Measuring subcompositional incoherence

Subcompositional coherence is a fundamental property of Aitchison s approach to compositional data analysis, and is the principal justification for using ratios of components. We maintain, however, that lack of subcompositional coherence, that is incoherence, can be measured in an attempt to evaluate whether any given technique is close enough, for all practical purposes, to being subcompositionally coherent. This opens up the field to alternative methods, which might be better suited to cope with problems such as data zeros and outliers, while being only slightly incoherent. The measure that we propose is based on the distance measure between components. We show that the two-part subcompositions, which appear to be the most sensitive to subcompositional incoherence, can be used to establish a distance matrix which can be directly compared with the pairwise distances in the full composition. The closeness of these two matrices can be quantified using a stress measure that is common in multidimensional scaling, providing a measure of subcompositional incoherence. The approach is illustrated using power-transformed correspondence analysis, which has already been shown to converge to log-ratio analysis as the power transform tends to zero.

Crecimiento de las regiones españolas: estructura sectorial, dinámica regional y distribución de rentas.

El análisis de las regiones españolas en el período 1980-1995 indicaque la composición sectorial explica la mayor parte de la evolución del empleo y de las diferencias en productividad, salarios medios y participación de las rentas del trabajo. Para el VAB el componenteregional es más importante que el sectorial, aunque éste no esdespreciable. Nuestro análisis permite identificar a lo largo del tiempo aquellas regiones que han crecido más (menos) que lo esperado dada su composición sectorial. Identificamos una clara relación inversa entre la participación de las rentas del trabajo en el producto y el componente puramente regional del crecimiento del empleo. Sin embargo no observamos relación entre la tasa de paro y la distribución del producto. Ello sugiere que los salarios son poco elásticos a las condiciones del mercado de trabajo, pero el crecimiento del empleo sí lo es a la evolución de las rentas del capital de la región.

Multimarket contact in pharmaceutical markets

We analyze the effect of multimarket contact on the pricing behavior of pharmaceutical firms controlling for different levels of regulatory constraints using the IMS MIDAS database for the industry. Theoretically, under product differentiation, firms may find it profitable to allocate their market power among markets where they are operating, specifically from more collusive to more competitive ones. We present evidence for nine OECD countries suggesting the existence of a multimarket effect for more market friendly countries (U.S. and Canada) and less regulated ones (U.K., Germany, Netherlands), while the results are more unstable for highly regulated countries with some countries being consistent with the theory (France) while others contradicting it (Japan, Italy and Spain). A key result indicates thatin the latter countries, price constraints are so intense, that there is little room for allocating market power. Thus equilibrium prices are expected in general to be lower in regulated countries.

A Hull and White formula for a general stochastic volatility jump-diffusion model with applications to the study of the short-time behavior of the implied volatility

In this paper, generalizing results in Alòs, León and Vives (2007b), we see that the dependence of jumps in the volatility under a jump-diffusion stochastic volatility model, has no effect on the short-time behaviour of the at-the-money implied volatility skew, although the corresponding Hull and White formula depends on the jumps. Towards this end, we use Malliavin calculus techniques for Lévy processes based on Løkka (2004), Petrou (2006), and Solé, Utzet and Vives (2007).

A scaled difference chi-square test statistic for moment structure analysis

A family of scaling corrections aimed to improve the chi-square approximation of goodness-of-fit test statistics in small samples, large models, and nonnormal data was proposed in Satorra and Bentler (1994). For structural equations models, Satorra-Bentler's (SB) scaling corrections are available in standard computer software. Often, however, the interest is not on the overall fit of a model, but on a test of the restrictions that a null model say ${\cal M}_0$ implies on a less restricted one ${\cal M}_1$. If $T_0$ and $T_1$ denote the goodness-of-fit test statistics associated to ${\cal M}_0$ and ${\cal M}_1$, respectively, then typically the difference $T_d = T_0 - T_1$ is used as a chi-square test statistic with degrees of freedom equal to the difference on the number of independent parameters estimated under the models ${\cal M}_0$ and ${\cal M}_1$. As in the case of the goodness-of-fit test, it is of interest to scale the statistic $T_d$ in order to improve its chi-square approximation in realistic, i.e., nonasymptotic and nonnormal, applications. In a recent paper, Satorra (1999) shows that the difference between two Satorra-Bentler scaled test statistics for overall model fit does not yield the correct SB scaled difference test statistic. Satorra developed an expression that permits scaling the difference test statistic, but his formula has some practical limitations, since it requires heavy computations that are notavailable in standard computer software. The purpose of the present paper is to provide an easy way to compute the scaled difference chi-square statistic from the scaled goodness-of-fit test statistics of models ${\cal M}_0$ and ${\cal M}_1$. A Monte Carlo study is provided to illustrate the performance of the competing statistics.

The donor problem

Donors often rely on local intermediaries to deliver benefits to target beneficiaries. Each selected recipient observes if the intermediary under-delivers to them, so they serve as natural monitors. However, they may withhold complaints when feeling unentitled or grateful to the intermediary for selecting them. Furthermore, the intermediary may distort selection (e.g. by picking richer recipients who feel less entitled) to reduce complaints. We design an experimental game representing the donor s problem. In one treatment, the intermediary selects recipients. In the other, selection is random - as by an uninformed donor. In our data, random selection dominates delegation of the selection task to the intermediary. Selection distortions are similar, but intermediaries embezzle more when they have selection power and (correctly) expect fewer complaints.

Analysis of matched matrices

We consider the joint visualization of two matrices which have common rowsand columns, for example multivariate data observed at two time pointsor split accord-ing to a dichotomous variable. Methods of interest includeprincipal components analysis for interval-scaled data, or correspondenceanalysis for frequency data or ratio-scaled variables on commensuratescales. A simple result in matrix algebra shows that by setting up thematrices in a particular block format, matrix sum and difference componentscan be visualized. The case when we have more than two matrices is alsodiscussed and the methodology is applied to data from the InternationalSocial Survey Program.

Measuring asymmetries in brand associations using correspondence analysis

Correspondence analysis is introduced in the brand associationliterature as an alternative tool to measure dominance, for theparticular case of free choice data. The method is also used to analysedifferences, or asymmetries, between brand-attribute associations whereattributes are associated with evoked brands, and brand-attributeassociations where brands are associated with the attributes. Anapplication to a sample of deodorants is used to illustrate the proposedmethodology.

An inequality for uniform deviations of sample averages from their means

We derive a new inequality for uniform deviations of averages from their means. The inequality is a common generalization of previous results of Vapnik and Chervonenkis (1974) and Pollard (1986). Usingthe new inequality we obtain tight bounds for empirical loss minimization learning.

Killing by lung cancer or by diabetes? The trade-off between smoking and obesity

As the prevalence of smoking has decreased to below 20%, health practitioners interest has shifted towards theprevalence of obesity, and reducing it is one of the major health challenges in decades to come. In this paper westudy the impact that the final product of the anti-smoking campaign, that is, smokers quitting the habit, had onaverage weight in the population. To these ends, we use data from the Behavioral Risk Factors Surveillance System,a large series of independent representative cross-sectional surveys. We construct a synthetic panel that allows us tocontrol for unobserved heterogeneity and we exploit the exogenous changes in taxes and regulations to instrumentthe endogenous decision to give up the habit of smoking. Our estimates, are very close to estimates issued in the 90sby the US Department of Health, and indicate that a 10% decrease in the incidence of smoking leads to an averageweight increase of 2.2 to 3 pounds, depending on choice of specification. In addition, we find evidence that the effectovershoots in the short run, although a significant part remains even after two years. However, when we split thesample between men and women, we only find a significant effect for men. Finally, the implicit elasticity of quittingsmoking to the probability of becoming obese is calculated at 0.58. This implies that the net benefit from reducingthe incidence of smoking by 1% is positive even though the cost to society is $0.6 billions.

Small-area estimation with spatial similarity

A class of composite estimators of small area quantities that exploit spatial (distancerelated)similarity is derived. It is based on a distribution-free model for the areas, but theestimators are aimed to have optimal design-based properties. Composition is applied alsoto estimate some of the global parameters on which the small area estimators depend.It is shown that the commonly adopted assumption of random effects is not necessaryfor exploiting the similarity of the districts (borrowing strength across the districts). Themethods are applied in the estimation of the mean household sizes and the proportions ofsingle-member households in the counties (comarcas) of Catalonia. The simplest version ofthe estimators is more efficient than the established alternatives, even though the extentof spatial similarity is quite modest.

A simple randomized algorithm for consistent sequential prediction of ergodic time series

We present a simple randomized procedure for the prediction of a binary sequence. The algorithm uses ideas from recent developments of the theory of the prediction of individual sequences. We show that if thesequence is a realization of a stationary and ergodic random process then the average number of mistakes converges, almost surely, to that of the optimum, given by the Bayes predictor.

Fighting against Malaria: Prevent wars while waiting for the "miraculous" vaccine

The World Health Organization estimates that 300 million clinical cases of malaria occur annually and observed that during the 80's and part of the 90's its incidence increased. In this paper we explore the influence of refugees from civil wars on the incidence of malaria in the refugee-receiving countries. Using civil wars as an instrumental variable we show that for each 1,000 refugees there are between 2,000 and 2,700 cases of malaria in the refugee receiving country. On average 13% of the cases of malaria reported by the WHO are caused by forced migration as a consequence of civil wars.

From correspondence analysis to multiple and joint correspondence analysis

The generalization of simple (two-variable) correspondence analysis to more than two categorical variables, commonly referred to as multiple correspondence analysis, is neither obvious nor well-defined. We present two alternative ways of generalizing correspondence analysis, one based on the quantification of the variables and intercorrelation relationships, and the other based on the geometric ideas of simple correspondence analysis. We propose a version of multiple correspondence analysis, with adjusted principal inertias, as the method of choice for the geometric definition, since it contains simple correspondence analysis as an exact special case, which is not the situation of the standard generalizations. We also clarify the issue of supplementary point representation and the properties of joint correspondence analysis, a method that visualizes all two-way relationships between the variables. The methodology is illustrated using data on attitudes to science from the International Social Survey Program on Environment in 1993.

Worst-case bounds for the logarithmic loss of predictors

We investigate on-line prediction of individual sequences. Given a class of predictors, the goal is to predict as well as the best predictor in the class, where the loss is measured by the self information (logarithmic) loss function. The excess loss (regret) is closely related to the redundancy of the associated lossless universal code. Using Shtarkov's theorem and tools from empirical process theory, we prove a general upper bound on the best possible (minimax) regret. The bound depends on certain metric properties of the class of predictors. We apply the bound to both parametric and nonparametric classes ofpredictors. Finally, we point out a suboptimal behavior of the popular Bayesian weighted average algorithm.