning, corresponding analysis, biplot, network analysis and graph theory, conjoint measurement, biclustering, visualization, and data and web mining. The second aspect is the variety of types of data including ranking, categorical, preference, functional, angle, contextual, nominal, multi-mode multi-way, contextual, continuous, discrete, high-dimensional, and sparse data. The third comprises the varied procedures by which the data are collected: by survey, experiment, sensor devices, and purchase records, and other means. The fourth aspect of the Behaviormetrics series is the diversity of fields from which the data are derived, including marketing and consumer behavior, sociology, psychology, education, archaeology, medicine, economics, political and policy science, cognitive science, public administration, pharmacy, engineering, urban planning, agriculture and forestry science, and brain science.In essence, the purpose of this series is to describe the new horizons opening up in behaviormetrics -approaches to understanding and disclosing human behaviors both in the analyses of diverse data by a wide range of methods and in the development of new methods to analyze these data.

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“…When categorical response variables are considered, multivariate logistic regression models are usually appropriate. Examples include logistic regression models estimated using a generalized estimating equation (Zeger, Liang, & Albert, 1988) approach, or the multivariate logistic distance model (Worku & De Rooij, 2018) that considers a dimensional structure of the response variables.…”

Section: Introductionmentioning

confidence: 99%

A Latent Block Distance-Association Model for Profile by Profile Cross-Classified Categorical Data

Vera¹,

Rooij

2019

Multivariate Behavioral Research

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Distance association models constitute a useful tool for the analysis and graphical representation of cross-classified data in which distances between points inversely describe the association between two categorical variables. When the number of cells is large and the data counts result in sparse tables, the combination of clustering and representation reduces the number of parameters to be estimated and facilitates interpretation. In this article, a latent block distance-association model is proposed to apply block clustering to the outcomes of two categorical variables while the cluster centers are represented in a low dimensional space in terms of a distance-association model. This model is particularly useful for contingency tables in which both the rows and the columns are characterized as profiles of sets of response variables. The parameters are estimated under a Poisson sampling scheme using a generalized EM algorithm. The performance of the model is tested in a Monte Carlo experiment, and an empirical data set is analyzed to illustrate the model.

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A Multivariate Logistic Distance Model for the Analysis of Multiple Binary Responses

Cited by 4 publications

References 38 publications

The MELODIC family for simultaneous binary logistic regression in a reduced space

The MELODIC family for simultaneous binary logistic regression in a reduced space

On Likelihood Ratio Tests for Dimensionality Selection

A Latent Block Distance-Association Model for Profile by Profile Cross-Classified Categorical Data

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