Multiple membership multiple classification (MMMC) models

@article{Browne2001MultipleMM,
  title={Multiple membership multiple classification (MMMC) models},
  author={William J. Browne and Harvey Goldstein and Jon Rasbash},
  journal={Statistical Modeling},
  year={2001},
  volume={1},
  pages={103 - 124}
}
In the social and other sciences many data are collected with a known but complex underlying structure. Over the past two decades there has been an increase in the use of multilevel modelling techniques that account for nested data structures. Often however the underlying data structures are more complex and cannot be fitted into a nested structure. First, there are cross-classified models where the classifications in the data are not nested. Secondly, we consider multiple membership models… 

Figures and Tables from this paper

Multiple imputation in multiple classification and multiple-membership structures
In data systems with complexities due to nested/nonnested clustering and multiple-membership, missing values present an added analytic challenge to the statistical analyses. We develop model-based
Estimating multiple-membership logit models with mixed effects: indirect inference versus data cloning
TLDR
A DC algorithm specifically for multiple-membership logit models with random effects is implemented, and an auxiliary model with the same dimension of parameter space as the target model is proposed, which is particularly convenient to reach good estimates very fast.
Alternative estimating procedures for multiple membership logit models with mixed effects: indirect inference and data cloning
TLDR
This work implements a data cloning algorithm specific for the case of multiple-membership logit models with random effects, and proposes an auxiliary model having the same dimension of parameter space as the target model, which is particularly convenient to reach good estimates very fast.
Multiple membership multilevel models
Multiple membership multilevel models are an extension of standard multilevel models for non-hierarchical data that have multiple membership structures. Traditional multilevel models involve
Fitting logistic multilevel models with crossed random effects via Bayesian Integrated Nested Laplace Approximations: a simulation study
TLDR
A systematic simulation study to assess the performance of Integrated Nested Laplace Approximations with cross-classified binary data under different scenarios defined by the magnitude of the variances of the random effects and the number of observations.
Multiple Imputation with Survey Weights: A Multilevel Approach
TLDR
This work demonstrates the application of multiple imputation to a weighted analysis of factors predicting reception-year readiness in children in the UK Millennium Cohort Study and shows it has promising performance both in terms of coverage levels of the model parameters and bias of the associated Rubin’s variance estimates.
Profile-Likelihood Approach for Estimating Generalized Linear Mixed Models With Factor Structures
TLDR
The profile-likelihood approach for estimating complex models by maximum likelihood (ML) using standard software and minimal programming works whenever setting some of the parameters of the model to known constants turns the model into a standard model.
Analyzing multiple membership hierarchical data using PROC GLIMMIX
TLDR
This work illustrates the use of PROC GLIMMIX in fitting multiple membership models to hierarchical binary data.
...
...

References

SHOWING 1-10 OF 50 REFERENCES
Estimation in large cross random‐effect models by data augmentation
TLDR
A data augmentation approach to computational difficulties in which the algorithm is repeatedly fit an overlapping series of submodels, incorporating the missing terms in each submodel as ‘offsets’.
A Crossed Random Effects Model for Unbalanced Data With Applications in Cross-Sectional and Longitudinal Research
Hierarchical linear models have found widespread application when the data have a nested structure—for example, when students are nested within classrooms (a two-level nested structure) or students
Approximate inference in generalized linear mixed models
Statistical approaches to overdispersion, correlated errors, shrinkage estimation, and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed
Improved Approximations for Multilevel Models with Binary Responses
TLDR
Improved approximations are introduced for the estimation of generalized linear multilevel models where the response is a proportion which largely eliminates the biases in the situation described by Rodriguez and Goldman.
The calculation of posterior distributions by data augmentation
TLDR
If data augmentation can be used in the calculation of the maximum likelihood estimate, then in the same cases one ought to be able to use it in the computation of the posterior distribution of parameters of interest.
Multilevel Modelling of Health Statistics
TLDR
This book is a collection of chapters that intended to be “a selfcontained general reference for graduate and higher-level courses for those with a knowledge of basic regression modeling” (ibid.), each chapter focuses on practical applications in the health sciences.
Hierarchical generalised linear models: A synthesis of generalised linear models, random-effect models and structured dispersions
SUMMARY Hierarchical generalised linear models are developed as a synthesis of generalised linear models, mixed linear models and structured dispersions. We generalise the restricted maximum
Multilevel Modeling of Educational Data With Cross-Classification and Missing Identification for Units
This paper presents a method for handling educational data in which students belong to more than one unit at a given level, but there is missing information on the identification of the units to
Empirical Bayes estimates of age-standardized relative risks for use in disease mapping.
TLDR
A new approach using empirical Bayes estimation is proposed to map incidence and mortality from diseases such as cancer and the resulting estimators represent a weighted compromise between the SMR, the overall mean relative rate, and a local mean of the relative rate in nearby areas.
...
...