Regression Analysis of Multivariate Binary Response Variables Using Rasch‐Type Models and Finite‐Mixture Methods
TL;DR: This work examines the relationship between this model and several other models, gives a tractable formulation of the likelihood function and likelihood equations, presents an algorithm for maximum-likelihood estimation, and analyze marginal and conditional latent structures.
Abstract: A model is considered for the regression analysis of multivariate binary data such as repeated-measures data (for example, panel data) or multiple-indicators with measures of some underlying characteristic such as attitude or ability (for example, surveys or tests). The model is related to the usual Rasch model, the usual latent-class model, and other familiar models such as logistic regression. In addition to a regression specification, the model includes parameters that describe heterogeneity not accounted for by the predictors. In contrast to most other approaches, a nonparametric specification of the latent mixing distribution is used, leading to a formulation based on scaled latent classes. We examine the relationship between this model and several other models, give a tractable formulation of the likelihood function and likelihood equations, present an algorithm for maximum-likelihood estimation, and analyze marginal and conditional latent structures. The approach is illustrated with longitudinal data from the German Socioeconomic Panel.
Citations
More filters
••
TL;DR: In this paper, the authors consider how to construct summary indices (e.g., quality-of-life [QOL] indices) for a social unit that will be endorsed by a majority of its citizens.
Abstract: The authors consider how to construct summary indices (e.g., quality-of-life [QOL] indices) for a social unit that will be endorsed by a majority of its citizens. They assume that many social indicators are available to describe the social unit, but individuals disagree about the relative weights to be assigned to each social indicator. The summary index that maximizes agreement among citizens can then be derived, along with conditions under which an index will be endorsed by a majority in the social unit. The authors show that intuition greatly underestimates the extent of agreement among individuals, and it is often possible to construct a QOL index that most citizens agree with (at least in direction). In particular, they show that the equal-weighting strategy is privileged in that it minimizes disagreement among all possible individuals' weights. They demonstrate these propositions by calculating real QOL indices for two surveys of citizens' actual importance weights.
192 citations
01 Jan 2004
TL;DR: In this paper, a model for measuring the extent to which individuals with differing importance weights for the component indicators agree on a summary QOL index was proposed, and conditions under which an index will be endorsed by a majority of a social group were derived.
Abstract: We consider problems associated with the construction of summary indices for a social unit (eg, cities, states, nations) These problems are motivated by the question of how to construct a social well-being or Quality-of-Life (QOL) index that summarizes many social indicators, and that a majority of individuals can agree with We specify a model for measuring the extent to which individuals with differing importance weights for the component indicators agree on a summary QOL index, and derive conditions under which an index will be endorsed by a majority of a social group We show that, in every case, intuition greatly underestimates the extent of agreement among individuals who have different importance weights for the components Two types of QOL indices are distinguished: (1) those rating multiple social units (eg, cities, states, countries) in the same time period (cross-sectional data), and (2) those rating a single social unit on multiple time periods (time-series data) In the first case, we show that it is easy to create a QOL index on which most people in society agree In the second case, we show that it is more difficult, but define conditions under which it is possible In particular, we show that the equal-weighting strategy is privileged in that it minimizes disagreement among all possible individuals’ weights When the actual distribution of individuals’ weights is known, one can improve agreement further by using the mean weights applied by individuals Finally, we examine nationally representative surveys of importance weights and show that they meet the conditions for successful construction of a QOL index that will be endorsed by a majority of individuals in a country We conclude with recommendations for measuring weights and creating QOL indices that have high levels of support among individual members of social units
17 citations
••
TL;DR: This work proposes a new hierarchical Bayesian multivariate probit mixture model with variable selection accommodating such forms of choice heterogeneity and provides a consumer psychology application involving consideration to buy choices for intended consumers of large Sports Utility Vehicles.
2 citations
References
More filters
••
TL;DR: In this article, an extension of generalized linear models to the analysis of longitudinal data is proposed, which gives consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence.
Abstract: SUMMARY This paper proposes an extension of generalized linear models to the analysis of longitudinal data. We introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence. The estimating equations are derived without specifying the joint distribution of a subject's observations yet they reduce to the score equations for multivariate Gaussian outcomes. Asymptotic theory is presented for the general class of estimators. Specific cases in which we assume independence, m-dependence and exchangeable correlation structures from each subject are discussed. Efficiency of the proposed estimators in two simple situations is considered. The approach is closely related to quasi-likelih ood. Some key ironh: Estimating equation; Generalized linear model; Longitudinal data; Quasi-likelihood; Repeated measures.
17,111 citations
••
TL;DR: In this article, categorical data analysis was used for categorical classification of categorical categorical datasets.Categorical Data Analysis, categorical Data analysis, CDA, CPDA, CDSA
Abstract: categorical data analysis , categorical data analysis , کتابخانه مرکزی دانشگاه علوم پزشکی تهران
10,964 citations
•
01 Jan 1994
TL;DR: In this paper, a generalized linear model for longitudinal data and transition models for categorical data are presented. But the model is not suitable for categric data and time dependent covariates are not considered.
Abstract: 1. Introduction 2. Design considerations 3. Exploring longitudinal data 4. General linear models 5. Parametric models for covariance structure 6. Analysis of variance methods 7. Generalized linear models for longitudinal data 8. Marginal models 9. Random effects models 10. Transition models 11. Likelihood-based methods for categorical data 12. Time-dependent covariates 13. Missing values in longitudinal data 14. Additional topics Appendix Bibliography Index
7,156 citations
•
25 Jul 1986TL;DR: In this paper, the authors propose a homogeneity test for linear regression models (analysis of covariance) and show that linear regression with variable intercepts is more consistent than simple regression with simple intercepts.
Abstract: 1. Introduction 2. Homogeneity test for linear regression models (analysis of covariance) 3. Simple regression with variable intercepts 4. Dynamic models with variable intercepts 5. Simultaneous-equations models 6. Variable-coefficient models 7. Discrete data 8. Truncated and censored data 9. Cross-sectional dependent panel data 10. Dynamic system 11. Incomplete panel data 12. Miscellaneous topics 13. A summary view.
6,234 citations
••
TL;DR: This article discusses extensions of generalized linear models for the analysis of longitudinal data in which heterogeneity in regression parameters is explicitly modelled and uses a generalized estimating equation approach to fit both classes of models for discrete and continuous outcomes.
Abstract: This article discusses extensions of generalized linear models for the analysis of longitudinal data. Two approaches are considered: subject-specific (SS) models in which heterogeneity in regression parameters is explicitly modelled; and population-averaged (PA) models in which the aggregate response for the population is the focus. We use a generalized estimating equation approach to fit both classes of models for discrete and continuous outcomes. When the subject-specific parameters are assumed to follow a Gaussian distribution, simple relationships between the PA and SS parameters are available. The methods are illustrated with an analysis of data on mother's smoking and children's respiratory disease.
4,303 citations