CUB Models Research Articles

Visitor satisfaction with WMAs: A case study from Oklahoma

Analyzing visitor satisfaction has been an important practice for outdoor recreation managers, as satisfaction influences visitor behavior including the decision to visit in the future. This study analyzed visitors' level of satisfaction relative to their overall recreational experience at the last Oklahoma Wildlife Management Area (WMA) they visited. Satisfaction with WMA characteristics such as accessibility, facility availability and condition, scenery, abundance of wildlife, and a feeling of privacy and safety were also analyzed. To accomplish the study objective, WMA visitor surveys were administered among Oklahoma hunting and fishing license and conservation passport holders during the 2020–2021 hunting season. CUB (Covariates in a Uniform and shifted Binomial mixture) models were used to analyze the effects of visitors' characteristics on the level of satisfaction. Results suggested that compared to their non-consumptive counterparts, consumptive visitors (hunters and anglers) reported a higher level of satisfaction. In contrast, WMA visitors generally had lower satisfaction and seemed to express higher consternation about their privacy and safety than other aspects of visitations. This study demonstrates the applicability of a relatively new consumer preference model for analyzing visitor satisfaction within the outdoor recreation field. Furthermore, it provides valuable visitor satisfaction results to help management agencies analyze WMA visitation levels and determine the best management practices.

What influences the perception of immigration in Italian adolescents? An analysis with CUB models for rating data

Surveys are the traditional means of measuring individuals’ opinions and perceptions through the expression of ratings on ordinal scales. CUB models, introduced by Piccolo in 2003 [1,2], are particularly useful for the analysis of such data, as they allow researchers to investigate the mechanism of selection and weighting of the two main latent components involved, uncertainty and feeling, with a mixture of a discrete Uniform and a shifted Binomial distributions, respectively. In order to understand how adolescents perceive the immigration phenomenon and the possibilities of social inclusion of migrants, a survey was conducted with about 1,200 students of some high schools participating in the Italian Ministry of Education Project for Scientific Degree in Statistics (PLS in Statistics) in Southern Italy. CUB regression models were used to investigate the main covariates that can explain different perceptions of the immigration phenomenon. Gender, Age, High school type, Geographic area of residence and Level of information emerged as the most important contextual factors, along with socio-demographic characteristics, influencing the development of critical thinking about the impact of immigration on the host society. In addition, the media and educators play a fundamental role in providing accurate information. Understanding the role of these factors could be useful in planning educational activities and thematic contents that address responsibility, the promotion of intercultural dialog, hospitality and cooperation. Educational institutions undoubtedly play a key role in building global citizenship among young people.

Rejoinder to the discussion of “The class of cub models: statistical foundations, inferential issues and empirical evidence”

The paper is the rejoinder to a series of Discussions on the class of cub models for rating data. The main topics advanced by Discussants are reviewed and debated, with focus on the most prominent issues. As a result, the trailhead of possible future research developments is outlined.

Assessing consumer attitudes and perceptions towards food authenticity

PurposeThe purpose of this paper is to identify and assess the factors that consumers evaluate significant in the assessment of food authenticity and guide them to make safe food choices.Design/methodology/approachIn this respect, a mixture model for consumer preferences, namely CUB, was employed due to the ability of discriminate features that are rated similarly allowing the detection of significant similarities and differences in consumers’ judgments. Moreover, introducing covariates in CUB models allow studying the influence that consumers’ socio-demographic characteristics have on the importance of the attributes used in the assessment of food authenticity.FindingsThe results demonstrate that organic certificate, traditional and homemade production practices, origin certificate as well as information about product’s origin country and raw materials production region are significant quality cues enable consumers to judge food authenticity. In addition, consumers further segmentation according to socio-demographic characteristics indicate that country of origin information are mainly used by middle-aged consumers, highly educated and paid, whereas production techniques and organic certification constitute the most effective indicators for judging food authenticity by older consumers.Originality/valueThe paper confirms that consumers can use extrinsic and intrinsic quality cues to judge food’s authenticity.

A review of: The class of CUB models: statistical foundations, inferential issues and empirical evidence by Domenico Piccolo and Rosaria Simone

This discussion consists of six comments to the review paper by Piccolo and Simone. The comments offer an expanded perspective designed to encourage further research in the important class of CUB model.

Comments on The class of cub models: statistical foundations, inferential issues and empirical evidence by D. Piccolo and R. Simone

Comments on The class of cub models: statistical foundations, inferential issues and empirical evidence by D. Piccolo and R. Simone

Modelling marginal ranking distributions: The uncertainty tree

In this paper a novel approach is proposed for ranking data analysis that is based on marginal distributions. The marginal scores for one of the items to be ranked can be considered as a proxy of preference ratings and thus they can be employed to investigate drivers of the outcome. The rationale is that a model for the univariate marginal distributions should suitably convey information about the veracity of ordinal scores given that it would disregard the ranking constraints. The method relies on cubremot (cubregression model trees), a tool for growing trees for ordinal resposes based on the local estimation of cub models, a class of models able to explain both preferences and related uncertainty. Here we propose the Uncertainty Tree to disclose preference patterns on the basis of the model uncertainty component. Two applications on real data are discussed; comparison with other model-based trees is provided and a synthetic index for the selection of the best cubremot is also advanced.

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.

Cubm package in R to fit CUB models

The class of CUB models is commonly used by practitioners to model ordinal data, in this paper we propose the cubm package which provides the class of CUB models in the R system for statistical computing. The cubm package allows to specify a formula for each parameter of the model, the Maximum Likelihood (ML) estimation is performed by optimization via the functions nlminb, optim and DEoptim and the variance-covariance matrix can be obtained by numerical approximation of the Hessian matrix or by bootstrap method. The utility of the package is illustrated by an application and a simulation study.

Cumulative and CUB Models for Rating Data: A Comparative Analysis

SummaryOrdinal measurements as ratings, preference and evaluation data are very common in applied disciplines, and their analysis requires a proper modelling approach for interpretation, classification and prediction of response patterns. This work proposes a comparative discussion between two statistical frameworks that serve these goals: the established class of cumulative models and a class of mixtures of discrete random variables, denoted as CUB models, whose peculiar feature is the specification of an uncertainty component to deal with indecision and heterogeneity. After surveying their definition and main features, we compare the performances of the selected paradigms by means of simulation experiments and selected case studies. The paper is tailored to enrich the understanding of the two approaches by running an extensive and comparative analysis of results, relative advantages and limitations, also at graphical level. In conclusion, a summarising review of the key issues of the alternative strategies and some final remarks are given, aimed to support a unifying setting.

Modelling uncertainty and response styles in ordinal data

Mixture models for ordinal responses in the tradition of cub models use the uniform distribution to account for uncertainty of respondents. A model is proposed that uses more flexible distributions in the uncertainty component: the discretized Beta distribution allows to account for response styles, in particular the preference for middle or extreme categories. The proposal is compared with traditional cub models in simulation studies and its use is illustrated by two applications.

A Proposal for a Model-Based Composite Indicator: Experience on Perceived Discrimination in Europe

In social sciences the need often arises to compare and rank groups of respondents by analyzing huge amounts of data and composite indicators are amongst the most effective tools. The paper aims to design an original procedure suitable for ordinal data and able to synthesize subjective evaluations while accounting for both agreement and heterogeneity in response patterns. A composite indicator for ordinal data based on cub models is introduced: the proposal discloses and preserves the heterogeneity also at an aggregated level. Empirical evidence relies on perceived discrimination analysis stemming from the Special Eurobarometer Survey 2015.

Valuing Consumer Perceptions of Olive Oil Authenticity

ABSTRACTNowadays, while the authenticity of agri-food products becomes a major concern for consumers, given the increasing rate of food fraud reports across the world, olive oil records the highest adulterations. The high selling price of olive oil is the main reason for conducting adulteration, which is often caused through false indications on the packaging (mislabeling). On the other hand, consumers are well aware of the alteration, and they are looking for authenticity signals during the purchase process. Authenticity, therefore, becomes an evaluation and decision-making criterion that guides consumer choices. The aim of this paper was twofold: to highlight the attributes in which Greek consumers attach great importance during the evaluation of olive oil’s authenticity, and second, through consumers’ demographic segmentation, to gain more detailed knowledge about the attributes that consumers evaluate in olive oil authenticity. CUB (Covariates in a mixture of Uniform and Binomial random variables) models are employed for the interpretation of ordinal data due to the ability of comparing and clustering the rating distributions consumers express about olive oil features, and due to the ability of detecting significant similarities and differences in consumer responses. Moreover, with the introduction of respondents’ social, demographic, and financial characteristics, CUB models allow the measurement of the influence that the consumers’ profile has upon the attributes of olive oil authenticity. The results showed that consumers attached great importance to taste, acidity, country and region of origin, olive variety, color, organic production, and regional certification in the evaluation of olive oil authenticity. In addition, secondary school graduates tend to use taste and olive variety, also indicating confidence in the authenticity of organic olive oil.

The relationship between CUB and loglinear models with latent variables

The “combination of uniform and shifted binomial” ( CUB ) model is a dis- tribution for ordinal variables that has received considerable recent attention and specialized development. This article notes that the CUB model is a special case of the well-known loglinear latent class model, an observation that is useful for two reasons. First, we show how it can be used to estimate the cub model in familiar standard software such as Mplus or Latent gold . Second, the mathematical equivalence of CUB with this well-known model and its correspondingly long history allows well-known results to be applied straightforwardly, subsuming a wide range of specialized recent developments of CUB and suggesting several possibly useful future ones. Thus, the observation that CUB and its extensions are restricted loglinear latent class models should be useful to both applied practitioners and methodologists.