Inferential Issues Research Articles

Comment on: The class of CUB models: statistical foundations, inferential issues and empirical evidence

Comment on: The class of CUB models: statistical foundations, inferential issues and empirical evidence

Discussion of The class of CUB models: statistical foundations, inferential issues and empirical evidence

This discussion focuses on time series applications of the CUB class of models, such that the key underlying parameters, namely the shifted binomial probability and the mixing probability, vary over time according to a measurable or latent variable.

Discussion of “The class of cub models: statistical foundations, inferential issues and empirical evidence” by Domenico Piccolo and Rosaria Simone

In this paper we discuss the article “The class of CUB models: statistical foundations, inferential issues and empirical evidence” by Domenico Piccolo e Rosaria Simone. The main considered topic is the decision process that, according to the CUB paradigm, leads the respondent to express a rating about a latent trait on a given ordinal scale. We discuss a generalized formalization of this decision process, comprising the basic CUB model, some already existing extensions and possible future developments.

Discussion of ‘The class of CUB models: statistical foundations, inferential issues and empirical evidence’ by Domenico Piccolo and Rosaria Simone

In this note we briefly discuss the structure of CUB models and their interpretation. Furthermore, we elaborate some issues related to the comparison of CUB models with mainstream approaches, focusing on generalized linear models for univariate ordinal responses and classical latent variable models for multivariate ordinal responses.

Discussion of “The class of CUB models: statistical foundations, inferential issues and empirical evidence”

We focus on on the multivariate extensions of CUB/GEM models. The interest of rating surveys is rarely focused on a single item or on a single aspect of an item. Respondents are often requested to express their opinion on different aspects of an issue and in such cases it is not negligible the roleof the interdependence of the answers of the same individual. With this aim in mind, we comment some existing classes of multivariate CUB models and present the advantages of a recent proposal.

The class of CUB models: statistical foundations, inferential issues and empirical evidence

The class of CUB models: statistical foundations, inferential issues and empirical evidence

The class of cub models: statistical foundations, inferential issues and empirical evidence

This paper discusses a general framework for the analysis of rating and preference data that is rooted on a class of mixtures of discrete random variables. These models have been extensively studied and applied in the last 15 years thanks to a flexible and parsimonious parametrization of data generating process and to prompt interpretation of results. The approach considers the final response as the combination of feeling and uncertainty, by allowing for finer model specifications to include refuge options, response styles and possible overdispersion, also in relation to subjects’ and objects’ covariates. The article establishes the state of art of the research inherent to this paradigm, in terms of methodology, inferential procedures and fitting measures, by emphasizing capabilities and limitations yet establishing new findings. In particular, explicative power and predictive performances of cub statistical models for ordinal data are examined and new topics that could boost and support the modelling of uncertainty in this framework are provided. Possible developments are outlined throughout the whole presentation and final comments conclude the paper.

Likelihood-based tests for a class of misspecified finite mixture models for ordinal categorical data

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.

Confidence, credibility and prediction

This paper examines, from a historical and model-based Bayesian perspective, two inferential issues: (1) the relation between confidence coverage and credibility of interval statements about model parameters; (2) the prediction of new values of a random variable. Confidence and credible intervals have different properties. This worries some statisticians, who want them to have the same properties, in frequentist repeated sampling coverage and Bayesian credibility content. Research continues on the conditions under which intervals have the same repeated sampling coverage and credibility content. We conclude that these two inferential approaches generally have incommensurable properties, which converge only asymptotically in sample size, and in a restricted class of samples. The repeated confusion, by new students of statistics, of the coverage of a confidence interval with the credibility of the observed interval, suggests that in general the credibility of the interval is the more important inferential aim. We show how the credibility of a confidence interval can be assessed generally. Bayesian prediction of new values is well established using the posterior predictive distribution. This has some curious features, known since Laplace but not well understood. The prediction of new Bernoullis highlights these features. We suggest that the credibility of predictive intervals needs to be reassessed.

A Review of Time Scale Fundamentals in the g-Formula and Insidious Selection Bias

We review recent examples of data analysis with the g-formula, a powerful tool for analyzing longitudinal data and survival analysis. Specifically, we focus on the common choices of time scale and review inferential issues that may arise. Researchers are increasingly engaged with questions that require time scales subject to left-truncation and right-censoring. The assumptions necessary for allowing right-censoring are well defined in the literature, whereas similar assumptions for left-truncation are not well defined. Policy and biologic considerations sometimes dictate that observational data must be analyzed on time scales that are subject to left-truncation, such as age. Further consideration of left-truncation is needed, especially when biologic or policy considerations dictate that age is the relevant time scale of interest. Methodologic development is needed to reduce potential for bias when left-truncation may occur.

Authors’ response to the contributors to the discussion on “Confidence, credibility and prediction”

This paper examines, from a historical and model-based Bayesian perspective, two inferential issues:

Findings about the BMMPP for modeling dependent and simultaneous data in reliability and queueing systems

The batch Markov‐modulated Poisson process (BMMPP) is a subclass of the versatile batch Markovian arrival process (BMAP), which has been widely used for the modeling of dependent and correlated simultaneous events (as arrivals, failures, or risk events). Both theoretical and applied aspects are examined in this paper. On one hand, the identifiability of the stationary BMMPPm(K ) is proven, where K is the maximum batch size and m is the number of states of the underlying Markov chain. This is a powerful result for inferential issues. On the other hand, some novelties related to the correlation and autocorrelation structures are provided.

The power of monitoring: how to make the most of a contaminated multivariate sample

Diagnostic tools must rely on robust high-breakdown methodologies to avoid distortion in the presence of contamination by outliers. However, a disadvantage of having a single, even if robust, summary of the data is that important choices concerning parameters of the robust method, such as breakdown point, have to be made prior to the analysis. The effect of such choices may be difficult to evaluate. We argue that an effective solution is to look at several pictures, and possibly to a whole movie, of the available data. This can be achieved by monitoring, over a range of parameter values, the results computed through the robust methodology of choice. We show the information gain that monitoring provides in the study of complex data structures through the analysis of multivariate datasets using different high-breakdown techniques. Our findings support the claim that the principle of monitoring is very flexible and that it can lead to robust estimators that are as efficient as possible. We also address through simulation some of the tricky inferential issues that arise from monitoring.

Experimental Design and Experimental Inference in Stone Artifact Archaeology

Lithic researchers rely heavily on experimentation to infer past behaviors and activities based on stone artifacts. This paper explores the analogical nature of archaeological inference and the relationship between experimental design and inference validity in stone artifact experimentation. We show that actualistic flintknapping lacks vital aspects of scientific experimentation, and thus has inherent inferential issues of analogical adequacy and confidence. It is argued that a greater emphasis on hypothesis construction and variable control is needed in order to establish sound referential linkages upon which constructive analogic inferences about the past can be built.

A proposal for modeling and simulating correlated discrete Weibull variables

Researchers in applied sciences are often concerned with multivariate random vari9ables. In particular, multivariate discrete data often arise in many fields (statistical10 quality control, biostatistics, failure and reliability analysis, etc.) and modeling such11 data is a relevant task, as well as simulating correlated discrete data satisfying some spe12cific constraints. Here we consider the discrete Weibull distribution as an alternative to13 the popular Poisson random variable and propose a procedure for simulating correlated14 discrete Weibull random variables, with marginal distributions and correlation matrix as15signed by the user. The procedure indeed relies upon the Gaussian copula model and an16 iterative algorithm for recovering the proper correlation matrix for the copula ensuring17 the desired correlation matrix on the discrete margins. A simulation study is presented,18 which empirically assesses the performance of the procedure in terms of accuracy and19 computational burden, also in relation to the necessary (but temporary) truncation of20 the support of the discrete Weibull random variable. Inferential issues for the proposed21 model are also discussed and are eventually applied to a dataset taken from the literature,22 which shows that the proposed multivariate model can satisfactorily fit real-life correlated23 counts even better than the most popular or recent existing ones.

Cubic rank transmuted distributions: inferential issues and applications

ABSTRACTIn this paper, we introduce a new family of transmuted distributions, the cubic rank transmutation map distribution. This new proposal increases the flexibility of the transmuted distributions enabling the modelling of more complex data such as ones possessing bimodal hazard rates. In order to illustrate the usefulness of the cubic rank transmutation map, we use two well-known lifetime distributions, namely the Weibull and log-logistic models. Several mathematical properties of these new distributions, namely the cubic rank transmuted Weibull distribution and the cubic rank transmuted log-logistic distribution, are derived. Then, the maximum likelihood estimation of the model parameters is described. A simulation study designed to assess the properties of this estimation procedure is then carried out. Finally, applications of the proposed models and their fit are illustrated with some datasets and the corresponding diagnostic analyses are also provided.

Pitfalls in Organizational Neuroscience: A Critical Review and Suggestions for Future Research

The potential of neuroscience to be a viable framework for studying human behavior in organizations depends on scholars’ ability to evaluate, design, analyze, and accurately interpret neuroscientific research. Prior to the publishing of this special issue, relatively little guidance has been available in the management literature for scholars seeking to integrate neuroscience and organization science in a balanced, informative and methodologically rigorous manner. In response to this need, we address design logic and inferential issues involved in evaluating and conducting neuroscience research capable of informing organizational science. Specifically, neuroscience methods of functional magnetic resonance imaging, electroencephalography, lesion studies, transcranial magnetic stimulation, and transcranial direct current stimulation are reviewed, with attention to how these methods might be combined to achieve convergent evidence. We then discuss strengths and limitations of various designs, highlighting the issue of reverse inference as precarious yet necessary for organizational neuroscience. We offer solutions for addressing limitations related to reverse inference, and propose features that allow stronger inferences to be made. The article concludes with a review of selected empirical work in organizational neuroscience in light of these critical design features.

Bivariate discrete generalized exponential distribution

ABSTRACTIn this paper, we develop a bivariate discrete generalized exponential distribution, whose marginals are discrete generalized exponential distribution as proposed by Nekoukhou, Alamatsaz and Bidram [Discrete generalized exponential distribution of a second type. Statistics. 2013;47:876–887]. It is observed that the proposed bivariate distribution is a very flexible distribution and the bivariate geometric distribution can be obtained as a special case of this distribution. The proposed distribution can be seen as a natural discrete analogue of the bivariate generalized exponential distribution proposed by Kundu and Gupta [Bivariate generalized exponential distribution. J Multivariate Anal. 2009;100:581–593]. We study different properties of this distribution and explore its dependence structures. We propose a new EM algorithm to compute the maximum-likelihood estimators of the unknown parameters which can be implemented very efficiently, and discuss some inferential issues also. The analysis of one data set has been performed to show the effectiveness of the proposed model. Finally, we propose some open problems and conclude the paper.

Differential Registration Bias in Voter File Data: A Sensitivity Analysis Approach

AbstractThe widespread availability of voter files has improved the study of participation in American politics, but the lack of comprehensive data on nonregistrants creates difficult inferential issues. Most notably, observational studies that examine turnout rates among registrants often implicitly condition on registration, a posttreatment variable that can induce bias if the treatment of interest also affects the likelihood of registration. We introduce a sensitivity analysis to assess the potential bias induced by this problem, which we call differential registration bias. Our approach is most helpful for studies that estimate turnout among registrants using posttreatment registration data, but it is also valuable for studies that estimate turnout among the voting‐eligible population using secondary sources. We illustrate our approach with two studies of voting eligibility effects on subsequent turnout among young voters. In both cases, eligibility appears to decrease turnout, but these effects are found to be highly sensitive to differential registration bias.

On the hidden truncated bivariate Pareto (IV) model and associated inferential issues

ABSTRACTIncome and wealth data are typically modelled by some variant of the classical Pareto distribution. Often, in practice, the observed data are truncated with respect to some unobserved covariate. In this paper, a hidden truncation formulation of this scenario is proposed and analysed. For this purpose, a bivariate Pareto (IV) distribution is assumed for the variable of interest and the unobserved covariate. Some important distributional properties of the resulting model as well as associated inferential methods are studied. An example is used finally to illustrate the results developed here. In this case, it is noted that hidden truncation on the left does not result in any new model, but the hidden truncation on the right does. The properties and fit of such a model pose a challenging problem and that is what is focused here in this work.