Showing papers in "Statistica in 2010"

The permutation testing approach: a review

Abstract: In recent years permutation testing methods have increased both in number of applications and in solving complex multivariate problems. A large number of testing problems may also be usefully and effectively solved by traditional parametric or rank-based nonparametric methods, although in relatively mild conditions their permutation counterparts are generally asymptotically as good as the best ones. Permutation tests are essentially of an exact nonparametric nature in a conditional context, where conditioning is on the pooled observed data as a set of sufficient statistics in the null hypothesis. Instead, the reference null distribution of most parametric tests is only known asymptotically. Thus, for most sample sizes of practical interest, the possible lack of efficiency of permutation solutions may be compensated by the lack of approximation of parametric counterparts. There are many complex multivariate problems (quite common in biostatistics, clinical trials, engineering, the environment, epidemiology, experimental data, industrial statistics, pharmacology, psychology, social sciences, etc.) which are difficult to solve outside the conditional framework and outside the nonparametric combination (NPC) method for dependent permutation tests. In this paper we review this method along with a number of applications in different experimental and observational situations (e.g. multi-sided alternatives, zero-inflated data and testing for a stochastic ordering) and we present properties specific to this methodology, such as: for a given number of subjects, when the number of variables diverges and the noncentrality of the combined test diverges accordingly, then the power of combination-based permutation tests converges to one.

Time series modeling and decomposition

Abstract: The paper provides an overview of techniques and methods in time series modeling and decomposition with focus on the business cycle, models for seasonality, the moving holiday component, the trading-day component and the irregular component.

Inferring causal relations by modelling structures

Abstract: This paper provides an overview of structural modelling in its close relation to explanation and causation. It stems from previous works by the authors and stresses the role and importance of the notions of invariance, recursive decomposition, exogeneity and background knowledge. It closes with some considerations about the importance of the structural approach for practicing scientists.

The Autoregressive metric for comparing time series models

Abstract: The Autoregressive metric was firstly introduced in 1983 as a tool for choosing a representative element from a large collection of time series and for clustering temporal data. The proposal has been extended to many contexts and has raised increasing interests in both time series methods and applications. The main results concerning this metric, its asymptotic distribution and some operational and comparative issues are presented. A discussion about the merits of this distance criterion and some caveats about its usage conclude the paper.

Intra-distribution dynamics of regional per-capita income in Europe: evidence from alternative conditional density estimators

Abstract: In this paper different conditional density estimators are employed to analyze the cross-sectional distribution dynamics of regional per-capita income in Europe during the period 1980-2002. First, a kernel estimator with fixed bandwidth (the method traditionally 20 R. Basile applied in the literature on intra-distribution dynamics) gives evidence of convergence. With a modified estimator, proposed by Hyndman et al. (1996), with variable bandwidth and mean-bias correction, the dominant income dynamics is that of persistence and lack of cohesion: only a fraction of very poor regions improves its position over time converging towards a low relative income (“poverty trap”). Moreover, an alternative graphical technique (more informative than the traditional contour plot) is applied to visualize conditional densities.

Proposed Optimal Orthogonal New Additive Model (POONAM)

Abstract: In this paper, the proposed optimal orthogonal new additive model (POONAM) is shown to remain more efficient than the recent additive model introduced by Gjestvang and Singh (2009). Several situations where the POONAM estimator shows efficiency over the Gjestvang and Singh (2009) model are simulated and investigated.

Note on conditional mode estimation for functional dependent data

Abstract: We consider α-mixing observations and deal with the estimation of the conditional mode of a scalar response variable Y given a random variable X taking values in a semi-metric space We provide a convergence rate in L p norm of the estimator

Material deprivation as marker of health need

Abstract: A relationship between socio-economic status and health has been widely documented both by individual-level and ecological regression studies. We addressed the problem known in the literature as using a material deprivation index as predictor of health needs and comparing results when adjusting or not the health outcome and the deprivation index for the same confounding variables. We focus on non-linear hierarchical models. We take as example the the issue of introducing socio-economic indicators in national or regional resources allocation formulas. We fitted a series of models with different data hierarchies to evaluate both the individual effect and the aggregate (census block) effect of material deprivation on heath status, disentagling the individual from the contextual effects. Individual mortality records came from the Florence census cohort 1991-1995 which is part of the Tuscan Longitudinal Study. Data on socio-economic factors derived from individual records of the 1991 census. Our results suggested that after adjusting for age, material deprivation is a good predictor of health needs both at individual and at aggregate level (census block). The presence of a contextual effect increases the interest in using deprivatin in the allocation formula, since it would permit a better distribution of resources to disadvantaged micro-areas. In the present paper, we stress the need to estimate the association between deprivation and health appropriately adjusting for age. The ideal goal would be having information at small geographical level on the joint distribution of age and deprivation to age-standardize both the response and the predictor. A temporary solution should be to regress crude mortality rates on deprivation and age. The current common practice, in absence of individual data, to regress standardized mortality on material deprivation may be inappropriate.

Inferrig Causal Relations by Modelling Structure

Abstract: This paper provides an overview of structural modeling in its close relation to explanation and causation It stems from previous works by the authors and stresses the role and importance of the notions of invariance, recursive decomposition, exogeneity and ackground knowledge It closes with some considerations about the importance of the structural approach for practicing scientists

Considering groups in the statistical modeling of spatio-temporal data

Abstract: Spatio-temporal statistical methods are developing into an important research topic that goes beyond the study of processes that generate independent, identically distributed observations. Hierarchical models are a suitable proposal for both continuous and discrete spatio-temporal domains. They are flexible and permit separation of the various sources of uncertainty by means of a sequence of conditional models. In this work, we expanded on spatio-temporal data modeling by considering data categorization with respect to certain differentiating features. We studied the impact of the presence of subgroups on model building, with emphasis on Bayesian modeling. We discussed how differences in spatial locations can be reflected in a hierarchical model and assessed the performances of different models via a simulation study.

Determinants of further survival in centenarians from the province of Mantova

Abstract: The MALVA project, one of the first Italian studies on population-based samples of centenarians, was addressed to the subjects aged 98+ residing in the province of Mantova (Northern Italy) at the 1st April 1998. The present study aims at analyzing the impact of selected clinical and socio-demographic variables on further survival of the 77 participants in the MALVA study. Adopting methods for multiple imputation of missing value, four distinct Cox regression models were estimated using groups of predefined variables describing sociodemographic characteristics, functional status, nutritional status, cardiovascular risk factors. Each model was adjusted for the effects of gender and age. Finally two complete models have been considered: the first one including the statistically significant variables in the previous analysis, and the second one obtained with a backward selection procedure. The variables included in the final models can be seen as markers of “frailty” or correlated conditions. Most of these variables maintained a significant influence on survival, however belonging to the “underweight” BMI category and being institutionalized emerged as the best “frailty” indicators in the centenarians from the province of Mantova. The results of this study are in agreement with several previous studies in recognizing that factors predicting mortality in centenarians are not the same well-known predictors of mortality in the middle-aged and younger elderly.

Comparative Study of Glutathione S-Transferase Activity of Three Human Erythrocyte Genotypes Infected With Plasmodium falciparum .

Abstract: Investigation to ascertain the levels of glutathione S-transferase (GST) activity of three human erythrocyte genotypes (HbAA, HbAS and HbSS) obtained from apparently healthy and clinically confirmed malarious subjects/volunteers was carried out. The incubation of human erythrocytes with 1-chloro-2,4dinitrobenzene (CDNB) resulted in almost quantitative conjugation of glutathione (GSH) to form S-(2,4dinitrophenyl) glutathione. The reaction formed the basis for the spectrophotometric determination of GST activity. The levels of GST activity of the red cell genotypes was in the order of HbAA 0.05) between GST activity of HbAA and HbAS erythrocytes. The results also showed red blood cells infected with Plasmodium falciparum exhibited significantly lower levels of GST activity compared to erythrocytes obtained from apparently healthy non-malarious individuals. Furthermore, gender did not significantly (p>0.05) affect erythrocyte GST activity of non-malarious subjects/volunteers. The study suggests that GST activity evaluation might be a reliable biochemical marker and possess promising rational for diagnostic potential in malaria. @ JASEM

Male-female discrimination: an analysis of gender gap and its determinants

Abstract: In recent years, the occupational dynamics have brought in significant innovations in Italy, as the increased participation of women in the labour market, that have stimulated studies about the gender wage gap, concerning the different remuneration reserved to male and female workers. In this work the Authors, following Oaxaca and Blinder approach, estimate the gap for Italian employers and proceed to its decomposition, one part due to differences in individual characteristics (endowment effect) and another part due to the different returns on the same characteristics (coefficient effect), related to discrimination. Then, the gender wage gap and its decomposition is analyzed with reference to Italian macro-areas considered separately with the aim to highlight the different fundamental dynamics. The model has also been modified using the Heckmann correction to eliminate the bias due to self-selection; i.e. the different propensity to work for men and women.

Intra-distribution dynamics of regional per-capita income in Europe: evidence from alternative conditional

Abstract: In this paper different conditional density estimators are employed to analyze the cross-sectional distribution dynamics of regional per-capita income in Europe during the period 1980-2002. First, a kernel estimator with fixed bandwidth (the method traditionally applied in the literature on intra-distribution dynamics) gives evidence of convergence. With a modified estimator, proposed by Hyndman et al. (1996), with variable bandwidth and mean-bias correction, the dominant income dynamics is that of persistence and lack of cohesion: only a fraction of very poor regions improves its position over time converging towards a low relative income (“poverty trap”). Moreover, an alternative graphical technique (more informative than the traditional contour plot) is applied to visualize conditional densities.

A quantile regression approach for modelling a Health-Related Quality of Life Measure

Abstract: Objective . The aim of this study is to propose a new approach for modeling the EQ-5D index and EQ-5D VAS in order to explain the lifestyle determinants effect using the quantile regression analysis. Methods . Data was collected within a cross-sectional study that involved a probabilistic sample of 1,622 adults randomly selected from the population register of two Health Authorities of Bologna in northern Italy. The perceived health status of people was measured using the EQ-5D questionnaire. The Visual Analogue Scale included in the EQ-5D Questionnaire, the EQ-VAS, and the EQ-5D index were used to obtain the synthetic measures of quality of life. To model EQ-VAS Score and EQ-5D index, a quantile regression analysis was employed. Quantile Regression is a way to estimate the conditional quantiles of the VAS Score distribution in a linear model, in order to have a more complete view of possible associations between a measure of Health Related Quality of Life (dependent variable) and socio-demographic and determinants data. This methodological approach was preferred to an OLS regression because of the EQ-VAS Score and EQ-5D index typical distribution. Main Results. The analysis suggested that age, gender, and comorbidity can explain variability in perceived health status measured by the EQ-5D index and the VAS.

Probability distribution relationships

Abstract: In this paper, we are interesting to show the most famous distributions and their relations to the other distributions in collected diagrams. Four diagrams are sketched as networks. The first one is concerned to the continuous distributions and their relations. The second one presents the discrete distributions. The third diagram is depicted the famous limiting distributions. Finally, the Balakrishnan skew-normal density and its relationship with the other distributions are shown in the fourth diagram.

Generalized linear models and Capture-Recapture Method in a closed population: strengths and weaknesses

Abstract: Capture-recapture methods are used by epidemiologists in order to estimate the size of hidden populations using incomplete and overlapping lists of cases. These models can be both continuous and discrete time and the particular population we want to obtain a quantitative evaluation can be assumed to be closed or open. Here we specifically consider discrete-time models for closed population. The problem was treated using Generalized Linear Models as they allow to treat simultaneously both forms of dependence between sources than observed heterogeneity due to covariates effects. Specifically, we analyzed the strengths and weaknesses of Multinomial Conditional Logistic Model and presented a comparison with a correspondent Bayesian approach. The estimates obtained on simulated and real data appear to be enough reliable.

Evolution towards a synthesis

Abstract: Since the present event motivates us to look back to the past and to consider the developments of disciplines within and around statistics during the last decades, we would certainly be able to point out many relevant novelties, each of us choosing according to his or her orientation the salient facts in various directions and interpreting them according to the personal viewpoint. The field is vast, the different specialists’ interests are being divided amongst numerous aspects, and the brewing of ideas is always exciting, which springs from exchanges and contrasts among different conceptions, schools and mentalities. From my specific visual angle, the aspect which appears dominant to me in this vast panorama and of which, hence, I choose to speak about on this present occasion is the evolution that I believe is taking place towards a synthesis, that is towards a unitary vision which is gaining hold· and in which it appears that a place and a link are found for theories and application fields, which were previously unconnected and were in the developing stage, as parts which are now recomposed in an organic way. And allow me, before I enter into the merit of this specific subject, to say why generally, according to me, such a type of synthesis has by itself the maximum value and interest, whatever is the implied field of concepts, and, that is, independent of the fact that the case in which we will be dealing is a topic of my own interest, and a confirmation of a line I support. In general there is a wide-spread tendency to break knowledge up into claustrophobic and self-contained compartments, an attitude which I consider to be deplorable and destructive. Temporarily such a separation might be, and always is, useful or necessary in order to explain and, for mnemonic facility or otherwise, in order to set the ideas by purposely leaving aside the aspects which would take us further away from the problem under consideration; but this process would be useful only provided we do not forget the fact that we are facing a momentary separation, only tolerable as such, and not an amputation which might be demanded as stable. If detached from the whole, no portion of thought is alive; instead it often appears that the cultivators of any small garden have a wrong supreme ambition of autarchic isolation (and even our ineffable, bureaucratic norms, talking about “didactic auton-

Test and asymptotic normality for mixed bivariate measure

Abstract: Consider a pair of random variables whose joint probability measure is the sum of an absolutely continuous measure, a discrete measure and a finite number of absolutely continuous measures on some lines called jum lines. The central limit theorem of the densities estimates is studied and its rate of convergence is given. A statistical test is developed to locate the jump points. An application on real data was conducted.

Some issues concerning the statistical evaluation of a screening test: the arfi ultrasound case

Abstract: In this paper we analyze some issues concerning the statistical evaluation of a screening test for classification. The case study is ARFI, an ultrasound device recently introduced, and used for the evaluation of liver fibrosis. First, we present a simple statistical evaluation based on a novel index that compare two competitors with respect to a gold standard, and then we propose a procedure that determines a table with the “acceptable” number of measurements to get an “accurate” diagnosis using the ARFI device.

Individual and school variables effects on science learning: a multilevel analysis of PISA 2006 data in

Abstract: The paper describes the outcomes of a two-level regression analysis of the PISA 2006 science test scores in the province of Bolzano (Alto-Adige). They are particularly interesting because of the peculiarity of this province, where the organization of the education system is the same in the whole territory but schools are divided on the basis of language group their students belong: German/Ladin or Italian. More than forty variables from student and school-questionnaires have been analyzed by means of a series of models to study their effects on science scores and to identify which of them were associated with better performances at student and school level. Some hypothesis are also formulated to try to explain the superior performance of German/Ladin students and schools in comparison with Italian ones.

Elderly mortality in Italian regions at the beginning of the health transition (1881-1921)

Abstract: The paper aims to highlight and analyze possible regional patterns of mortality at advanced age (70-90 years) in Italy at the turn of the nineteenth century. The available data are referred to four distinct occasions, namely 1881-82, 1900-01, 1911-12 and 1921-22. After focusing attention on several elderly mortality indicators, we propose to analyze the resulting three-way array (with modes regionsindicatorsoccasions) using the STATIS method. As a critical preliminary step, new regional life tables for 1881-82 are constructed in order to reduce the possible bias due to the inaccuracy of the age distribution of the population and of the deaths in 1881. The resulting life tables are compared with Gini and Galvani’s ones and those available in the Human Mortality Database.

Prediction intervals for characteristics of future normal sample under moving ranked set sampling

Abstract: In this article, we derive prediction intervals for the characteristics of a future sample from normal population when the sample is selected via moving extreme ranked set sampling. We conduct a simulation study to compare these intervals with their counterparts using simple random sampling. Finally, we apply our findings on grassland biodiversity real data set in central Europe.

Which economic analysis is really enabled by district maps in Italy

Abstract: Industrial clusters have played a central role for economies of many countries during the past decades. While there is an abundance of qualitative analysis on these, for a long time many observers lament the lack of a statistical operational definition of industrial agglomerations, which may constitute a classificatory paradigm whereby data may be organized on a geographical basis so as to submit theoretical hypotheses to both measurement and econometric testing. The present paper aims at disentangling which economic analysis is really enabled by the available district maps for the Italian territory. To this purpose the two most relevant maps, one of whom is by the National Office of Statistics (ISTAT), are compared to highlight the different descriptions of the industrial districts geography and its transformations. The two approaches reveal many notes of disagreement. As a whole, the method adopted by ISTAT represents a fundamentally important contribution to local economic analysis; nonetheless, some useful suggestions might be received by means of this comparison.

Improving robust ratio estimation in longitudinal surveys with outlier observations

Abstract: The Hulliger’s robust estimation technique consists in the re-weighting of units identified as outliers through a Robustified Ratio Estimator (RRE), according to which outliers contribute to the final estimate with a sample weight reduced with respect to the original one. Outlier observations are identified through a standardised function founded on the difference between observed and expected values. A crucial aspect concerns the choice of the acceptation threshold, which plays a role in the re-weighting process as well. In this context, we propose some potential improvements of the RRE, concerning the use of an objective criterion for fixing the threshold and the re-weighting rules. Results of two empirical attempts based on real data derived from longitudinal surveys show that, in the most part of case studies, the proposed changes contribute to improve efficiency of estimates with respect to the ordinary ratio estimator.

Modeling the relationship between perceived neighbourhood characteristics and adult hospitalization frequencies

Abstract: Interest in the quantitative effects of neighbourhood characteristics on urban health has recently increased in social epidemiology. Such effects are mostly studied employing multilevel models based on some definition of the neighbourhood. We investigate the statistical relationship between health and the neighourhood quality as perceived by individuals, thus avoiding the need of choosing a specific definition of neighbourhood. We use data from the Los Angeles Family and Neighbourhood Survey (L.A.FANS). We measure health status of an individual as the number of hospitalizations in the last two years. This number is related to individual carachteristics (including neighbourhood perceptions) through generalized additive models (GAM), focusing particularly on the Zero Inflated Poisson (ZIP), which is an unusual choice in this context. We also overcome to some extent the difficulties in interpreting the results from a GAM with a ZIP distribution by simulating predicted values under varying assumptions in order to reveal the relationship of interest. The analysis confirms that the quality of neighbourhood – as measured by perceptions of individuals – significantly relates to the health status of inhabitants – as measured by the number of hospitalizations.

Some properties of a generalized type-1 Dirichlet distribution

Abstract: This paper deals with a generalization of type-1 Dirichlet density by incorporating partial sums of the component variables. We study various proportions, structural decompositions, connections to random volumes and p -parallelotopes. We will also look into the regression function of x k on x 1 ,..., x k- 1 , Bayes’ estimates for the probabilities of a multinomial distribution by using this generalized Dirichlet model as the prior density are given. Other results illustrate the importance of the study of variable x 1 in this model. It is found that the variable x 1 in this model can be represented as the ratio of squares of volumes of two parallelotopes. Under certain conditions, x 1 can be used to study the structural representations of the likelihood ratio criteria in MANOVA, MANCOVA etc.

Distributions of products involving the type II Bessel function random variable

Abstract: The aim of the present paper is to study the distributions of product of two independent random variables X and Y which are not everywhere positive. We have taken X to be a type II Bessel function random variate whereas Y belongs to one of normal, Pearson VII or Maxwell-Boltzmann families of distributions. Several special cases have also been obtained.

A simplified procedure of linear regression in a preliminary analysis

Abstract: The analysis of a statistical large data-set can be led by the study of a particularly interesting variable Y – regressed – and an explicative variable X, chosen among the remained variables, conjointly observed. The study gives a simplified procedure to obtain the functional link of the variables y = y (x) by a partition of the data-set into m subsets, in which the observations are synthesized by location indices (mean or median) of X and Y. Polynomial models for y (x) of order r are considered to verify the characteristics of the given procedure, in particular we assume r = 1 and 2. The distributions of the parameter estimators are obtained by simulation, when the fitting is done for m = r + 1. Comparisons of the results, in terms of distribution and efficiency, are made with the results obtained by the ordinary least square methods. The study also gives some considerations on the consistency of the estimated parameters obtained by the given procedure.