Models For Binary Data Research Articles

A Multivariate Randomized Response Model for Sensitive Binary Data

A new statistical method is proposed to combine the randomized response technique, probit modeling, and Bayesian analysis to analyze large-scale online surveys of multiple binary randomized responses. The proposed method is illustrated by analyzing sensitive dichotomous randomized responses on different types of drug administration error from nurses in a hospital cluster. A statistical challenge is that nurses’ true sensitive responses are unobservable because of a randomization scheme that protects their data privacy to answer the sensitive questions. Four main contributions of the paper are highlighted. The first is the construction of a generic statistical approach in modeling multivariate sensitive binary data collected from the randomized response technique. The second is studying the dependence of multivariate sensitive responses via statistical measures. The third is the calculation of an overall attitude score using sensitive responses. The last one is an illustration of the proposed statistical method for analyzing administration policies that potentially involve sensitive topics which are important to study but are not easily investigated via empirical studies. The particular healthcare example on drug administration policies demonstrated in this paper also presents a scientific way to elicit managerial strategies while protecting data privacy through analytics.

A likelihood-based boosting algorithm for factor analysis models with binary data

Statistical boosting represents a very effective method for fitting complex models, while performing variable selection and preventing overfitting at the same time. However, the available methods are not directly applicable to factor analysis models for binary data, since any gradient descent method is not able to move from the starting point with zero loadings. The proposed algorithm, exploiting the directions of negative curvature of the log-likelihood function, is able to escape from the regions of local non-convexity. The component-wise approach followed leads to a sparse solution, which has the advantage of facilitating the interpretation without requiring a posterior rotation of the loadings. The method also performs regularization of the estimates, hence reducing their mean square error. To lighten the computational burden of the inferential procedure, a suitable pseudolikelihood, called pairwise likelihood, is exploited. In addition, a group lasso penalty is considered in order to automatically select the number of latent variables included in the model. The good performance of the proposal is illustrated through a simulation study and a real-data example.

Recursive Computation of the Conditional Probability Function of the Quadratic Exponential Model for Binary Panel Data

Recursive Computation of the Conditional Probability Function of the Quadratic Exponential Model for Binary Panel Data

The Robustness of Conditional Logit for Binary Response Panel Data Models with Serial Correlation

Abstract We examine the conditional logit estimator for binary panel data models with unobserved heterogeneity. A key assumption used to derive the conditional logit estimator is conditional serial independence (CI), which is problematic when the underlying innovations are serially correlated. A Monte Carlo experiment suggests that the conditional logit estimator is not robust to violation of the CI assumption. We find that higher persistence and smaller time dimension both increase the magnitude of the bias in slope parameter estimates. We also compare conditional logit to unconditional logit, bias corrected unconditional logit, and pooled correlated random effects logit.

A Latent Class Model for Multivariate Binary Data Subject to Missingness

When researchers are interested in measuring social phenomena that cannot be measured using a single variable, the appropriate statistical tool to be used is a latent variable model. A number of manifest variables is used to define the latent phenomenon. The manifest variables may be incomplete due to different forms of non-response that may or may not be random. In such cases, especially when the missingness is nonignorable, it is inevitable to include a missingness mechanism in the model to obtain valid estimates for parameters. In social surveys, categorical items can be considered the most common type of variable. We thus propose a latent class model where two categorical latent variables are defined; one represents the latent phenomenon of interest, and another represents a respondent’s propensity to respond to survey items. All manifest items are considered to be categorical. The proposed model incorporates a missingness mechanism that accounts for forms of missingness that may not be random by allowing the latent response propensity class to depend on the latent phenomenon under consideration, given a set of covariates. The Expectation-Maximization (EM) algorithm is used for estimating the proposed model. The proposed model is used to analyze data from 2014 Egyptian Demographic and Health Survey (EDHS14). Missing data is artificially created in order to study results under the three types of missingness: missing completely at random (MCAR), missing at random (MAR), and missing not at random (MNAR).

SiGMoiD: A super-statistical generative model for binary data.

In modern computational biology, there is great interest in building probabilistic models to describe collections of a large number of co-varying binary variables. However, current approaches to build generative models rely on modelers' identification of constraints and are computationally expensive to infer when the number of variables is large (N~100). Here, we address both these issues with Super-statistical Generative Model for binary Data (SiGMoiD). SiGMoiD is a maximum entropy-based framework where we imagine the data as arising from super-statistical system; individual binary variables in a given sample are coupled to the same 'bath' whose intensive variables vary from sample to sample. Importantly, unlike standard maximum entropy approaches where modeler specifies the constraints, the SiGMoiD algorithm infers them directly from the data. Due to this optimal choice of constraints, SiGMoiD allows us to model collections of a very large number (N>1000) of binary variables. Finally, SiGMoiD offers a reduced dimensional description of the data, allowing us to identify clusters of similar data points as well as binary variables. We illustrate the versatility of SiGMoiD using multiple datasets spanning several time- and length-scales.

A modified expectation‐maximization algorithm for latent Gaussian graphical model

This paper considers the latent Gaussian graphical model, which extends the Gaussian graphical model to handle discrete data as well as mixed data with both continuous and discrete variables by assuming that discrete variables are generated by discretizing latent Gaussian variables. We propose a modified expectation‐maximization (EM) algorithm to estimate parameters in the latent Gaussian model for binary data. We also extend the proposed modified EM algorithm to the latent Gaussian model for mixed data. The conditional dependence structure can be consequently constructed by exploring the sparsity pattern of the precision matrix of the latent variables. We illustrate the performance of our proposed estimator through comprehensive numerical studies and an application to voting data of the United Nations General Assembly.

Some Observations in Likelihood Based Fitting of Longitudinal Models for Binary Data

Different models are used in practice for describing a binary lon- gitudinal data. In this paper we consider the joint probability models, the marginal models, and the combined models for describing such the best. The combined model consists of a joint probability model and a marginal model at two different levels. We present some striking empirical observa- tions on the closeness of the estimates and their standard errors for some parameters of the models considered in describing a from Fitzmaurice and Laird (1993) and consequently giving new insight from this data. We present the in a complete factorial arrangement with 4 factors at 2 levels. We introduce the concept of data representing a model completely and explain data balance as well as chance balance. We also consider the best model selection problem for describing this and use the Search Linear Model concepts known in Fractional Factorial Design research (Sri- vastava (1975)).

Some Observations in Likelihood Based Fitting of Longitudinal Models for Binary Data

Some Observations in Likelihood Based Fitting of Longitudinal Models for Binary Data

Confidence intervals for assessing equivalence of two treatments with combined unilateral and bilateral data

Responses from the paired organs are generally highly correlated in bilateral studies, statistical procedures ignoring the correlation could lead to incorrect results. Note the intraclass correlation in the study of combined unilateral and bilateral outcomes; 11 confidence intervals (CIs) including 7 asymptotic CIs and 4 Bootstrap-resampling CIs for assessing the equivalence of 2 treatments are derived under Rosner's correlated binary data model. Performance is evaluated with respect to the empirical coverage probability (ECP), the empirical coverage width (ECW) and the ratio of the mesial non-coverage probability to the non-coverage probability (RMNCP) via simulation studies. Simulation results show that (i) all CIs except for the Wald CI and the bias-corrected Bootstrap percentile CI generally produce satisfactory ECPs and hence are recommended; (ii) all CIs except for the bias-corrected Bootstrap percentile CI provide preferred RMNCPs and are more symmetrical; (iii) as the measurement of the dependence increases, the ECWs of all CIs except for the score CI and the profile likelihood CI show increasing patterns that look like linear, while there is no obvious pattern on the ECPs of all CIs except for the profile likelihood CI. A data set from an otolaryngologic study is used to illustrate the proposed methods.

Use of the Lagrange Multiplier Test for Assessing Measurement Invariance Under Model Misspecification.

This article studies the Type I error, false positive rates, and power of four versions of the Lagrange multiplier test to detect measurement noninvariance in item response theory (IRT) models for binary data under model misspecification. The tests considered are the Lagrange multiplier test computed with the Hessian and cross-product approach, the generalized Lagrange multiplier test and the generalized jackknife score test. The two model misspecifications are those of local dependence among items and nonnormal distribution of the latent variable. The power of the tests is computed in two ways, empirically through Monte Carlo simulation methods and asymptotically, using the asymptotic distribution of each test under the alternative hypothesis. The performance of these tests is evaluated by means of a simulation study. The results highlight that, under mild model misspecification, all tests have good performance while, under strong model misspecification, the tests performance deteriorates, especially for false positive rates under local dependence and power for small sample size under misspecification of the latent variable distribution. In general, the Lagrange multiplier test computed with the Hessian approach and the generalized Lagrange multiplier test have better performance in terms of false positive rates while the Lagrange multiplier test computed with the cross-product approach has the highest power for small sample sizes. The asymptotic power turns out to be a good alternative to the classic empirical power because it is less time consuming. The Lagrange tests studied here have been also applied to a real data set.

Mapping of the descriptive logic into RDF using binary relational data model

This paper is dedicated to the data integration problem. To establish relationships between data models is one of the key tasks in this solution. The descriptive logic and the relational data model are at the heart of a study. They have been used to create a mapping method on the theoretical level. The binary relational data model has been developed as a part of a mapping method. The previous studies are continued in this paper to prove on practice a mapping creation method between the descriptive logic and the binary relational data model. The method uses the binary relational data model as an integrating model. This paper continues the previous research of practical implementation of the mapping creation between the descriptive logic and the binary relational data model. The task to prove the theoretical mapping method on practice was formulated. A question how to map the binary relational data model into RDF-triples was considered. A brief overview of the R2R ML conversion tool was given. Triple maps were created to convert a conceptual information model of descriptive logic into RDF triplets with the help of R2R ML. Also, triples maps are described to convert basic mapping mechanisms into RDF with the help of R2R ML.

Conditional inference for binary panel data models with predetermined covariates

A fixed-effects logit model that accounts for feedback effects of the dependent variable on the covariates is proposed. The model is formulated by including leads of the predetermined covariates among the regressors and it is proved to satisfy certain theoretical properties under some regularity conditions on the distribution of the covariates. Estimation is based on the Conditional Maximum Likelihood (cml) method for the static logit model and the Pseudo-cml (pcml) method for the corresponding dynamic formulation. Both methods have good finite-sample properties even when the required regularity conditions are not satisfied. An application is provided about female labor supply where we jointly account for the predetermined number of children and husbands’ income. Differently from previous studies, it emerges that female employment history does not affect future fertility choices and the husband’s earnings, as no evidence of feedback effects is found.

Optimal shrinkage estimations in partially linear single-index models for binary longitudinal data

This paper focuses on the optimal estimation strategies of partially linear single-index models (PLSIM) for binary longitudinal data. Fitting model between the response and covariates may cause complexity and the linear terms may not be adequate to represent the relationship. In this situation, the PLSIM containing both linear and nonlinear terms is preferable. The objective of this paper is to develop optimal estimation strategies such as, pretest and shrinkage methods, for the analysis of binary longitudinal data under the PLSIM where some regression parameters are subject to restrictions. We estimate the nonparametric component using kernel estimating equations, and then use profile estimating equations to estimate the unrestricted and restricted estimators. To apply the pretest and shrinkage methods, we fit two models: one includes all covariates and the other restricts the regression parameters based on the auxiliary information. The unrestricted and restricted estimators are then combined optimally to get the pretest and shrinkage estimators. We also derive the asymptotic properties of the estimators in terms of biases and risks. Monte Carlo simulations are also conducted to examine the relative performance of the proposed estimators to the unrestricted estimator. An empirical application is also be used to illustrate the usefulness of our methodology.

Association of blood uric acid and cognitive impairment in oldest-old aged 80 years and older in 9 longevity areas of China

Objective: To examine the association of blood uric acid (UA) and cognitive impairment (CI) among oldest-old adults in China. Methods: Data was collected in 9 longevity areas of China from Healthy Aging and Biomarkers Cohort Study (HABCS) conducted during 2017-2018. Finally,1, 622 elderly aged 80 years and older with complete information on blood UA and cognitive function score were included in this study. Information on demographic characteristics, lifestyle, and health status were collected through questionnaire and physical examination. Venous blood samples of the participants were collected to test blood UA level. Cognitive impairment (CI) was assessed using the Chinese Mini-Mental State Examination (MMSE) according to personal educational level. Generalized Estimating Equations (GEE) model for binary data was used to analyze the association of blood UA and CI, and further compared the associations among different age and body mass index (BMI) groups. Results: Of the 1 622 oldest-old, the mean age was (92.2±8.1) years, 656 (40.4%) were male, the mean level of blood UA was (343.3±86.2) μmol/L, and 482 (29.7%) oldest-old had CI. Compared with the lowest quartile of UA, the risks of CI in the second, third and highest quartiles were gradually reduced, the corresponding ORs and 95%CI were 0.99 (0.71-1.33), 0.87 (0.68-0.94) and 0.69 (0.48-0.85), respectively; and the linear trend test was statistically significant (P<0.001). Subgroup analysis showed that the effects of higher UA associated with lower risk of CI were stronger in younger oldest-old (aged 80-89 years) and thinner group (BMI<24) (Pinteraction<0.05). Conclusions: Blood UA was negatively associated with the risk of having CI in the oldest-old among the nine longevity areas of China.

A case study of Stroke patients in Senegal: application of Generalized extreme value regression model

Logistic regression model is widely used in many studies to investigate the relationship between a binary response variable Y and a set of potential predictors X. The binary response may represent, for example, the occurrence of some outcome of interest (Y=1 if the outcome occurred and Y=0 otherwise). When the dependent variable Y represents a rare event, the logistic regression model shows relevant drawbacks. In order to overcome these drawbacks we propose the Generalized Extreme Value (GEV) regression model. In particularly, we suggest the quantile function of the GEV distribution as link function. Strokes are a serious pathology and a neurological emergency involving the vital prognosis and the functional prognosis. In Senegal, strokes account for more than 30% of hospitalizations and are responsible for nearly two thirds of mortality. In this work, we use the GVE regression model for binary data to determine the risk factors leading to stroke and to develop a predictive model of life-threatening outcomes in central Sénégal.

A case study of Stroke patients in Senegal: application of Generalized extreme value regression model

Logistic regression model is widely used in many studies to investigate the relationship between a binary response variable Y and a set of potential predictors X. The binary response may represent, for example, the occurrence of some outcome of interest (Y=1 if the outcome occurred and Y=0 otherwise). When the dependent variable Y represents a rare event, the logistic regression model shows relevant drawbacks. In order to overcome these drawbacks we propose the Generalized Extreme Value (GEV) regression model. In particularly, we suggest the quantile function of the GEV distribution as link function. Strokes are a serious pathology and a neurological emergency involving the vital prognosis and the functional prognosis. In Senegal, strokes account for more than 30% of hospitalizations and are responsible for nearly two thirds of mortality. In this work, we use the GVE regression model for binary data to determine the risk factors leading to stroke and to develop a predictive model of life-threatening outcomes in central Sénégal.

Local influence analysis of the 2PL IRT model for binary responses

Detecting influence is an important diagnostic stage in every statistical analysis. This paper examines the local influence of minor perturbations of the model and data for the two-parameter logistic item response model for binary data. By applying Cook's approach in the corresponding EM algorithm used to obtain the maximum likelihood estimate of the model parameters, the normal curvature and the conformal normal curvature - building blocks for obtaining the diagnostic measures – are computed. The methodology is illustrated with two real examples and an artificial one.

Implementation of mappings between the description logic and the binary relational data model on the RDF level

This paper is dedicated to the data integration problem. In article the task of practical implementation of mappings between description logic and a binary relational data model is discussed. This method was formulated earlier at a theoretical level. A practical technique to test mapping engines using RDF is provided in the current paper. To transform the constructs of the description logic ALC and its main extensions into RDF triplets the OWL 2-to-RDF mappings are used. To convert RDB to RDF graph, the R2R Mapping Language (R2R ML) was chosen. The mappings DL ALC and its main extensions to the RDF triplets are described in the publication. The mapping of the DL axioms into an RDF triplet also is considered in the publication. The main difficulties in describing DL-to-RDF transformations are given in the corresponding section. For each constructor of concepts and roles a corresponding expression in OWL 2 and its mapping into the RDF triplet. A schematic representation of the resulting RDF graph for each mapping is created. The paper also provides an overview of existing methods that relate to the use of RDF when mapping RDB to ontology and vice versa.

Automated Test Assembly for Large-Scale Standardized Assessments: Practical Issues and Possible Solutions

In testing situations, automated test assembly (ATA) is used to assemble single or multiple test forms that share the same psychometric characteristics, given a set of specific constraints, by means of specific solvers. However, in complex situations, which are typical of large-scale assessments, ATA models may be infeasible due to the large number of decision variables and constraints involved in the problem. The purpose of this paper is to formalize a standard procedure and two different strategies—namely, additive and subtractive—for overcoming practical ATA concerns with large-scale assessments and to show their effectiveness in two case studies. The MAXIMIN and MINIMAX ATA methods are used to assemble multiple test forms based on item response theory models for binary data. The main results show that the additive strategy is able to identify the specific constraints that make the model infeasible, while the subtractive strategy is a faster but less accurate process, which may not always be optimal. Overall, the procedures are able to produce parallel test forms with similar measurement precision and contents, and they minimize the number of items shared among the test forms. Further research could be done to investigate the properties of the proposed approaches under more complex testing conditions, such as multi-stage testing, and to blend the proposed approaches in order to obtain the solution that satisfies the largest set of constraints.