Michel Mouchart

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.

A Note on Noncausality

In this note the relationship between alternative concepts of noncausality is analyzed using the tool of conditional independence among a-fields. (For the reader who is unfamiliar with this technique, the Appendix sketches the proofs and the basic technical apparatus, along with some basic motivations.) Furthermore, the relationship between the concepts of noncausality and transitivity is made explicit in order to facilitate, in econometric modelling, the use of results already obtained in sequential analysis.

Do we necessarily need longitudinal data to infer causal relations

A-t-on nécessairement besoin de données longitudinales pour inférer des relations causales ? Il est généralement admis que les causes précèdent leurs effets dans le temps. Cela justifie usuellement la préférence pour les études longitudinales par rapport aux études transversales, parce que les premières permettent la modèlisation du processus dynamique engendrant le résultat, tandis que les secondes ne le peuvent pas. Les partisans de l’approche longitudinale proposent deux justifications interdépendantes : (i) l’inférence causale nécessite le suivi des mêmes personnes au fil du temps, et (ii) aucune inférence causale ne peut être tirée de données transversales. Dans cet article, nous remettons en question ce point de vue et proposons des objections à ces deux arguments. Nous soutenons également que la possibilité d’établir des relations de cause à effet ne dépend pas tant de l’utilisation de données longitudinales ou transversales, mais plutôt de savoir si la stratégie de modélisation est d’ordre structurel ou non. It is generally admitted that causes precede their effects in time. This usually justifies the preference for longitudinal studies over cross-sectional ones, because the former allow the modelling of the dynamic process generating the outcome, while the latter cannot. Supporters of the longitudinal view make two interrelated claims: (i) causal inference requires following the same individuals over time, and (ii) no causal inference can be drawn from cross-sectional data. In this paper, we challenge this view and offer counter-arguments to both claims. We also argue that the possibility of establishing causal relations does not so much depend upon whether we use longitudinal or cross-sectional data, but rather on whether or not the modelling strategy is structural.

Noncausality and Marginalization of Markov-processes

In this paper it is shown that a subprocess of a Markov process is markovian if a suitable condition of noncausality is satisfied. Furthermore, a markovian condition is shown to be a natural condition when analyzing the role of the horizon (finite or infinite) in the property of noncausality. We also give further conditions implying that a process is both jointly and marginally markovian only if there is both finite and infinite noncausality and that a process verifies both finite and infinite noncausality only if it is markovian. Counterexamples are also given to illustrate the cases where these further conditions are not satisfied.

Structural Modelling, Exogeneity, and Causality

This paper deals with causal analysis in the social sciences. We first present a conceptual framework according to which causal analysis is based on a rationale of variation and invariance, and not only on regularity. We then develop a formal framework for causal analysis by means of structural modelling. Within this framework we approach causality in terms of exogeneity in a structural conditional model based which is based on (i) congruence with background knowledge, (ii) invariance under a large variety of environmental changes, and (iii) model fit. We also tackle the issue of confounding and show how latent confounders can play havoc with exogeneity. This framework avoids making untestable metaphysical claims about causal relations and yet remains useful for cognitive and action-oriented goals.

Inferring causality through counterfactuals in observational studies - Some epistemological issues

L’inférence causale par contrefactuels dans les études observationnelles — Quelques épistémologiques : Cet article contribue au débat sur les vertus et les vices de contrefactuels comme base pour l’inférence causale. L’objectif est de mettre l’approche contrefactuelle dans une perspective épistémologique. Nous discutons d’un certain nombre de questions, allant de sa base non observable au parallélisme établi entre cette approche en statistique et en philosophie. Nous soutenons que la question n’est pas de rejeter ou d’approuver l’approche contrefactuelle par principe, mais de décider quel cadre de modélisation est préférable en fonction du contexte de la recherche. This paper contributes to the debate on the virtues and vices of counterfactuals as a basis for causal inference. The goal is to put the counterfactual approach in an epistemological perspective. We discuss a number of issues, ranging from its non-observable basis to the parallelisms drawn between the counterfactual approach in statistics and in philosophy. We argue that the question is not to oppose or to endorse the counterfactual approach as a matter of principle, but to decide what modelling framework is best to adopt depending on the research context.

Specification and identification issues in models involving a latent hierarchical structure

The object of this paper is to consider specification and identification problems for the case of models involving a latent hierarchical structure. After making some characteristics of such models explicit, the paper proposes a strategy of model specification characterized by a progressive introduction of hypotheses. Such a strategy allows us a suitable control of the contextual interpretability of each hypothesis. A particular care is devoted to the statistical role of each statistical unit. The difficult identification problem of a mixture is analysed by taking advantage of the decomposition of a global model into contextually meaningful submodels; general results for the identifiability of the statistical model are given. The last section exemplifies how to use the results of the paper for the case of ultrastructural models, mainly known in the biometric literature

Specification and inference in linear models

Abstract In the framework of I.I.D. sampling, a general class of linear models is analyzed. Incidental parameters are shown to naturally arise in this class of models. More fundamentally, special attention is paid to the high dimensionality of the parameter space. The objective of the paper is to offer a strategy for progressively specifying a model within that class of linear models. By so doing, we aim at displaying the precise role of each assumption, at offering alternatives to unnecessarily restrictive specifications, and, thereby, at improving the robustness of the inference procedures we discuss. Decompositions of the inference process are obtained through a systematic use of (Bayesian) cuts. Maximum Likelihood Estimation and Bayesian Inference are discussed. An objective of the progressive specification is to preserve the computational tractability and the interpretability of the procedures we develop by relying on known properties of the usual multivariate regression model.

Polynomial approximation of distributed lags and linear restrictions: A Bayesian approach

In this paper, the polynomial approximation of distributed lags is investigated within the framework of linear restrictions in linear regression models.In the first part, the polynomial approximation is analysed assuming well known the truncation point and the degree of the polynomial. The polynomial approximation is shown to involve linear restrictions on regression coefficients; two equivalent representations of these restrictions are used to clarify relationships between previous works byAlmon and byShiller. The difficulties related to the treatment of exact restrictions in a Bayesian framework are then tackled in the present context and alternative procedures are presented.In the second part, the analysis is extended to the case of unknown truncation point and/or unknown degree of the polynomial. This leads to consider mixed prior distributions as for the problem of choosing among different models. The paper ends by investigating the sensitivity of a particular set of data w.r.t. changes in the truncation point, in the degreee of the polynomial and in the prior tightness of the polynomial approximation.

Bayesian Encompassing Tests of a Unit Root Hypothesis

The object of this paper is to report, for a simple testing problem of a unit root hypothesis, some experience regarding the numerical problems involved by using a Bayesian encompassing test, i.e., a Bayesian procedure that treats the null and the alternative hypotheses as different models, the null one and the alternative one, that share a same sample space but with different parameter spaces. Numerical procedures and efficient simulations are discussed briefly, and the numerical results so obtained are used to evaluate the meaning of the prior specification and of the empirical evidence about a unit root inference.