Models For Binary Data Research Articles

Local Dependence Diagnostics in IRT Modeling of Binary Data

Local dependence (LD) for binary IRT models can be diagnosed using Chen and Thissen’s bivariate X2 statistic and the score test statistics proposed by Glas and Suárez-Falcón, and Liu and Thissen. Alternatively, LD can be assessed using general purpose statistics such as bivariate residuals or Maydeu-Olivares and Joe’s M r statistic. The authors introduce a new general statistic for assessing the source of model misfit, R2, and compare its performance to the above statistics using a simulation study. Results suggest that the bivariate and trivariate X2 statistics have unacceptable Type I error rates. As for the remaining statistics, if their computation involves the information matrix (bivariate residuals and score tests), they show good power; if not ( M r and R2), they lack power. Of course, the performance of the bivariate residuals and score tests depends on how the information matrix is approximated.

MOn the efficiency of some semi- and nonparametric kernel estimators in the modeling of binary response data

The semiparametric estimation procedure of binary response data is composed of two steps. In the first step, various semiparametric estimators are used for estimating the model parameters, whereas nonparametric regression type estimators are required in the second step to obtain the probability estimates dependent on the estimated model parameters in the first step. In this study, we have investigated the efficiency level of the Klein and Spady estimator which is widely used in the current literature in first step of the semiparametric modelling and the classical Nadaraya-Watson kernel estimator used in the second step of the estimation procedure of binary response data when the parametric model assumptions are satisfied. We have also wanted to see the variation in the estimates when the adaptive Nadaraya-Watson kernel estimator has been used instead of the classical estimator. So far, there has neither been any simulation study nor a study comparing those methods, analytically in Statistics literature. Therefore, a comprehensive simulation study has been conducted and data sets from the logistic distribution have been generated to display that success in practice. Four different sample sizes have been considered to see the differences along with the variation in the sample sizes. All findings have been assessed in terms of both the mean averaged square error and the correct classification rate criteria for ordinary, Pearson and deviance residuals, respectively. Additionally, a real data set has been used to demonstrate the effectiveness of the simulation results with the results in practice. The simulation results indicate that the semiparametric Klein and Spady estimations give considerable close results to the parametric counterparts when parametric model assumptions are satisfied. This obviously means that there is no significance difference between the parametric and the semiparametric approaches in case of satisfaction of the parametric model assumptions. Another considerable finding is that there is no clear superiority between classical and adaptive Nadaraya-Watson estimators. Key words: Nonparametric regression, kernel estimation, semiparametric estimation, binary data.

Experimental determination and modeling of excess molar volumes, viscosities and refractive indices of the binary systems (pyridine + 1-propanol, +1,2-propanediol, +1,3-propanediol, and +glycerol). New UNIFAC-VISCO parameters determination

Densities, viscosities and refractive indices of four binary systems consisting of pyridine with mono-, di-, and three- hydroxyl alcohols (1-propanol, 1,2-propanediol, 1,3-propanediol, and glycerol) were measured at eight temperatures (288.15, 293.15, 298.15, 303.15, 308.15, 313.15, 318.15, and 323.15)K and atmospheric pressure. From these data, excess molar volumes, viscosity deviations and deviations in refractive indices were calculated and fitted to the Redlich–Kister equation. The obtained results have been analyzed in terms of specific molecular interactions and mixing behavior between mixture components, taking into considerations effect of number and position of OH groups in polyols, as well as the influence of temperature on them. The modeling of VE binary data was performed with the Peng–Robinson–Stryjek–Vera cubic equation of state (PRSV CEOS) coupled with the van der Waals (vdW1) and CEOS/GE mixing rule introduced by Twu, Coon, Bluck, and Tilton (TCBT). The refractive indices of binary mixtures were predicted by various mixing rules and compared with experimental data. The viscosity modeling was done by two types of models: predictive UNIFAC-VISCO and correlative Teja–Rice and McAlister equations. In addition, due to the high importance of the prediction models, the experimental values of viscosity were used to determine the interaction parameters of following groups C6H5N–CH3, C6H5N–CH2, C6H5N–OH, C6H5N–CH, CH–CH3, CH–CH2, and CH–OH for their application in the UNIFAC-VISCO model.

Multilevel models for binary data

AbstractThis chapter discusses multilevel models for binary outcomes. Models for categorical data analysis and their multilevel extensions have been used extensively in biostatistics, psychometrics, sociology, and economics but are used somewhat less in other branches of the behavioral and social sciences. After a brief overview of models for binary data and a discussion of multilevel models, two example analyses on institutional data are presented.

A combined beta and normal random-effects model for repeated, overdispersed binary and binomial data

Non-Gaussian outcomes are often modeled using members of the so-called exponential family. Notorious members are the Bernoulli model for binary data, leading to logistic regression, and the Poisson model for count data, leading to Poisson regression. Two of the main reasons for extending this family are (1) the occurrence of overdispersion, meaning that the variability in the data is not adequately described by the models, which often exhibit a prescribed mean-variance link, and (2) the accommodation of hierarchical structure in the data, stemming from clustering in the data which, in turn, may result from repeatedly measuring the outcome, for various members of the same family, etc. The first issue is dealt with through a variety of overdispersion models, such as, for example, the beta-binomial model for grouped binary data and the negative-binomial model for counts. Clustering is often accommodated through the inclusion of random subject-specific effects. Though not always, one conventionally assumes such random effects to be normally distributed. While both of these phenomena may occur simultaneously, models combining them are uncommon. This paper starts from the broad class of generalized linear models accommodating overdispersion and clustering through two separate sets of random effects. We place particular emphasis on so-called conjugate random effects at the level of the mean for the first aspect and normal random effects embedded within the linear predictor for the second aspect, even though our family is more general. The binary and binomial cases are our focus. Apart from model formulation, we present an overview of estimation methods, and then settle for maximum likelihood estimation with analytic-numerical integration. The methodology is applied to two datasets of which the outcomes are binary and binomial, respectively.

A factor mixture analysis model for multivariate binary data

The paper proposes a latent variable model for binary data coming from an unobserved heterogeneous population. The heterogeneity is taken into account by replacing the traditional assumption of Gaussian distributed factors by a finite mixture of multivariate Gaussians. The aim of the proposed model is twofold: it allows to achieve dimension reduction when the data are dichotomous and, simultaneously, it performs model based clustering in the latent space. Model estimation is obtained by means of a maximum likelihood method via a generalized version of the EM algorithm. In order to evaluate the performance of the model a simulation study and two real applications are illustrated.

GMM versus GQL inferences in semiparametric linear dynamic mixed models

Linear dynamic mixed models are commonly used for continuous panel data analysis in economic statistics. There exists generalized method of moments (GMM) and generalized quasi-likelihood (GQL) inferences for binary and count panel data models, the GQL estimation approach being more efficient than the GMM approach. The GMM and GQL estimating equations for the linear dynamic mixed model can not, however, be obtained from the respective estimating equations under the nonlinear models for binary and count data. In this paper, we develop the GMM and GQL estimation approaches for the linear dynamic mixed models and demonstrate that the GQL approach is more efficient than the GMM approach, also under such linear models. This makes the GQL approach uniformly more efficient than the GMM approach in estimating the parameters of both linear and nonlinear dynamic mixed models.

Bayesian multiple comparison of models for binary data with inequality constraints

In this paper we consider generalized linear models for binary data subject to inequality constraints on the regression coefficients, and propose a simple and efficient Bayesian method for parameter estimation and model selection by using Markov chain Monte Carlo (MCMC). In implementing MCMC, we introduce appropriate latent variables and use a simple approximation of a link function, to resolve computational difficulties and obtain convenient forms for full conditional posterior densities of elements of parameters. Bayes factors are computed via the Savage-Dickey density ratios and the method of Oh (Comput. Stat. Data Anal. 29:411---427, 1999), for which posterior samples from the full model with no degenerate parameter and the full conditional posterior densities of elements are needed. Since it uses one set of posterior samples from the full model for any model in consideration, it performs simultaneous comparison of all possible models and is very efficient compared with other model selection methods which require one to fit all candidate models. A simulation study shows that significant improvements can be made by taking the constraints into account. Real data on purchase intention of a product subject to order constraints is analyzed by using the proposed method. The analysis results show that there exist some price changes which significantly affect the consumer behavior. The results also show the importance of simultaneous comparison of models rather than separate pairwise comparisons of models since the latter may yield misleading results from ignoring possible correlations between parameters.

Pseudo conditional maximum likelihood estimation of the dynamic logit model for binary panel data

We show how the dynamic logit model for binary panel data may be approximated by a quadratic exponential model. Under the approximating model, simple sufficient statistics exist for the subject-specific parameters introduced to capture the unobserved heterogeneity between subjects. The latter must be distinguished from the state dependence which is accounted for by including the lagged response variable among the regressors. By conditioning on the sufficient statistics, we derive a pseudo conditional likelihood estimator of the structural parameters of the dynamic logit model, which is simple to compute. Asymptotic properties of this estimator are studied in detail. Simulation results show that the estimator is competitive in terms of efficiency with estimators recently proposed in the econometric literature.

Estimating vaccination coverage for the trivalent measles–mumps–rubella vaccine from trivariate serological data

The effectiveness of childhood immunization programs depends on the vaccination coverage actually achieved. Routinely collected coverage data are not always available, and comparability between countries is often compromised because of different data collection methods. In 2000, Gay developed a method to estimate trivalent vaccination coverage from readily available trivariate serological data on the basis of parametric assumptions related to the rate of seroconversion for each vaccine component and probabilities of natural exposure to infection. Gay's work was indirectly published in a paper by Altmann and Altmann, who derived exact solutions for the parameters on the basis of Gay's modeling equations. In this paper, we propose a general likelihood-based marginal model framework to extend Gay's model by relaxing two of its main assumptions. We use the Bahadur model for trivariate binary data to explicitly account for an association between the disease-specific exposure probabilities. We fit several correlation structures to measles, mumps, and rubella serology from Belgium and Ireland. For both countries, we estimate a small positive pairwise exposure correlation, which improves the fit to the data. However, the effect on the estimated vaccination coverage and its associated variability is fairly moderate. For both Belgium and Ireland, all models reveal that the vaccination coverage achieved during the first 15 years since the introduction of measles, mumps, and rubella immunization is insufficient to eliminate measles.

Graphical modeling of binary data using the LASSO: a simulation study

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.

Fault diagnosis and comparing risk for the steel coil manufacturing process using statistical models for binary data

Advanced statistical models can help industry to design more economical and rational investment plans. Fault detection and diagnosis is an important problem in continuous hot dip galvanizing. Increasingly stringent quality requirements in the automotive industry also require ongoing efforts in process control to make processes more robust. Robust methods for estimating the quality of galvanized steel coils are an important tool for the comprehensive monitoring of the performance of the manufacturing process. This study applies different statistical regression models: generalized linear models, generalized additive models and classification trees to estimate the quality of galvanized steel coils on the basis of short time histories. The data, consisting of 48 galvanized steel coils, was divided into sets of conforming and nonconforming coils. Five variables were selected for monitoring the process: steel strip velocity and four bath temperatures.The present paper reports a comparative evaluation of statistical models for binary data using Receiver Operating Characteristic (ROC) curves. A ROC curve is a graph or a technique for visualizing, organizing and selecting classifiers based on their performance. The purpose of this paper is to examine their use in research to obtain the best model to predict defective steel coil probability. In relation to the work of other authors who only propose goodness of fit statistics, we should highlight one distinctive feature of the methodology presented here, which is the possibility of comparing the different models with ROC graphs which are based on model classification performance. Finally, the results are validated by bootstrap procedures.

An Exponential Class of Dynamic Binary Choice Panel Data Models with Fixed Effects

This paper develops a model for dynamic binary choice panel data that allows for unobserved heterogeneity to be arbitrarily correlated with covariates. The model is of the exponential type. We derive moment conditions that enable us to eliminate the unobserved heterogeneity term and at the same time to identify the parameters of the model. We then propose GMM estimators that are consistent and asymptotically normally distributed at the root-N rate. We also study the conditional likelihood approach, which can only identify the effect of state dependence in our case. Monte Carlo experiments demonstrate the finite sample performance of our GMM estimators.

On Selecting Spatial-Temporal Autologistic Regression Models for Binary Lattice Data

On Selecting Spatial-Temporal Autologistic Regression Models for Binary Lattice Data

An Exponential Class of Dynamic Binary Choice Panel Data Models with Fixed Effects

An Exponential Class of Dynamic Binary Choice Panel Data Models with Fixed Effects

Effective detection methods for medium-sized ground-dwelling mammals: a comparison between infrared digital cameras and hair tunnels

Context Conservation planning for threatened species depends on improved knowledge of the whereabouts of critical populations and thus the development of optimal detection methods. Aims To compare the effectiveness of infrared cameras and hair tunnels for detecting small to medium-sized ground-dwelling mammals in south-eastern Australian forests. Methods Reconyx PC90 cameras were paired with Handiglaze hair tunnels at 110 stations in south-eastern New South Wales. All devices were baited using rolled oats, peanut butter and pistachio essence and left in situ for a minimum duration of 30 days. Camera detection data were analysed for the first 15 and 30 days, whereas hair-tunnel detection data were analysed for the entire duration of deployment. Linear mixed models with site as a random effect and device as a fixed effect were developed for mammal species richness. Linear mixed logistic regression models for binary data were developed for detection probabilities of five taxa of interest, namely, Isoodon, Perameles, Potorous, Trichosurus and Wallabia. Key results Hair tunnels detected eight mammal species, whereas cameras detected 18 species. Modelled detection rates using cameras were 3.16 ± 0.21 species per site after 15 days and 4.24 ± 0.23 species per site after 30 days, whereas hair tunnels detected 0.34 ± 0.21 species over the entire deployment. Cameras were therefore approximately 9–12 times better at measuring mammal richness than were hair tunnels, depending on survey duration. In all calculations, the probability of detecting the five taxa of interest was significantly greater using cameras than using hair tunnels. Conclusions Infrared cameras and hair tunnels offer ethical advantages over direct detection methods such as cage trapping for small to medium-sized ground-dwelling mammals. Cameras also offer practical benefits because they work for protracted periods, without frequent checking by field researchers. Cameras are more effective at detecting a wide range of species than are hair tunnels and are significantly better for detecting the taxa we examined. Unlike hair tunnels, cameras sometimes allow for the identification of individual animals, and provide information about frequency of habitat use, reproductive status and aspects of behaviour. Implications On a unit by unit basis, infrared cameras are a far more efficient way to census a broad spectrum of ground-dwelling mammals than are hair tunnels.

A Predictive Model for Daily Inoculum Levels ofGibberella zeaein Passo Fundo, Brazil

The deposition of spores ofGibberella zeae, the causal agent ofFusariumhead blight of wheat, was monitored during 2008–2011, in Passo Fundo, RS, Brazil. The sampling was carried out in a 31-day period around wheat flowering. The numbers of colonies formed were related to meteorological variables. In this study, a hierarchical autoregressive binary data model was used. The model relates a binary response variable to potential covariates while accounting for dependence over discrete time points. This paper proposes an approach for both model parameter inference and prediction at future time points using the Markov chain Monte Carlo (MCMC). The developed model appeared to have a high degree of accuracy and may have implications in the disease control and risk-management planning.

Bayesian Approaches to Copula Modelling

Copula models have become one of the most widely used tools in the applied modelling of multivariate data. Similarly, Bayesian methods are increasingly used to obtain efficient likelihood-based inference. However, to date, there has been only limited use of Bayesian approaches in the formulation and estimation of copula models. This article aims to address this shortcoming in two ways. First, to introduce copula models and aspects of copula theory that are especially relevant for a Bayesian analysis. Second, to outline Bayesian approaches to formulating and estimating copula models, and their advantages over alternative methods. Copulas covered include Archimedean, copulas constructed by inversion, and vine copulas; along with their interpretation as transformations. A number of parameterisations of a correlation matrix of a Gaussian copula are considered, along with hierarchical priors that allow for Bayesian selection and model averaging for each parameterisation. Markov chain Monte Carlo sampling schemes for fitting Gaussian and D-vine copulas, with and without selection, are given in detail. The relationship between the prior for the parameters of a D-vine, and the prior for a correlation matrix of a Gaussian copula, is discussed. Last, it is shown how to compute Bayesian inference when the data are discrete-valued using data augmentation. This approach generalises popular Bayesian methods for the estimation of models for multivariate binary and other ordinal data to more general copula models. Bayesian data augmentation has substantial advantages over other methods of estimation for this class of models.

A combined overdispersed and marginalized multilevel model

Overdispersion and correlation are two features often encountered when modeling non-Gaussian dependent data, usually as a function of known covariates. Methods that ignore the presence of these phenomena are often in jeopardy of leading to biased assessment of covariate effects. The beta-binomial and negative binomial models are well known in dealing with overdispersed data for binary and count data, respectively. Similarly, generalized estimating equations (GEE) and the generalized linear mixed models (GLMM) are popular choices when analyzing correlated data. A so-called combined model simultaneously acknowledges the presence of dependency and overdispersion by way of two separate sets of random effects. A marginally specified logistic-normal model for longitudinal binary data which combines the strength of the marginal and hierarchical models has been previously proposed. These two are brought together to produce a marginalized longitudinal model which brings together the comfort of marginally meaningful parameters and the ease of allowing for overdispersion and correlation. Apart from model formulation, estimation methods are discussed. The proposed model is applied to two clinical studies and compared to the existing approach. It turns out that by explicitly allowing for overdispersion random effect, the model significantly improves.

A model-based approach for the analysis of the calibration of probability judgments

AbstractThe calibration of probability or confidence judgments concerns the association between the judgments and some estimate of the correct probabilities of events. Researchers rely on estimates using relative frequencies computed by aggregating data over observations. We show that this approach creates conceptual problems, and may result in the confounding of explanatory variables or unstable estimates. To circumvent these problems we propose using probability estimates obtained from statistical models—specifically mixed models for binary data—in the analysis of calibration. We illustrate this methodology by re-analyzing data from a published study and comparing the results from this approach to those based on relative frequencies. The model-based estimates avoid problems with confounding variables and provided more precise estimates, resulting in better inferences.