Ernesto San Martín

The local spatial autocorrelation and the kernel method for identifying black zones. A comparative approach

This article aims to determine the location and the length of road sections characterized by a concentration of accidents (black zones). Two methods are compared: one based on a local decomposition of a global autocorrelation index, the other on kernel estimation. After explanation, both methods are applied and compared in terms of operational results, respective advantages and shortcomings, as well as underlying conceptual elements. The operationality of both methods is illustrated by an application to one Belgian road.

Linear mixed models with skew-elliptical distributions: A Bayesian approach

Normality of random effects and error terms is a routine assumption for linear mixed models. However, such an assumption may be unrealistic, obscuring important features of within- and among-unit variation. A simple and robust Bayesian parametric approach that relaxes this assumption by using a multivariate skew-elliptical distribution, which includes the Skew-t, Skew-normal, t-Student, and Normal distributions as special cases and provides flexibility in capturing a broad range of non-normal and asymmetric behavior is presented. An appropriate posterior simulation scheme is developed and the methods are illustrated with an application to a longitudinal data example.

IRT Models for Ability-Based Guessing:

An ability-based guessing model is formulated and applied to several data sets regarding educational tests in language and in mathematics. The formulation of the model is such that the probability of a correct guess does not only depend on the item but also on the ability of the individual, weighted with a general discrimination parameter. By so doing, the possibility that the individual uses his or her ability to some extent for differentiating among responses while guessing is also considered. Some important properties of the model are described and compared with analogous properties of related models. After simulation studies, the model is applied to different data sets of the Chilean Sistema de Medición de la Calidad ń (SIMCE) tests of mathematics and language. The conclusion of this analysis seems relevant—namely, that the examinees use their ability to guess in the language test but not in the mathematics test.

School system evaluation by value added analysis under endogeneity

Value added is a common tool in educational research on effectiveness. It is often modeled as a (prediction of a) random effect in a specific hierarchical linear model. This paper shows that this modeling strategy is not valid when endogeneity is present. Endogeneity stems, for instance, from a correlation between the random effect in the hierarchical model and some of its covariates. This paper shows that this phenomenon is far from exceptional and can even be a generic problem when the covariates contain the prior score attainments, a typical situation in value added modeling. Starting from a general, model-free definition of value added, the paper derives an explicit expression of the value added in an endogeneous hierarchical linear Gaussian model. Inference on value added is proposed using an instrumental variable approach. The impact of endogeneity on the value added and the estimated value added is calculated accurately. This is also illustrated on a large data set of individual scores of about 200,000 students in Chile.

On the Unidentifiability of the Fixed-Effects 3PL Model

The paper offers a general review of the basic concepts of both statistical model and parameter identification, and revisits the conceptual relationships between parameter identification and both parameter interpretability and properties of parameter estimates. All these issues are then exemplified for the 1PL, 2PL, and 1PL-G fixed-effects models. For the 3PL model, however, we provide a theorem proving that the item parameters are not identified, do not have an empirical interpretation and that it is not possible to obtain consistent and unbiased estimates of them.

Identification of the 1PL Model with Guessing Parameter: Parametric and Semi-parametric Results

In this paper, we study the identification of a particular case of the 3PL model, namely when the discrimination parameters are all constant and equal to 1. We term this model, 1PL-G model. The identification analysis is performed under three different specifications. The first specification considers the abilities as unknown parameters. It is proved that the item parameters and the abilities are identified if a difficulty parameter and a guessing parameter are fixed at zero. The second specification assumes that the abilities are mutually independent and identically distributed according to a distribution known up to the scale parameter. It is shown that the item parameters and the scale parameter are identified if a guessing parameter is fixed at zero. The third specification corresponds to a semi-parametric 1PL-G model, where the distribution G generating the abilities is a parameter of interest. It is not only shown that, after fixing a difficulty parameter and a guessing parameter at zero, the item parameters are identified, but also that under those restrictions the distribution G is not identified. It is finally shown that, after introducing two identification restrictions, either on the distribution G or on the item parameters, the distribution G and the item parameters are identified provided an infinite quantity of items is available.

Voucher system and school effectiveness: Reassessing school performance difference and parental choice decision-making

This paper discusses the potential contribution of employing school effectiveness methodological approach within the ongoing research debate on school choice issues. Using the first approach, we estimate the effectiveness of a sample of Chilean schools after controlling by a baseline at the student level. In order to avoid the endogeneity of such a baseline with respect to the school effect, we use a longitudinal data set (SIMCE 2004 and SIMCE 2006) from which a natural pseudo-experiment is defined in such a way that the baseline is by design uncorrelated with the school effect. Thereafter, we investigate possible relationships between parental school choice (as declared in public standardized surveys) and the schools classified by their effectiveness. The main conclusions of this paper are, on the one hand, that there is not remarkable difference between municipal (public) and subsidised schools in terms of their effectiveness analyzed under value-added; and, on the other hand, that there is no relation between parental school choice preferences and school effectiveness.

Identified Parameters, Parameters of Interest and Their Relationships.

The goal of this commentary is to provide some additional results to the interesting and provocative paper of Maris and Bechger (this issue). More specifically, we have three aims. First, we want to distinguish between three fundamental concepts that are important in studying identification in statistical models: the statistical model, the identified parametrization, and the parameters of interest. Second, we want to take the analysis of Maris and Bechger (this issue) one step further by showing what restrictions are needed to identify the 3PL with discriminations equal to 1 (which, following San Martin, Del Pino, and De Boeck, 2006, we term 1PL-G) in a meaningful way. Third, we want to point to an implicit problem in the analysis of Maris and Bechger (this issue), but one that has much broader consequences than appear at first sight. Let us begin with explaining the three fundamental concepts (statistical model, identified parametrization and parameters of interest) that we think are necessary to be distinguished in any identification enterprise. These concepts will be reviewed and explained using a more convenient, but otherwise equivalent, parameterization of the Rasch model as it is specified in Maris and Bechger (this issue):

A note on the parameterization of multivariate skewed-normal distributions

Abstract. Azzalini’s skew-normal distribution is obtained through a condi-tional reduction of a multivariate normal distribution parameterized with acorrelation matrix. It seems natural that when the parameterization of thatmultivariate normal distribution is complexified, more flexible skew-normaldistributions could be obtained. In this note this specification strategy, previ-ously explored by Azzalini [ Scand. J. Stat. 33 (2006) 561–574] among manyother authors, is formally analyzed through an identification analysis. 1 Introduction Skewed-normal distributions can be obtained as a conditional reduction of a mul-tivariate normal distribution as follows (see Capitanio et al., 2003; Arellano-Valleand Azzalini, 2006): let U 0 ∈R and U 1 ∈R d be two random vectors such that U = U 0 U 1 ∼ N 1+ d 0 0 , ∗ =1 δ T δ ¯ , where δ ∈ ( −1 , 1 ) d , ¯ ∈R d × d is a positive definite symmetric matrix and ∗ isa correlation matrix. Let Z = d ( U 1 | U 0 > − γ), where= d means equal distribution .Thus, the probability density function (p.d.f.) of

Measuring the relation between computer use and reading literacy in the presence of endogeneity

This work studies the relation between computer use for reading activities and academic literacy in 15-year-old students in Chile, Uruguay, Spain, and Portugal. Data used is from the PISA 2009 test. Special attention is given to potential bias problems when the computer use is an endogenous variable. Few studies in this area address this issue: existing literature has shown that different types of computer use have different implications on performance. The limitations of observational data have also been emphasized to establish cause-effect relations between computer use and academic performance. It is important, however, to consider the computer use endogeneity hypothesis (above all at home) since students decide on the frequency of computer use at home. The results found show that by controlling for endogeneity, computer use for reading is not related to reading performance neither in digital or printed format, with the exception of Chile that shows a negative relation in the case of reading from a printed format. The results considering endogeneity differ considerably from results when endogeneity is not taken into account. The work shows the relevance of experimental type studies in order to make sound statements with regard to the computer use and academic performance relation. In turn, school reading activities in a digital environment are suggested that could have an impact on reading performance. We study the relation between computer use for reading and academic literacy.Our results differ considerably when endogeneity is taken into account.Computer use is not related to reading performance when endogeneity is considered.We suggest experimental studies to measure computer use-reading score relation.