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The main purpose of this paper is to apply likelihood-based hypothesis testing procedures to a class of latent variable models for ordinal responses that allow for uncertain answers (Colombi et al. in Scand J Stat, 2018. https://doi.org/10.1111/sjos.12366). As these models are based on some assumptions, needed to describe different respondent behaviors, it is essential to discuss inferential issues without assuming that the tested model is correctly specified. By adapting the works of White (Econometrica 50(1):1–25, 1982) and Vuong (Econometrica 57(2):307–333, 1989), we are able to compare nested models under misspecification and then contrast the limiting distributions of Wald, Lagrange multiplier/score and likelihood ratio statistics with the classical asymptotic Chi-square to show the consequences of ignoring misspecification.

This paper considers the estimation of Kumbhakar et al. (J Prod Anal, doi:10.1007/s11123-012-0303-1, 2012) (KLH) four random components stochastic frontier (SF) model using MLE techniques. We derive the loglikelihood function of the model using results from the closed-skew normal distribution. Our Monte Carlo analysis shows that MLE is more efficient and less biased than the multi-step KLH estimator. Moreover, we obtain closedform expressions for the posterior expected values of the random effects, used to estimate short-run and long-run (in)efficiency as well as random-firm effects. The model is general enough to nest most of the currently used panel SF models; hence, its appropriateness can be tested. This is exemplified by analyzing empirical results from three different applications.

This work deals with the analysis of longitudinal ordinal responses. The novelty of the proposed approach is in modeling simultaneously the temporal dynamics of a latent trait of interest, measured via the observed ordinal responses, and the answering behaviors influenced by response styles, through hidden Markov models (HMMs) with two latent components. This approach enables the modeling of (i) the substantive latent trait, controlling for response styles; (ii) the change over time of latent trait and answering behavior, allowing also dependence on individual characteristics. For the proposed HMMs, estimation procedures, methods for standard errors calculation, measures of goodness of fit and classification, and full-conditional residuals are discussed. The proposed model is fitted to ordinal longitudinal data from the Survey on Household Income and Wealth (Bank of Italy) to give insights on the evolution of households financial capability.

The Probabilistic Graphical Models use graphs in order to represent the joint distribution of q variables. These models are useful for their ability to capture and represent the system of independence relationships among the variables involved, even when complex. This work concerns categorical variables and the possibility to represent symmetric and asymmetric dependences among categorical variables. For this reason we use the Chain Graphical Models proposed by Andersson, Madigan and Perlman (Scand. J. Stat. 28 (2001) 33-85), also known as Chain Graphical Models of type II (GMs II). The GMs II allow for symmetric relationships typical of log-linear models and, at the same time, asymmetric dependences typical of Graphical Models for Directed Acyclic Graphs. In general, GMs II are not smooth, however this work provides a subclass of smooth GMs II by parametrizing the probability function through marginal log-linear models. Furthermore, the proposed models are applied to a data-set from the European Value Study for the year 2008 (EVS (2010)).

A mixture of logit models is proposed that discriminates between responses to rating questions that are affected by a tendency to prefer middle or extremes of the scale regardless of the content of the item (response styles) and purely content-driven preferences. Explanatory variables are used to characterize the content-driven way of answering as well as the tendency to middle or extreme categories. The proposed model is extended to account for the presence of response styles in the case of several items, and the association among responses is described, both when they are content driven or dictated by response styles. In addition, stochastic orderings, related to the tendency to select middle or extreme categories, are introduced and investigated. A simulation study describes the effectiveness of the proposed model, and an application to a questionnaire on attitudes toward ethnic minorities illustrates the applicability of the modeling approach.

In responding to a rating question, an individual may give answers either according to his/her knowledge/awareness or to his/her level of indecision/uncertainty, typically driven by a response style. As ignoring this dual behavior may lead to misleading results, we define a multivariate model for ordinal rating responses by introducing, for every item and every respondent, a binary latent variable that discriminates aware from uncertain responses. Some independence assumptions among latent and observable variables characterize the uncertain behavior and make the model easier to interpret. Uncertain responses are modeled by specifying probability distributions that can depict different response styles. A marginal parameterization allows a simple and direct interpretation of the parameters in terms of association among aware responses and their dependence on explanatory factors. The effectiveness of the proposed model is attested through an application to real data and supported by a Monte Carlo study.

We contribute to the discussion of the paper of Piccolo and Simone by examining some issues concerning the multivariate extension of CUB and GEM models.

We show that a deeper insight into the relations among marginal processes of a multivariate Markov chain can be gained by testing hypotheses of Granger noncausality, contemporaneous independence and monotone dependence. Granger noncausality and contemporaneous independence conditions are read off a mixed graph, and the dependence of an univariate component of the chain on its parents—according to the graph terminology—is described in terms of stochastic dominance criteria. The examined hypotheses are proven to be equivalent to equality and inequality constraints on some parameters of a multivariate logistic model for the transition probabilities. The introduced hypotheses are tested on real categorical time series.

We extend Bergsma and Rudas (2002)'s hierarchical complete marginal parameterization to allow for logits and higher order effects of global and continuation type which may be more suitable with ordinal data. We introduce a general definition of marginal interaction parameters and show that this parameterization constitutes a link function so that linear models defined by equality and inequality constraints may be fitted and tested by extending the methods of Colombi and Forcina (2001). Computation and asymptotic properties of maximum likelihood estimators are discussed, and the asymptotic distribution of the likelihood ratio test is derived.

This paper introduces some new models of ecological inference within the context of estimation of voter transitions across elections. In particular, we assume that voters of a given party in a given occasion may be split into two latent types: faithful voters, who will certainly vote again for the same party and movers, who will reconsider their choice. Our models allow for unobserved heterogeneity across polling stations both in the weights of the two latent classes within each party and also when modelling the choice of unfaithful voters. Different ways of modelling the unobserved heterogeneity are considered by exploiting properties of the Dirichlet-multinomial distribution and the Brown Payne model of voting transitions can be seen as a special case within the class of models presented here. We discuss pseudo-maximum likelihood estimation and present an application to recent elections in Italy.