Domenico Piccolo

Time series clustering and classification by the autoregressive metric

The statistical properties of the autoregressive (AR) distance between ARIMA processes are investigated. In particular, the asymptotic distribution of the squared AR distance and an approximation which is computationally efficient are derived. Moreover, the problem of time series clustering and classification is discussed and the performance of the AR distance is illustrated by means of some empirical applications.

A mixture model for preferences data analysis

A mixture model for preferences data, which adequately represents the composite nature of the elicitation mechanism in ranking processes, is proposed. Both probabilistic features of the mixture distribution and inferential and computational issues arising from the maximum likelihood parameters estimation are addressed. Moreover, empirical evidence from different data sets confirming the goodness of fit of the proposed model to many real preferences data is shown.

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.

Statistical methods for the evaluation of educational services and quality of products

Latent variable models for ordinal data.- Issues on item response theory modelling.- Nonlinearity in the analysis of longitudinal data.- Multilevel models for the evaluation of educational institutions: a review.- Multilevel mixture factor models for the evaluation of educational programs#x2019 effectiveness.- A class of statistical models for evaluating services and performances.- Choices and conjoint analysis: critical aspects and recent developments.- Robust diagnostics in university performance studies.- A novel global performance score with an application to the evaluation of new detergents.- Nonparametric tests for the randomized complete block design with ordered categorical variables.- A permutation test for umbrella alternatives.- Nonparametric methods for measuring concordance between rankings: a case study on the evaluation of professional profiles of municipal directors.

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.

Inferential Issues on CUBE Models with Covariates

We introduce cube models with covariates, a class of discrete mixture distributions able to take uncertainty and overdispersion of ordinal data into account. The main result of the paper concerns the analytical derivation of the observed variance–covariance matrix of this model, a necessary step for the asymptotic inference about estimated parameters and model validation. We emphasize some computational aspects of the procedure and discuss the usefulness of the approach on a real case study.

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.