Maria Iannario

A class of statistical models for evaluating services and performances

Evaluation can be described as the psychological process which a subject has to perform when a subject is requested to give a determination of merit regarding an item (the attributes of a service, a product or in general, any tangible or intangible object) using a certain ordinal scale. This process is rooted in the subject’s perception of the value/quality/performance of the object under evaluation.

A New Statistical Model for the Analysis of Customer Satisfaction

Abstract We present a new statistical approach to measure customer satisfaction aimed at understanding theoretical and empirical evidence about the causal relationships among motivations, personal characteristics and expressed agreement. The approach is based on a mixture model that is able to express the stated evaluation via the subjects’ covariates. Specifically, it examines and compares the uncertainty of the answer and the feeling towards the items. After a brief review of current approaches to statistical methods for ordinal data, we provide a discussion of our proposal for modelling the responses of customers. Two case studies illustrate the benefit of model and some general considerations conclude the paper.

Sensory analysis in the food industry as a tool for marketing decisions

In the food industry, sensory analysis can be useful to direct marketing decisions concerning not only products, for example product positioning with respect to competitors, but also market segmentation, customer relationship management, advertising strategies and price policies. In this paper we show how interesting information useful for marketing management can be obtained by combining the results from cub models and algorithmic data mining techniques (specifically, variable importance measurements from Random Forest). A case study on sensory evaluation of different varieties of Italian espresso is presented.

A generalized framework for modelling ordinal data

In several applied disciplines, as Economics, Marketing, Business, Sociology, Psychology, Political science, Environmental research and Medicine, it is common to collect data in the form of ordered categorical observations. In this paper, we introduce a class of models based on mixtures of discrete random variables in order to specify a general framework for the statistical analysis of this kind of data. The structure of these models allows the interpretation of the final response as related to feeling, uncertainty and a possible shelter option and the expression of the relationship among these components and subjects’ covariates. Such a model may be effectively estimated by maximum likelihood methods leading to asymptotically efficient inference. We present a simulation experiment and discuss a real case study to check the consistency and the usefulness of the approach. Some final considerations conclude the paper.

Measuring Job Satisfaction with CUB Models

In this paper we present two statistical approaches for discussing and modelling job satisfaction based on data collected in the Survey on Household Income and Wealth (SHIW) conducted by the Bank of Italy. In particular, we analyse these data by means of a mixture model introduced for ordinal data and compare results with the Ordinal Probit model. The aim is to establish common outcomes and differences in the estimated patterns of global job satisfaction, but also to stress the potential for curbing the effects of measurement errors on estimates by using CUB models [a Combination of discrete Uniform and (shifted) Binomial distributions], allowing control for the effect of uncertainty and shelter choices in the response process.

Varying uncertainty in CUB models

This paper presents a generalization of a mixture model used for the analysis of ratings and preferences by introducing a varying uncertainty component. According to the standard mixture model, called CUB model, the response probabilities are defined as a convex combination of shifted Binomial and discrete Uniform random variables. Our proposal introduces uncertainty distributions with different shapes, which could capture response style and indecision of respondents with greater effectiveness. Since we consider several alternative specifications that are nonnested, we suggest the implementation of a Vuong test for choosing among them. In this regard, some simulation experiments and real case studies confirm the usefulness of the approach.

Mixture models for ordinal responses to account for uncertainty of choice

In CUB models the uncertainty of choice is explicitly modelled as a Combination of discrete Uniform and shifted Binomial random variables. The basic concept to model the response as a mixture of a deliberate choice of a response category and an uncertainty component that is represented by a uniform distribution on the response categories is extended to a much wider class of models. The deliberate choice can in particular be determined by classical ordinal response models as the cumulative and adjacent categories model. Then one obtains the traditional and flexible models as special cases when the uncertainty component is irrelevant. It is shown that the effect of explanatory variables is underestimated if the uncertainty component is neglected in a cumulative type mixture model. Visualization tools for the effects of variables are proposed and the modelling strategies are evaluated by use of real data sets. It is demonstrated that the extended class of models frequently yields better fit than classical ordinal response models without an uncertainty component.

Improved tests of independence in singly-ordered two-way contingency tables

A new approach is described for improving statistical tests of independence between two categorical variables R and C , where C is ordinal and R may or may not be ordinal. Common tests of independence that exploit the ordinality of C use a restricted-alternative approach. A different, relaxed-null approach to improving tests of independence is considered. Specifically, the M -moment score test is introduced and shown to be an attractive alternative to well known restricted-alternative tests, such as the row-means Cochran-Mantel-Haenszel test, the Kruskal-Wallis test, and the likelihood-ratio test based on the cumulative-logit row-effects model or the log-linear row-effects model. Unlike these restricted-alternative tests, which are designed to detect location shifts, the M -moment score test is designed to be powerful for detecting shifts in any of the first M conditional moments of C across the values of R . Using multinomial-Poisson homogeneous modeling theory, the M -moment score tests are shown to be computationally and conceptually simple, with an attractive complement consistency property. Results of a simulation study compare the M -moment score test to several other commonly-used tests on the basis of their operating characteristics.

Assessing risk perception by means of ordinal models

This paper presents a discrete mixture model as a suitable approach for the analysis of data concerning risk perception, when they are expressed by means of ordered scores (ratings). The model, which is the result of a personal feeling (risk perception) towards the object and an inherent uncertainty in the choice of the ordinal value of responses, reduces the collective information, synthesising different risk dimensions related to a preselected domain. After a brief introduction to risk management, the presentation of the CUB model and related inferential issues, we illustrate a case study concerning risk perception for the workers of a printing press factory.

Robust inference for ordinal response models

The present paper deals with the robustness of estimators and tests for ordinal response models. In this context, gross-errors in the response variable, specific deviations due to some respondents’ behavior, and outlying covariates can strongly affect the reliability of the maximum likelihood estimators and that of the related test procedures. The paper highlights that the choice of the link function can affect the robustness of inferential methods, and presents a comparison among the most frequently used links. Subsequently robust M -estimators are proposed as an alternative to maximum likelihood estimators. Their asymptotic properties are derived analytically, while their performance in finite samples is investigated through extensive numerical experiments either at the model or when data contaminations occur. Wald and t-tests for comparing nested models, derived from M -estimators, are also proposed. M based inference is shown to outperform maximum likelihood inference, producing more reliable results when robustness is a concern.