Francesco Bartolucci

A multivariate extension of the dynamic logit model for longitudinal data based on a latent markov heterogeneity structure

For the analysis of multivariate categorical longitudinal data, we propose an extension of the dynamic logit model. The resulting model is based on a marginal parameterization of the conditional distribution of each vector of response variables given the covariates, the lagged response variables, and a set of subject-specific parameters for the unobserved heterogeneity. The latter ones are assumed to follow a first-order Markov chain. For the maximum likelihood estimation of the model parameters, we outline an EM algorithm. The data analysis approach based on the proposed model is illustrated by a simulation study and an application to a dataset, which derives from the Panel Study on Income Dynamics and concerns fertility and female participation to the labor market.

Latent Markov model for longitudinal binary data: An application to the performance evaluation of nursing homes

Performance evaluation of nursing homes is usually accomplished by the repeated administration of questionnaires aimed at measuring the health status of the patients during their period of residence in the nursing home. We illustrate how a latent Markov model with covariates may effectively be used for the analysis of data collected in this way. This model relies on a not directly observable Markov process, whose states represent different levels of the health status. For the maximum likelihood estimation of the model we apply an EM algorithm implemented by means of certain recursions taken from the literature on hidden Markov chains. Of particular interest is the estimation of the effect of each nursing home on the probability of transition between the latent states. We show how the estimates of these effects may be used to construct a set of scores which allows us to rank these facilities in terms of their efficacy in takingcare of the health conditions of their patients. The method is used within an application based on data concerning a set of nursing homes located in the Region of Umbria, Italy, which were followed for the period 2003–2005. 1. Introduction. Both in European countries and in the United States, elderly people with chronic conditions or functional limitations can access nursing homes whenever they are no longer able or choose not to remain in their own homes. These facilities provide a diverse array of services such as housing, support systems, nursing and medical care for a sustained period of time. These services range from minimal personal assistance to virtually total care for the patients. The challenge for the nursing homes is to provide the opportunity for elderly people to live with dignity even though they may be physically or cognitively impaired. The quality of the assistance and the

A Class of Latent Marginal Models for Capture–Recapture Data With Continuous Covariates

We introduce a new family of latent class models for the analysis of capture–recapture data where continuous covariates are available. The present approach exploits recent advances in marginal parameterizations to model simultaneously, and conditionally on individual covariates, the size of the latent classes, the marginal probabilities of being captured by each list given the latent, and possible higher-order marginal interactions among lists conditionally on the latent. An EM algorithm for maximum likelihood estimation is described, and an expression for the expected information matrix is derived. In addition, a new method for computing confidence intervals for the size of the population having given covariate configurations is proposed and its asymptotic properties are derived. Applications to data on patients with human immunodeficiency virus, in the region of Veneto, Italy, and to new cases of cancer in Tuscany are discussed.

Positive Quadrant Dependence and Marginal Modeling in Two-Way Tables With Ordered Margins

For a collection of two-way tables, where subjects are cross-classified according to the same pair of ordinal categorical variables conditionally on the value of one or more discrete explanatory variables, we propose a general approach to likelihood inference that combines marginal modeling with fitting and testing of inequality constraints such as those implied by the assumption that one marginal distribution is stochastically larger than the other, positive dependence and stronger positive dependence. The approach is based on parameterizing bivariate conditional distributions with global logits and global log-odds ratios, and we provide a general framework for handling models defined by equality and inequality constraints on these parameters. In this way, such models as marginal homogeneity, proportional odds among row or columns margins, and Plackett distribution may be treated together with various models defined by inequality constraints on the same parameters, such as, for instance, those implied by the positive quadrant dependence. For this class of models, we define a Fisher scoring algorithm for computing maximum likelihood estimates and derive the asymptotic distribution of the likelihood ratio tests that turn out to be of the chi-bar squared type when inequalities are involved. When the main interest is on positive dependence, we derive tight bounds on the asymptotic distribution of these statistics that are independent of the marginal logits. These also may be removed by conditioning on one or both observed margins in each table, and we describe in detail how the approach may be adapted to these sampling schemes. Three applications to real datasets are discussed.

Assessment of School Performance Through a Multilevel Latent Markov Rasch Model

An extension of the latent Markov Rasch model is described for the analysis of binary longitudinal data with covariates when subjects are collected in clusters, such as students clustered in classes. For each subject, a latent process is used to represent the characteristic of interest (e.g., ability) conditional on the effect of the cluster to which he or she belongs. The latter effect is modeled by a discrete latent variable associated to each cluster. For the maximum likelihood estimation of the model parameters, an Expectation-Maximization algorithm is outlined. Through the analysis of a data set collected in the Lombardy Region (Italy), it is shown how the proposed model may be used for assessing the development of cognitive achievement. The data set is based on test scores in mathematics observed over 3 years on middle school students attending public and non-state schools. Manuscript received March 20, 2009 Revision received July 2, 2010 Accepted July 10, 2010

A Dynamic Model for Binary Panel Data With Unobserved Heterogeneity Admitting a √n‐Consistent Conditional Estimator

A model for binary panel data is introduced which allows for state dependence and unobserved heterogeneity beyond the effect of available covariates. The model is of quadratic exponential type and its structure closely resembles that of the dynamic logit model. However, it has the advantage of being easily estimable via conditional likelihood with at least two observations (further to an initial observation) and even in the presence of time dummies among the regressors. Copyright 2010 The Econometric Society.

The use of mixtures for dealing with non-normal regression errors

In many situations, the distribution of the error terms of a linear regression model departs significantly from normality. It is shown, through a simulation study, that an effective strategy to deal with these situations is fitting a regression model based on the assumption that the error terms follow a mixture of normal distributions. The main advantage, with respect to the usual approach based on the least-squares method is a greater precision of the parameter estimates and confidence intervals. For the parameter estimation we make use of the EM algorithm, while confidence intervals are constructed through a bootstrap method.

A discrete time event‐history approach to informative drop‐out in mixed latent Markov models with covariates

Mixed latent Markov (MLM) models represent an important tool of analysis of longitudinal data when response variables are affected by time-fixed and time-varying unobserved heterogeneity, in which the latter is accounted for by a hidden Markov chain. In order to avoid bias when using a model of this type in the presence of informative drop-out, we propose an event-history (EH) extension of the latent Markov approach that may be used with multivariate longitudinal data, in which one or more outcomes of a different nature are observed at each time occasion. The EH component of the resulting model is referred to the interval-censored drop-out, and bias in MLM modeling is avoided by correlated random effects, included in the different model components, which follow common latent distributions. In order to perform maximum likelihood estimation of the proposed model by the expectation-maximization algorithm, we extend the usual forward-backward recursions of Baum and Welch. The algorithm has the same complexity as the one adopted in cases of non-informative drop-out. We illustrate the proposed approach through simulations and an application based on data coming from a medical study about primary biliary cirrhosis in which there are two outcomes of interest, one continuous and the other binary.

Assessing user satisfaction in the era of user experience: comparison of the SUS, UMUX and UMUX-LITE as a function of product experience

Nowadays, practitioners extensively apply quick and reliable scales of user satisfaction as part of their user experience analyses to obtain well-founded measures of user satisfaction within time and budget constraints. However, in the human–computer interaction literature the relationship between the outcomes of standardized satisfaction scales and the amount of product usage has been only marginally explored. The few studies that have investigated this relationship have typically shown that users who have interacted more with a product have higher satisfaction. The purpose of this article was to systematically analyze the variation in outcomes of three standardized user satisfaction scales (SUS, UMUX, UMUX-LITE) when completed by users who had spent different amounts of time with a website. In two studies, the amount of interaction was manipulated to assess its effect on user satisfaction. Measurements of the three scales were strongly correlated and their outcomes were significantly affected by the amount of interaction time. Notably, the SUS acted as a unidimensional scale when administered to people who had less product experience but was bidimensional when administered to users with more experience. Previous findings of similar magnitudes for the SUS and UMUX-LITE (after adjustment) were replicated but did not show the previously reported similarities of magnitude for the SUS and the UMUX. Results strongly encourage further research to analyze the relationships of the three scales with levels of product exposure. Recommendations for practitioners and researchers in the use of the questionnaires are also provided.

A class of Multidimensional Latent Class IRT models for ordinal polytomous item responses

We propose a class of multidimensional Item Response Theory models for polytomously-scored items with ordinal response categories. This class extends an existing class of multidimensional models for dichotomously-scored items in which the latent abilities are represented by a random vector assumed to have a discrete distribution, with support points corresponding to different latent classes in the population. In the proposed approach, we allow for different parameterizations for the conditional distribution of the response variables given the latent traits, which depend on the type of link function and the constraints imposed on the item parameters. Moreover, we suggest a strategy for model selection that is based on a series of steps consisting of selecting specific features, such as the dimension of the model (number of latent traits), the number of latent classes, and the specific parameterization. In order to illustrate the proposed approach, we analyze a dataset from a study on anxiety and depression on a sample of oncological patients.