CUB models: a preliminary fuzzy approach to heterogeneity

In line with the increasing attention paid to deal with uncertainty in ordinal data models, we propose to combine Fuzzy models with \cub models within questionnaire analysis. In particular, the focus will be on \cub models' uncertainty parameter and its interpretation as a preliminary measure of heterogeneity, by introducing membership, non-membership and uncertainty functions in the more general framework of Intuitionistic Fuzzy Sets. Our proposal is discussed on the basis of the Evaluation of Orientation Services survey collected at University of Naples Federico II.Comment: 10 pages, invited contribution at SIS2016 (Salerno, Italy), in SIS2016 proceeding

A comparison of statistical models for short categorical or ordinal time series with applications in ecology

We study two statistical models for short-length categorical (or ordinal) time series. The first one is a regression model based on generalized linear model. The second one is a parametrized Markovian model, particularizing the discrete autoregressive model to the case of categorical data. These models are used to analyze two data-sets: annual larch cone production and weekly planktonic abundance.Comment: 18 page

Partisanship, political constraints and employment protection reforms in an era of austerity

Why do some governments adopt unpopular reforms entailing far-reaching liberalization of the labour market, while others opt only for marginal adjustments or even regulatory reforms? This paper explains the likelihood of different types of reform as an effect of different constellations of government partisanship and veto players. Combining the ‘blame avoidance’ and ‘veto players’ logics of politics, the paper argues that veto players have either a constraining or enabling effect depending on the partisan orientation of government. Correspondingly, liberalization is most likely to be adopted either by right parties facing few veto players, or by left parties in contexts with a high degree of power sharing. Regulatory reforms are most likely when left governments enjoy strong power concentration, but marginal regulation may be also adopted under external pressure by right governments facing many veto players. An analysis of employment protection reforms in 24 EU countries during 1990-2007 supports the argument that the effect of political constraints and opportunities on the choice of reforms is shaped by partisan difference

Fitting stratified proportional odds models by amalgamating conditional likelihoods

Classical methods for fitting a varying intercept logistic regression model to stratified data are based on the conditional likelihood principle to eliminate the stratum-specific nuisance parameters. When the outcome variable has multiple ordered categories, a natural choice for the outcome model is a stratified proportional odds or cumulative logit model. However, classical conditioning techniques do not apply to the general K -category cumulative logit model ( K >2) with varying stratum-specific intercepts as there is no reduction due to sufficiency; the nuisance parameters remain in the conditional likelihood. We propose a methodology to fit stratified proportional odds model by amalgamating conditional likelihoods obtained from all possible binary collapsings of the ordinal scale. The method allows for categorical and continuous covariates in a general regression framework. We provide a robust sandwich estimate of the variance of the proposed estimator. For binary exposures, we show equivalence of our approach to the estimators already proposed in the literature. The proposed recipe can be implemented very easily in standard software. We illustrate the methods via three real data examples related to biomedical research. Simulation results comparing the proposed method with a random effects model on the stratification parameters are also furnished. Copyright © 2008 John Wiley & Sons, Ltd.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/60967/1/3325_ftp.pd

Computing Functions of Random Variables via Reproducing Kernel Hilbert Space Representations

We describe a method to perform functional operations on probability distributions of random variables. The method uses reproducing kernel Hilbert space representations of probability distributions, and it is applicable to all operations which can be applied to points drawn from the respective distributions. We refer to our approach as {\em kernel probabilistic programming}. We illustrate it on synthetic data, and show how it can be used for nonparametric structural equation models, with an application to causal inference

BClass: A Bayesian Approach Based on Mixture Models for Clustering and Classification of Heterogeneous Biological Data

Based on mixture models, we present a Bayesian method (called BClass) to classify biological entities (e.g. genes) when variables of quite heterogeneous nature are analyzed. Various statistical distributions are used to model the continuous/categorical data commonly produced by genetic experiments and large-scale genomic projects. We calculate the posterior probability of each entry to belong to each element (group) in the mixture. In this way, an original set of heterogeneous variables is transformed into a set of purely homogeneous characteristics represented by the probabilities of each entry to belong to the groups. The number of groups in the analysis is controlled dynamically by rendering the groups as 'alive' and 'dormant' depending upon the number of entities classified within them. Using standard Metropolis-Hastings and Gibbs sampling algorithms, we constructed a sampler to approximate posterior moments and grouping probabilities. Since this method does not require the definition of similarity measures, it is especially suitable for data mining and knowledge discovery in biological databases. We applied BClass to classify genes in RegulonDB, a database specialized in information about the transcriptional regulation of gene expression in the bacterium Escherichia coli. The classification obtained is consistent with current knowledge and allowed prediction of missing values for a number of genes. BClass is object-oriented and fully programmed in Lisp-Stat. The output grouping probabilities are analyzed and interpreted using graphical (dynamically linked plots) and query-based approaches. We discuss the advantages of using Lisp-Stat as a programming language as well as the problems we faced when the data volume increased exponentially due to the ever-growing number of genomic projects.