Refusal to Answer Specific Questions in a Survey: A Case Study

It is well known that non ignorable item non response may occur when the cause of the non response is the value of the latent variable of interest. In these cases, a refusal by a respondent to answer specific questions in a survey should be treated sometimes as a non ignorable item non response. The Rasch-Rasch model (RRM) is a new two-dimensional item response theory model for addressing non ignorable non response. This article demonstrates the use of the RRM on data from an Italian survey focused on assessment of healthcare workers’ knowledge about sudden infant death syndrome (that is, a context in which non response is presumed to be more likely among individuals with a low level of competence). We compare the performance of the RRM with other models within the Rasch model family that assume the unidimensionality of the latent trait. We conclude that this assumption should be considered unreliable for the data at hand, whereas the RRM provides a better fit of the data.     

Longitudinal data: different approaches in the context of item-response theory models

In this paper, some extended Rasch models are analyzed in the presence of longitudinal measurements of a latent variable. Two main approaches, multidimensional and multilevel, are compared: we investigate the different information that can be obtained from the latent variable, and we give advice on the use of the different kinds of models. The multidimensional and multilevel approaches are illustrated with a simulation study and with a longitudinal study on the health-related quality of life in terminal cancer patients.     

Latent Variable Models for Mixed Discrete and Continuous Outcomes

We propose a latent variable model for mixed discrete and continuous outcomes. The model accommodates any mixture of outcomes from an exponential family and allows for arbitrary covariate effects, as well as direct modelling of covariates on the latent variable. An EM algorithm is proposed for parameter estimation and estimates of the latent variables are produced as a by-product of the analysis. A generalized likelihood ratio test can be used to test the significance of covariates affecting the latent outcomes. This method is applied to birth defects data, where the outcomes of interest are continuous measures of size and binary indicators of minor physical anomalies. Infants who were exposed in utero to anticonvulsant medications are compared with controls.     

Selection of Latent Variables for Multiple Mixed‐outcome Models

Latent variable models have been widely used for modelling the dependence structure of multiple outcomes data. However, the formulation of a latent variable model is often unknown a priori, the misspecification will distort the dependence structure and lead to unreliable model inference. Moreover, multiple outcomes with varying types present enormous analytical challenges. In this paper, we present a class of general latent variable models that can accommodate mixed types of outcomes. We propose a novel selection approach that simultaneously selects latent variables and estimates parameters. We show that the proposed estimator is consistent, asymptotically normal and has the oracle property. The practical utility of the methods is confirmed via simulations as well as an application to the analysis of the World Values Survey, a global research project that explores peoples’ values and beliefs and the social and personal characteristics that might influence them.     

On the Convergence of the Monte Carlo Maximum Likelihood Method for Latent Variable Models

While much used in practice, latent variable models raise challenging estimation problems due to the intractability of their likelihood. Monte Carlo maximum likelihood (MCML), as proposed by Geyer & Thompson (1992 ), is a simulation-based approach to maximum likelihood approximation applicable to general latent variable models. MCML can be described as an importance sampling method in which the likelihood ratio is approximated by Monte Carlo averages of importance ratios simulated from the complete data model corresponding to an arbitrary value of the unknown parameter. This paper studies the asymptotic (in the number of observations) performance of the MCML method in the case of latent variable models with independent observations. This is in contrast with previous works on the same topic which only considered conditional convergence to the maximum likelihood estimator, for a fixed set of observations. A first important result is that when is fixed, the MCML method can only be consistent if the number of simulations grows exponentially fast with the number of observations. If on the other hand, is obtained from a consistent sequence of estimates of the unknown parameter, then the requirements on the number of simulations are shown to be much weaker.     

Testing list effects and diagnosing individual catchabilities in the Rasch model

The Rasch model is useful in the problem of estimating the population size from multiple incomplete lists. It is of great interest to tell whether there are list effects and whether individuals differ in their catchabilities. These two important model selection problems can be easily addressed conditionally. A conditional likelihood ratio test is used to evaluate the list effects and several graphical methods are used to diagnose the individual catchabilities, while neither the unknown population size nor the unknown mixing distribution of individual catchabilities is required to be estimated. Three epidemiological applications are used for illustration.     

Modeling Longitudinal Obesity Data with Intermittent Missingness Using a New Latent Variable Model

We propose a latent variable model for informative missingness in longitudinal studies which is an extension of latent dropout class model. In our model, the value of the latent variable is affected by the missingness pattern and it is also used as a covariate in modeling the longitudinal response. So the latent variable links the longitudinal response and the missingness process. In our model, the latent variable is continuous instead of categorical and we assume that it is from a normal distribution. The EM algorithm is used to obtain the estimates of the parameter we are interested in and Gauss–Hermite quadrature is used to approximate the integration of the latent variable. The standard errors of the parameter estimates can be obtained from the bootstrap method or from the inverse of the Fisher information matrix of the final marginal likelihood. Comparisons are made to the mixed model and complete-case analysis in terms of a clinical trial dataset, which is Weight Gain Prevention among Women (WGPW) study. We use the generalized Pearson residuals to assess the fit of the proposed latent variable model.     

The partial least squares-fix point method of estimating interdependent systems with latent variables

This paper describes a method for estimating the unknown parameters of an interdependent simultaneous equations model with latent variables. For each latent variable there may be single or multiple indicators. Estimation proceeds in three stages: first, estimates of the latent variables are constructed from the associated manifest indicators; second, treating the estimates as directly observed, fix-point estimates of the structural form parameters are obtained; third, the location parameters are estimated. The method involves only repeated application of ordinary least squares and no distributional assumptions are needed. The paper concludes with an empirical application of the method.     

ASSESSING FAMILIAL AGGREGATION WITH AN ORDINAL RESPONSE

A latent variable model is considered for the analysis of twin data with an ordinal response. The underlying latent multivariate normally distributed variable is expressed in terms of genetic and environmental effects, and the variance components associated with these effects are estimated. We illustrate this approach with analysis of the NHLBI Twin Study. Model assessment is ascertained by proposing a goodness-of-fit test for ordered categorical data. Extensions of this approach for the investigation of how genetic effects vary over time are discussed.     

A proposal for categorizing the severity of non uniform differential item functioning: The polytomous case

Abstract

Differential item functioning (DIF) is present when something about the characteristics of a test taker interferes with the relationship between ability and item response. Non uniform DIF (NUDIF) exists when there is interaction between ability level and group membership. The aim of this study is to propose guidelines to evaluate the severity of NUDIF, taking into account the family of Rasch models. The severity of NUDIF is evaluated trying to quantify the overall biasing impact of the presence in the test of NUDIF items, on the estimated measure of the latent trait of interest.     

Semiparametric transformation models with Bayesian P-splines

In this paper, we aim to develop a semiparametric transformation model. Nonparametric transformation functions are modeled with Bayesian P-splines. The transformed variables can be fitted to a general nonlinear mixed model, including linear or nonlinear regression models, mixed effect models, factor analysis models, and other latent variable models as special cases. Markov chain Monte Carlo algorithms are implemented to estimate transformation functions and unknown quantities in the model. The performance of the developed methodology is demonstrated with a simulation study. Its application to a real study on polydrug use is presented.     

A Latent-Variable Model of Quality Determination

Because of data difficulties, there has been little empirical work analyzing the determination of the quality of a firm's output. This article constructs a latent variable model for this problem that uses easily obtainable data. The model is developed from the relationship between the firm's input demand functions and reduced-form output functions, and it has a novel multiple indicator multiple cause (MIMIC) interpretation. The model also allows identification of an intercept, implying that an index of quality that is comparable across samples can be constructed. As an example, a latent variable model of nursing-home quality is estimated.     

A mixture latent variable model for modeling mixed data in heterogeneous populations and its applications

Latent variable models are widely used for jointly modeling of mixed data including nominal, ordinal, count and continuous data. In this paper, we consider a latent variable model for jointly modeling relationships between mixed binary, count and continuous variables with some observed covariates. We assume that, given a latent variable, mixed variables of interest are independent and count and continuous variables have Poisson distribution and normal distribution, respectively. As such data may be extracted from different subpopulations, consideration of an unobserved heterogeneity has to be taken into account. A mixture distribution is considered (for the distribution of the latent variable) which accounts the heterogeneity. The generalized EM algorithm which uses the Newton–Raphson algorithm inside the EM algorithm is used to compute the maximum likelihood estimates of parameters. The standard errors of the maximum likelihood estimates are computed by using the supplemented EM algorithm. Analysis of the primary biliary cirrhosis data is presented as an application of the proposed model.     

Mixture of latent trait analyzers for model-based clustering of categorical data

Model-based clustering methods for continuous data are well established and commonly used in a wide range of applications. However, model-based clustering methods for categorical data are less standard. Latent class analysis is a commonly used method for model-based clustering of binary data and/or categorical data, but due to an assumed local independence structure there may not be a correspondence between the estimated latent classes and groups in the population of interest. The mixture of latent trait analyzers model extends latent class analysis by assuming a model for the categorical response variables that depends on both a categorical latent class and a continuous latent trait variable; the discrete latent class accommodates group structure and the continuous latent trait accommodates dependence within these groups. Fitting the mixture of latent trait analyzers model is potentially difficult because the likelihood function involves an integral that cannot be evaluated analytically. We develop a variational approach for fitting the mixture of latent trait models and this provides an efficient model fitting strategy. The mixture of latent trait analyzers model is demonstrated on the analysis of data from the National Long Term Care Survey (NLTCS) and voting in the U.S. Congress. The model is shown to yield intuitive clustering results and it gives a much better fit than either latent class analysis or latent trait analysis alone.     

Accelerated life tests for log-normal series system with dependent masked data under Type-I progressive hybrid censoring

This article considers the constant stress accelerated life test for series system products, where independent log-normal distributed lifetimes are assumed for the components. Based on Type-I progressive hybrid censored and masked data, the expectation-maximization algorithm is applied to obtain the estimation for the unknown parameters, and the parametric bootstrap method is used for the standard deviation estimation. In addition, Bayesian approach combining latent variable with Gibbs sampling is developed. Further, the reliability functions of the system and components are estimated at use stress level. The proposed method is illustrated through a numerical example under different masking probabilities and censoring schemes.     

Influence Diagnostics for a Skew Extension of the Grubbs Measurement Error Model

Influence diagnostics methods are extended in this article to the Grubbs model when the unknown quantity x (latent variable) follows a skew-normal distribution. Diagnostic measures are derived from the case-deletion approach and the local influence approach under several perturbation schemes. The observed information matrix to the postulated model and Delta matrices to the corresponding perturbed models are derived. Results obtained for one real data set are reported, illustrating the usefulness of the proposed methodology.     

Identification of Multivariate Responders/Non-Responders Using Bayesian Growth Curve Latent Class Models

In this paper, we propose a multivariate growth curve mixture model that groups subjects based on multiple symptoms measured repeatedly over time. Our model synthesizes features of two models. First, we follow Roy and Lin (2000) in relating the multiple symptoms at each time point to a single latent variable. Second, we use the growth mixture model of Muthén and Shedden (1999) to group subjects based on distinctive longitudinal profiles of this latent variable. The mean growth curve for the latent variable in each class defines that class's features. For example, a class of "responders" would have a decline in the latent symptom summary variable over time. A Bayesian approach to estimation is employed where the methods of Elliott et al (2005) are extended to simultaneously estimate the posterior distributions of the parameters from the latent variable and growth curve mixture portions of the model. We apply our model to data from a randomized clinical trial evaluating the efficacy of Bacillus Calmette-Guerin (BCG) in treating symptoms of Interstitial Cystitis. In contrast to conventional approaches using a single subjective Global Response Assessment, we use the multivariate symptom data to identify a class of subjects where treatment demonstrates effectiveness. Simulations are used to confirm identifiability results and evaluate the performance of our algorithm. The definitive version of this paper is available at onlinelibrary.wiley.com.     

Sparse Change-point HAR Models for Realized Variance

Change-point time series specifications constitute flexible models that capture unknown structural changes by allowing for switches in the model parameters. Nevertheless most models suffer from an over-parametrization issue since typically only one latent state variable drives the switches in all parameters. This implies that all parameters have to change when a break happens. To gauge whether and where there are structural breaks in realized variance, we introduce the sparse change-point HAR model. The approach controls for model parsimony by limiting the number of parameters which evolve from one regime to another. Sparsity is achieved thanks to employing a nonstandard shrinkage prior distribution. We derive a Gibbs sampler for inferring the parameters of this process. Simulation studies illustrate the excellent performance of the sampler. Relying on this new framework, we study the stability of the HAR model using realized variance series of several major international indices between January 2000 and August 2015.     

Comparison of some goodness of fit tests for a single non-isotropic hypothetical principal component

Kshirsagar (1961) proposed a t e s t criterion for the null hypothesis that a covariance matrix with known smaller latent root of mu1tip1icity p?1 has its single non-isotropic principal component in a specified direction. It is shown that the power function of this criterion lacks some desirable properties. Another test criterion is proposed. The case in which the covariance matrix has an unknown smaller latent root of multi-plicity p?1 is also investigated.