Laura Deldossi

Measurement Errors and Uncertainty: A Statistical Perspective

Evaluation of measurement systems is necessary in many industrial contexts. The literature on this topic is mainly focused on how to measure uncertainties for systems that yield continuous output. Few references are available for categorical data and they are briefly recalled in this paper. Finally a new proposal to measure uncertainty when the output is bounded ordinal is introduced.

PKL-Optimality Criterion in Copula Models for Efficacy-Toxicity Response

In recent years, there has been an increasing interest in developing dose finding methods incorporating both efficacy and toxicity outcomes. It is reasonable to assume that efficacy and toxicity are associated; therefore, we need to model their stochastic dependence. Copula functions are very useful tools to model different kinds of dependence with arbitrary marginal distributions. We consider a binary efficacy-toxicity response with logit marginal distributions. Since the dose which maximizes the probability of efficacy without toxicity (P-optimal dose) changes depending on different copula functions, we propose a criterion which is useful for choosing between the rival copula models but also protects patients against doses that are far away from the P-optimal dose. The performance of this compromise criterion (called PKL) is illustrated for different choices of the parameter values.

A Novel Approach to Evaluate Repeatability and Reproducibility for Ordinal Data

We propose a novel usage of CUB models in order to evaluate Repeatability and Reproducibility (R&R) for ordinal data in business and industrial experiments. This is a context where there is a small group of appraisers who have to evaluate a sample of objects classifying them according to ordinal categories. By comparing the cumulative distribution functions obtained fitting CUB models to judgments given by appraisers, we give both graphical and analytical instruments to assess R&R for an ordinal measurement system. The approach is applied to the real-life example reported in de Mast and van Wieringen (2010).

Inference on the CUB model: an MCMC approach

We consider a special finite mixture model for ordinal data expressing the preferences of raters with regards to items or services, named CUB (Covariate Uniform Binomial), recently introduced in statistical literature. The mixture is made up of two components that belong to different families of distributions: a shifted Binomial and a discrete Uniform. Bayesian analysis of the CUB model naturally comes from the elicitation of some priors on its parameters. In this case the parameters estimation must be performed through the analysis of the posterior distribution. In the theory of finite mixture models complex posterior distributions are usually evaluated through computational methods of simulation such as the Markov Chain Monte Carlo (MCMC) algorithms. Since the mixture type of the CUB model is non-standard, a suitable MCMC algorithm has been developed and its performance has been evaluated via a simulation study and an application on real data.

Confidence Intervals for Variance Components in Measurement System Capability Studies

In Measurement System Analysis a relevant issue is how to find confidence intervals for the parameters used to evaluate the capability of a gauge. In literature approximate solutions are available but they produce so wide intervals that they are often not effective in the decision process. In this article we introduce a new approach and, with particular reference to the parameter γR, i.e., the ratio of the variance due to the process and the variance due to the instrument, we show that, under quite realistic assumptions, we obtain confidence intervals narrower than other methods. An application to a real microelectronic case study is reported.

Testing the Hypotheses on the Fixed Effects in the Taguchi Approach with Combined Arrays

The paper examines a particular aspect of robustness related to the Taguchi approach to off-line quality control. In particular, the ‘combined array’ approach to experimental design is considered, which requires the noise factors to be reproduced as controllable factors in a laboratory or on a pilot plant level. We propose a statistical method for assessing the existence of controllable factor effects on the mean, in signifying that they are clearly distinguishable from the error random fluctuations even if there are noise factors typically affecting a response of interest in the real production or utilization of some goods. The method has recourse to a statistical test, whose percentage point, defining the acceptance/rejection regions of the hypothesis under study, is the appropriate percentile of a doubly non-central F distribution. The study of the power function of the test suggested the simplification of the latter, which is dealt with in the paper also with regard to an example of application of the proposed method. Copyright

Bayesian variable selection in a class of mixture models for ordinal data: a comparative study

In this paper, we consider a special finite mixture model named Combination of Uniform and shifted Binomial (CUB), recently introduced in the statistical literature to analyse ordinal data expressing the preferences of raters with regards to items or services. Our aim is to develop a variable selection procedure for this model using a Bayesian approach. Bayesian methods for variable selection and model choice have become increasingly popular in recent years, due to advances in Markov chain Monte Carlo computational algorithms. Several methods have been proposed in the case of linear and generalized linear models (GLM). In this paper, we adapt to the CUB model some of these algorithms: the Kuo–Mallick method together with its ‘metropolized’ version and the Stochastic Search Variable Selection method. Several simulated examples are used to illustrate the algorithms and to compare their performance. Finally, an application to real data is introduced.