A factor mixture analysis model for multivariate binary data

Multivariate binary data are widely collected in many disciplines, including in finance, psychometrics, and ecology. Often, many binary responses are driven by only a subset of predictors, and groups of binary responses may exhibit similar effects to a predictor. Motivated by a survey containing presence-absence records of 22 demersal fish species recorded across the U.S. Northeast shelf, we propose a novel method for simultaneous coefficient clustering and variable selection in multivariate binary data using a penalized Ising regression model. The Ising regression model formulates an explicit joint distribution for a binary response vector via main and pairwise interaction coefficients, where the former is modeled as a function of covariates and the latter captures conditional dependence relationships between responses. To cluster coefficients within each covariate, and encourage sparsity across both covariates and pairwise interaction coefficients, we propose to augment the Ising regression model with adaptive fused lasso and adaptive lasso penalties. Such a structured penalty to encourage simultaneous sparsity and groupings is aligned with goals of achieving sparse species-covariate relationships, and homogeneity of environmental responses across species, in the motivating demersal fish survey. Through a reparametrization, we show that the proposed estimator can be efficiently obtained by fitting a single, adaptive lasso logistic regression model. Simulation studies and an application to the demersal fish survey demonstrate competitive performance of the proposed method relative to several existing Ising regression models for multivariate binary data, and leads to an interpretable and parsimonious set of response-covariate relationships.

Conventional approaches for handling missingness in substance use disorder trials commonly rely upon a single deterministic "worst value" imputation that posits a perfect relationship between missingness and drug use ("missing value = presumed drug use"); this yields biased estimates of treatment effects and their standard errors. Instead, deterministic imputations should be replaced by probabilistic versions that encode researchers prior beliefs that those with missing data are more likely to be using drugs at those occasions. Motivated by this problem, we present a method for handling non-monotone missing binary data in longitudinal studies. Specifically, we consider a joint model that combines a not missing at random (NMAR) selection model with a generalized linear mixed model for longitudinal binary data. The selection model links the distribution of a missing outcome to the corresponding distribution of the outcome for those observed at that occasion via a fixed and known sensitivity parameter. The mixed model for longitudinal binary data assumes the random effects have bridge distributions; the latter yields regression parameters that have both subject-specific and marginal interpretations. This approach is completely transparent about what is being assumed about missing data and can be used as the basis for sensitivity analysis.

This paper focuses on the analysis of clustered multivariate binary data that arise from developmental toxicity studies. In these studies, pregnant mice are exposed to chemicals to assess possible adverse effects on developing fetuses. Multivariate binary outcomes arise when each fetus in a litter is assessed for the presence of malformations and/or low birth weight. We analyse the data using a multivariate exponential family model which is flexible in terms of allowing response rates to depend on cluster size. Maximum likelihood estimation of model parameters and the construction of score tests for dose effect are discussed. Copyright © 1999 John Wiley & Sons, Ltd.

Maximum likelihood estimation of an extended latent Markov model for clustered binary panel data

A pedigree model for binary data, motivated by log-linear modelling, has been developed to examine evidence for familial aggregation in disease status. From an epidemiological point of view a convenient way to express disease concordance between a pair of relatives is in terms of the odds ratio. For a rare disease this is almost equivalent to the relative risk of one family member being affected given that the other is affected, and in extending this to pedigrees it is assumed that these relative risks are multiplicative. In applying the model to the breast cancer data, pedigrees on a rare disease ascertained through an affected proband, it has been shown that estimation of concordance is dependent critically on knowing the probability that a sampled individual is affected. Therefore known population estimates of prevalence or cumulative risk, and an appropriate ascertainment correction, need to be invoked for the model to give proper estimates of disease concordance. The model is flexible in that measured ancillary risk factors, including genetic marker information, can be incorporated into the analysis. Therefore in future studies this information should be collected on all individuals, not just those affected. Suggested statistics for examining a fitted model are presented.

BackgroundGraphical models were identified as a promising new approach to modeling high-dimensional clinical data. They provided a probabilistic tool to display, analyze and visualize the net-like dependence structures by drawing a graph describing the conditional dependencies between the variables. Until now, the main focus of research was on building Gaussian graphical models for continuous multivariate data following a multivariate normal distribution. Satisfactory solutions for binary data were missing. We adapted the method of Meinshausen and Bühlmann to binary data and used the LASSO for logistic regression. Objective of this paper was to examine the performance of the Bolasso to the development of graphical models for high dimensional binary data. We hypothesized that the performance of Bolasso is superior to competing LASSO methods to identify graphical models.MethodsWe analyzed the Bolasso to derive graphical models in comparison with other LASSO based method. Model performance was assessed in a simulation study with random data generated via symmetric local logistic regression models and Gibbs sampling. Main outcome variables were the Structural Hamming Distance and the Youden Index.We applied the results of the simulation study to a real-life data with functioning data of patients having head and neck cancer.ResultsBootstrap aggregating as incorporated in the Bolasso algorithm greatly improved the performance in higher sample sizes. The number of bootstraps did have minimal impact on performance. Bolasso performed reasonable well with a cutpoint of 0.90 and a small penalty term. Optimal prediction for Bolasso leads to very conservative models in comparison with AIC, BIC or cross-validated optimal penalty terms.ConclusionsBootstrap aggregating may improve variable selection if the underlying selection process is not too unstable due to small sample size and if one is mainly interested in reducing the false discovery rate. We propose using the Bolasso for graphical modeling in large sample sizes.

This study focuses on relational data obtained through object relations. Traditional analysis of relational data often ignores attribute information. Therefore, Mikawa et al. proposed a method to estimate the latent structure of continuous relational data using a generative model and parameter estimation. However, real-world relational data can be discrete, and therefore, we propose a new model for binary relational data using a generative model based on the Bernoulli distribution and the Monte Carlo Expectation-Maximization (EM) algorithm for parameter estimation. We also clarify the effectiveness of the proposed model through simulation experiments using artificial data and real data.

In this study, we have considered the modeling and analyses of binary data. We modeled binary data with categorical predictors, using logistic regression to develop a statistical method. We found that ANOVA-type analyses often performed unsatisfactory, even when using arcsine-square-root trans-formations. We concluded that such methods are not appropriate, especially in cases where the fractions were close to 0 or 1. The logistic transformation of fraction data could be a promising alternative, but it is not desirable in the statistical sense. The major purpose of this paper is to demonstrate that logistic regression with an ANOVA-model like parameterization aids our understanding and provides a somewhat different, but sound, statistical background. We examined a simple real world example to show that we can efficiently test the significance of regression parameters, look for interactions, estimate related confidence intervals, and calculate the difference between the mean values of the referent and experimental subgroups. This paper demonstrates that precise confidence interval estimates can be obtained using the proposed ANOVA-model like approach. The method discussed here can be extended to any type of experimental fraction data analysis, particularly for experimental design.

This study proposes a new model in the family zero-inflated (ZI) binary models, it is called as a ZI Probit Bernoulli (ZIPBer) model. This model can be performed to model or simulate binary data that has an excessive amount of zero counts. At the framework of this research, we first introduce the classical formula, estimating equation (EE) and related functions for the ZIPBer model. Next, the results of asymptotic inferences for the ZIPBer model is studied based on the widespread regularity conditions. For the numerical illustrations, many simulation studies and a practical data set are executed in this paper. Specifically, we perform the fishing data set (FDS) to check the working effectiveness and robustness of the maximum likelihood estimation (MLE) approach in estimating parameters for the ZIPBer model. We also illustrate that this actual data set is more suitable for the proposed model: ZIPBer than other binary models such as logit, probit and ZIBer. The achieved results in this study are very unanimous with reality. It also illustrates that this is a dependable verification for us to know the solution as well as how to proceed to how to catch or take the most fish. This is the contribution of this work in terms of application. Finally, some crucial discussions and conclusions are given in this paper.

Bayesian Approaches to Copula Modelling

In this chapter we consider dependent data but move from the linear models of Chap.8 to general regression models. As in Chap.6, we consider generalized linear models (GLMs) and, more briefly, nonlinear models. We first give an outline of this chapter. In Sect.9.2 we describe three motivating datasets to which we return throughout the chapter. The GLMs discussed in Sect.6.3 can be extended to incorporate dependences in observations on the same unit; as with the linear model, an obvious way to carry out modeling in this case is to introduce unit-specific random effects. Within a GLM a natural approach is for these random effects to be included on the linear predictor scale. The resultant conditional models are known as generalized linear mixed models (GLMMs), and these are introduced in Sect.9.3. In Sects.9.4 and9.5 we describe likelihood and conditional likelihood methods of estimation, with Sect.9.6 devoted to a Bayesian treatment. Section9.7 illustrates some of the flexibility of GLMMs by describing and applying a particular model for spatial dependence. An alternative random effects specification, based on conjugacy, is described in Sect.9.8. An important approach to the modeling and analysis of dependent data that is philosophically different from the random effects formulation is via marginal models and generalized estimating equations (GEE), and these are the subject of Sect.9.9. In Sect.9.10, a second GEE approach is described in which the estimating equations for the mean are supplemented with a second set for the variances/covariances. For GLMMs, extra care must be taken with parameter interpretation, and Sect.9.11 discusses this issue, emphasizing how interpretation differs between conditional and marginal models. In PartII of the book, which focused on independent data, Chap.7 was devoted to models for binary data. For dependent data, models binary data are less well developed, and so we do not devote a complete chapter to their description. However, Sect.9.12 introduces the modeling of dependent binary data, and, subsequently, Sects.9.13 and 9.14 describe conditional (mixed) and marginal models for binary data. Section 9.15 considers how nonlinear models, as defined in Sect.6.10, can be extended to the dependent data case. For such models, many applications concentrate on inference for units, and so the introduction of random effects is again suggested. We refer to the resultant class of models as nonlinear mixed models (NLMMs). Section9.16 considers issues related to the parameterization of the nonlinear model. Inference for nonlinear mixed models via likelihood and Bayes approaches is covered in Sects.9.17 and9.18, while GEE is briefly considered in Sect.9.19. The assessment of assumptions for general regression models is described in Sect.9.20, with concluding comments contained in Sect.9.21. Additional references appear in Sect.9.22.

Multi-view intact space clustering

We consider measurement error in covariates in the marginal hazards model for multivariate failure time data. We explore the bias implications of normal additive measurement error without assuming a distribution for the underlying true covariate. To correct measurement-error-induced bias in the regression coefficient of the marginal model, we propose to apply the SIMEX procedure and demonstrate its large and small sample properties for both known and estimated measurement error variance. We illustrate this method using the Lipid Research Clinics Coronary Primary Prevention Trial data with total cholesterol as the covariate measured with error and time until angina and time until nonfatal myocardial infarction as the correlated outcomes of interest.

A visualization plot of a data set of molecular data is a useful tool for gaining insight into a set of molecules. In chemoinformatics, most visualization plots are of molecular descriptors, and the statistical model most often used to produce a visualization is principal component analysis (PCA). This paper takes PCA, together with four other statistical models (NeuroScale, GTM, LTM, and LTM-LIN), and evaluates their ability to produce clustering in visualizations not of molecular descriptors but of molecular fingerprints. Two different tasks are addressed: understanding structural information (particularly combinatorial libraries) and relating structure to activity. The quality of the visualizations is compared both subjectively (by visual inspection) and objectively (with global distance comparisons and local k-nearest-neighbor predictors). On the data sets used to evaluate clustering by structure, LTM is found to perform significantly better than the other models. In particular, the clusters in LTM visualization space are consistent with the relationships between the core scaffolds that define the combinatorial sublibraries. On the data sets used to evaluate clustering by activity, LTM again gives the best performance but by a smaller margin. The results of this paper demonstrate the value of using both a nonlinear projection map and a Bernoulli noise model for modeling binary data.

We develop a new class of spatial voting models for binary preference data that can accommodate both monotonic and non-monotonic response functions, and are more flexible than alternative “unfolding” models previously introduced in the literature. We then use these models to estimate revealed preferences for legislators in the U.S. House of Representatives and justices on the U.S. Supreme Court. The results from these applications indicate that the new models provide superior complexity-adjusted performance to various alternatives and that the additional flexibility leads to preferences’ estimates that more closely match the perceived ideological positions of legislators and justices.