Luisa Scaccia

The use of mixtures for dealing with non-normal regression errors

In many situations, the distribution of the error terms of a linear regression model departs significantly from normality. It is shown, through a simulation study, that an effective strategy to deal with these situations is fitting a regression model based on the assumption that the error terms follow a mixture of normal distributions. The main advantage, with respect to the usual approach based on the least-squares method is a greater precision of the parameter estimates and confidence intervals. For the parameter estimation we make use of the EM algorithm, while confidence intervals are constructed through a bootstrap method.

Bayesian Growth Curves Using Normal Mixtures With Nonparametric Weights

Reference growth curves estimate the distribution of a measurement as it changes according to some covariate, often age. We present a new methodology to estimate growth curves based on mixture models and splines. We model the distribution of the measurement with a mixture of normal distributions with an unknown number of components, and model dependence on the covariate through the weights, using smooth functions based on B-splines. In this way the growth curves respect the continuity of the covariate and there is no need for arbitrary grouping of the observations. The method is illustrated with data on triceps skinfold in Gambian girls and women.

Testing for positive association in contingency tables with fixed margins

An exact conditional approach is developed to test for certain forms of positive association between two ordinal variables (e.g. positive quadrant dependence, total positivity of order 2). The approach is based on the use of a test statistic measuring the goodness-of-fit of the model formulated according to the type of positive association of interest. The nuisance parameters, corresponding to the marginal distributions of the two variables, are eliminated by conditioning the inference on the observed margins. This, in turn, allows to remove the uncertainty on the conclusion of the test, which typically arises in the unconditional context where the null distribution of the test statistic depends on such parameters. Since the multivariate generalized hypergeometric distribution, which results from conditioning, is normally intractable, Markov chain Monte Carlo methods are used to obtain maximum likelihood estimates of the parameters of the constrained model. The Pearsons chi-squared statistics is used as a test statistic; a p-value for this statistic is computed through simulation, when the data are sparse, or exploiting the asymptotic theory based on the chi-bar squared distribution. The extension of the present approach to deal with bivariate contingency tables, stratified according to one or more explanatory discrete variables, is also outlined. Finally, three applications based on real data are presented.

Can CDS indexes signal future turmoils in the stock market? A Markov switching perspective

Single-name Credit Default Swaps (CDS) are considered the main providers of direct information related with a reference entity’s creditworthiness and, for this reason, they have often been the core of news on the current financial crisis. The academic research has focused mainly on the capacity of CDS in anticipating agencies’ official rating changes and—in this respect—on their superior signalling power, compared to bond and stock markets. The aim of this work is, instead, to investigate the ability of fluctuations in CDS indexes in anticipating the occurrence of stock market crises. Our goal is to show that CDS indexes may provide investors and institutions with early warning signals of financial distresses in the stock market. We make use of a Markov switching model with states characterized by increasing levels of volatility and compare the times in which the first switch in a high volatility state occurs, respectively, in CDS and stock market index quotes. The data set consists of daily closing quotes for 5 years CDS and stock market index prices, covering the time period from 2004 to 2010. In order to capture possible geographic differences in CDS index capacity of foreseeing stock market distresses, data referring to two different regions, Europe and United States, are analyzed.

Bayesian inference through encompassing priors and importance sampling for a class of marginal models for categorical data

A Bayesian approach is developed for selecting the model that is most supported by the data within a class of marginal models for categorical variables, which are formulated through equality and/or inequality constraints on generalized logits (local, global, continuation, or reverse continuation), generalized log-odds ratios, and similar higher-order interactions. For each constrained model, the prior distribution of the model parameters is specified following the encompassing prior approach. Then, model selection is performed by using Bayes factors estimated through an importance sampling method. The approach is illustrated by three applications based on different datasets, which also include explanatory variables. In connection with one of these examples, a sensitivity analysis to the prior specification is also performed.

Testing for Simplification in Spatial Models

Data collected on a rectangular lattice occur frequently in many areas such as field trials, geostatistics, remotely sensed data, and image analysis. Models for the spatial process often make simplifying assumptions, including axial symmetry and separability. We consider methods for testing these assumptions and compare tests based on sample covariances, tests based on the sample spectrum, and model-based tests.

A Markov Switching Re-evaluation of Event-Study Methodology

This paper reconsiders event-study methodology in light of evidences showing that Cumulative Abnormal Return (CAR) can result in misleading inferences about financial market efficiency and pre(post)-event behavior. In particular, CAR can be biased downward, due to the increased volatility on the event day and within event windows. We propose the use of Markov Switching Models to capture the effect of an event on security prices. The proposed methodology is applied to a set of 45 historical series on Credit Default Swap (CDS) quotes subject to multiple credit events, such as reviews for downgrading. Since CDSs provide insurance against the default of a particular company or sovereign entity, this study checks if market anticipates reviews for downgrading and evaluates the time period the announcements lag behind the market.

Answering Two Biological Questions with a Latent Class Model via MCMC Applied to Capture-Recapture Data

A well-known method for estimating the size, N, of a certain population is the capture-recapture method (for a review see Yip et al., 1995a and Schwarz and Seber, 1999). The first motivations to the development of these methods arose in biology where researchers were interested in estimating the number of animals of a certain species (see, for instance, Schnabel, 1938, and Darroch, 1958). Subsequently, this methodology was also applied in medical and social contexts where it is important to estimate the number of subjects with a certain disease or in a particular situation (Yip et al., 1995b).

Bayesian Hidden Markov Models for Financial Data

Hidden Markov Models, also known as Markov Switching Models, can be considered an extension of mixture models, allowing for dependent observations. The main problem associated with Hidden Markov Models is represented by the choice of the number of regimes, i.e. the number of generating data processes, which differ one from another just for the value of the parameters. Applying a hierarchical Bayesian framework, we show that Reversible Jump Markov Chain Monte Carlo techniques can be used to estimate the parameters of the model, as well as the number of regimes, and to simulate the posterior predictive densities of future observations. Assuming a mixture of normal distributions, all the parameters of the model are estimated using a well known exchange rate data set.

A nonparametric multidimensional latent class IRT model in a Bayesian framework

We propose a nonparametric item response theory model for dichotomously-scored items in a Bayesian framework. The model is based on a latent class (LC) formulation, and it is multidimensional, with dimensions corresponding to a partition of the items in homogenous groups that are specified on the basis of inequality constraints among the conditional success probabilities given the latent class. Moreover, an innovative system of prior distributions is proposed following the encompassing approach, in which the largest model is the unconstrained LC model. A reversible-jump type algorithm is described for sampling from the joint posterior distribution of the model parameters of the encompassing model. By suitably post-processing its output, we then make inference on the number of dimensions (i.e., number of groups of items measuring the same latent trait) and we cluster items according to the dimensions when unidimensionality is violated. The approach is illustrated by two examples on simulated data and two applications based on educational and quality-of-life data.