Results 1  10
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11
Multiple imputation for model checking: Completeddata plots with missing and latent data
 Biometrics
, 2005
"... Summary. In problems with missing or latent data, a standard approach is to first impute the unobserved data, then perform all statistical analyses on the completed dataset—corresponding to the observed data and imputed unobserved data—using standard procedures for completedata inference. Here, we ..."
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Cited by 23 (3 self)
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Summary. In problems with missing or latent data, a standard approach is to first impute the unobserved data, then perform all statistical analyses on the completed dataset—corresponding to the observed data and imputed unobserved data—using standard procedures for completedata inference. Here, we extend this approach to model checking by demonstrating the advantages of the use of completeddata model diagnostics on imputed completed datasets. The approach is set in the theoretical framework of Bayesian posterior predictive checks (but, as with missingdata imputation, our methods of missingdata model checking can also be interpreted as “predictive inference ” in a nonBayesian context). We consider the graphical diagnostics within this framework. Advantages of the completeddata approach include: (1) One can often check model fit in terms of quantities that are of key substantive interest in a natural way, which is not always possible using observed data alone. (2) In problems with missing data, checks may be devised that do not require to model the missingness or inclusion mechanism; the latter is useful for the analysis of ignorable but unknown data collection mechanisms, such as are often assumed in the analysis of sample surveys and observational studies. (3) In many problems with latent data, it is possible to check qualitative features of the model (for example, independence of two variables) that can be naturally formalized with the help of the latent data. We illustrate with several applied examples.
Generalizing the probability matrix decomposition model: an example of Bayesian model checking and model expansion
, 1998
"... Probability matrix decomposition (PMD) models can be used to explain observed associations between two sets of elements. More specifically, observed associations are modeled as a deterministic function of B latent Bernoulli variables that are realized for each element. To estimate the parameters of ..."
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Cited by 4 (4 self)
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Probability matrix decomposition (PMD) models can be used to explain observed associations between two sets of elements. More specifically, observed associations are modeled as a deterministic function of B latent Bernoulli variables that are realized for each element. To estimate the parameters of this model, a sample of the posterior distribution is computed with a data augmentation algorithm. The obtained posterior sample can also be used to assess the fit of the model with the technique of posterior predictive checks. In this paper a PMD model is applied to data on psychiatric diagnosis. In checking the model for this analysis, we focus on the appropriateness of the prior distribution for a set of latent parameters. Based on the posterior distribution for the values of the parameters corresponding to the observed data, we conclude that a relatively flat prior distribution is inappropriate. In order to solve this problem, a mixture prior density with two beta distributed components ...
A generic disjunctive/conjunctive decomposition model for naxy relations
 Journal of Mathematical Psychology
, 1999
"... This paper discusses a generic decomposition model that represents an arbitrary nary relation as a disjunctive or conjunctive combination of a number of nary component relations of a prespecified type. An important subclass of orderpreserving decompositions is defined and its properties are deriv ..."
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Cited by 4 (3 self)
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This paper discusses a generic decomposition model that represents an arbitrary nary relation as a disjunctive or conjunctive combination of a number of nary component relations of a prespecified type. An important subclass of orderpreserving decompositions is defined and its properties are derived. The generic model is shown to subsume various known models as special cases, including the models of Boolean factor analysis, hierarchical classes analysis, and disjunctiveconjunctive nonmetric factor analysis. Moreover, it also subsumes a broad range of new models as exemplified with a novel model for multidimensional parallelogram analysis and novel threeway extensions of nonmetric factor analysis. 1999 Academic Press
Clusterwise HICLAS: a generic modeling strategy to trace similarities and differences in multiblock binary data, Behav. Res. Methods 44
, 2012
"... Abstract In many areas of the behavioral sciences, different groups of objects are measured on the same set of binary variables, resulting in coupled binary object × variable data blocks. Take, as an example, success/failure scores for different samples of testees, with each sample belonging to a di ..."
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Cited by 4 (2 self)
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Abstract In many areas of the behavioral sciences, different groups of objects are measured on the same set of binary variables, resulting in coupled binary object × variable data blocks. Take, as an example, success/failure scores for different samples of testees, with each sample belonging to a different country, regarding a set of test items. When dealing with such data, a key challenge consists of uncovering the differences and similarities between the structural mechanisms that underlie the different blocks. To tackle this challenge for the case of a single data block, one may rely on HICLAS, in which the variables are reduced to a limited set of binary bundles that represent the underlying structural mechanisms, and the objects are given scores for these bundles. In the case of multiple binary data blocks, one may perform HICLAS on each data block separately. However, such an analysis strategy obscures the similarities and, in the case of many data blocks, also the differences between the blocks. To resolve this problem, we proposed the new Clusterwise HICLAS generic modeling strategy. In this strategy, the different data blocks are assumed to form a set of mutually exclusive clusters. For each cluster, different bundles are derived. As such, blocks belonging to the same cluster have the same bundles, whereas blocks of different clusters are modeled with different bundles. Furthermore, we evaluated the performance of Clusterwise HICLAS by means of an extensive simulation study and by applying the strategy to coupled binary data regarding emotion differentiation and regulation.
Probability Matrix Decomposition (PMD)...
"... check, psychometrics Probability Matrix Decomposition models may be used to model observed binary associations between two sets of elements. More specifically, to explain observed associations between two elements, it is assumed that B latent Bernoulli variables are realized for each element and th ..."
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check, psychometrics Probability Matrix Decomposition models may be used to model observed binary associations between two sets of elements. More specifically, to explain observed associations between two elements, it is assumed that B latent Bernoulli variables are realized for each element and that these variables are subsequently mapped into an observed data point according to a prespecified deterministic rule. In this paper, we present a fully Bayesian analysis for the PMD model making use of the Gibbs sampler. This approach is shown to yield three distinct advantages: (a) in addition to posterior mean estimates it yields (1 — a) % posterior intervals for the parameters, (b) it allows for an investigation of hypothesized indeterminacies in the model's parameters and for the visualization of the best possible reduction of the posterior distribution in a lowdimensional space, and (c) it allows for a broad range of goodnessoffit tests, making use of the technique of posterior predictive checks. To illustrate the approach, we applied the PMD model to opinions of respondents of different countries concerning the possibility of contracting AIDS in a specific situation.
Research Track Paper A General Model for Clustering Binary Data
"... Clustering is the problem of identifying the distribution of patterns and intrinsic correlations in large data sets by partitioning the data points into similarity classes. This paper studies the problem of clustering binary data. This is the case for market basket datasets where the transactions co ..."
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Clustering is the problem of identifying the distribution of patterns and intrinsic correlations in large data sets by partitioning the data points into similarity classes. This paper studies the problem of clustering binary data. This is the case for market basket datasets where the transactions contain items and for document datasets where the documents contain “bag of words”. The contribution of the paper is threefold. First a general binary data clustering model is presented. The model treats the data and features equally, based on their symmetric association relations, and explicitly describes the data assignments as well as feature assignments. We characterize several variations with different optimization procedures for the general model. Second, we also establish the connections between our clustering model with other existing clustering methods. Third, we also discuss the problem for determining the number of clusters for binary clustering. Experimental results show the effectiveness of the proposed clustering model.