this paper we will describe how to extend search algorithms developed for non-latent variable DAG models to the case of DAG models with latent variables. We will introduce two generalizations of DAGs, called mixed ancestor graphs (or MAGs) and partial ancestor graphs (or PAGs), and briefly describe how they can be used to search for latent variable DAG models, to classify, and to predict the effects of interventions in causal systems.

Weakliem agrees that Bayes factors are useful for model selection and hypothesis testing. He reminds us that the simple and convenient BIC approximation corresponds most closely to one particular prior on the parameter space, the unit information prior, and points out that researchers may have different prior information or opinions. Clearly a prior that represents the available information should be used, although the unit information prior often seems reasonable in the absence of strong prior information. It seems that, among the Bayes factors likely to be used in practice, BIC is conservative in the sense of tending to provide less evidence for additional parameters or "effects". Thus if a Bayes factor based on additional prior information favors an effect, but BIC does not, the prior information is playing a crucial role and this should be made clear when the research is reported. BIC may well have a role as a baseline reference analysis to be provided in routine reporting of research results, perhaps along with Bayes factors based on other priors. In Weakliem's 2 x 2 table examples, BIC and Bayes factors based on Weakliem's preferred priors lead to similar substantive conclusions, but both differ from those based on P values. When there is additional prior information, the technology now exists to express it as

In recursive linear models, the multivariate normal joint distribution of all variables exhibits a dependence structure induced by recursive systems of linear structural equations. Such models appear in particular in seemingly unrelated regressions, structural equation modelling, simultaneous equation systems, and in Gaussian graphical modelling. We show that recursive linear models that are ‘bow-free’ are well-behaved statistical models, namely, they are everywhere identifiable and form curved exponential families. Here, ‘bow-free ’ refers to models satisfying the condition that if a variable x occurs in the structural equation for y, then the errors for x and y are uncorrelated. For the computation of maximum likelihood estimates in ‘bow-free ’ recursive linear models we introduce the Residual Iterative Conditional Fitting (RICF) algorithm. Compared to existing algorithms RICF is easily implemented requiring only least squares computations, has clear convergence properties, and finds parameter estimates in closed form whenever possible. KEY WORDS: Linear structural equation model; curved exponential family; maximum likelihood estimation; residual iterative conditional fitting; bow-free acyclic path diagrams; BAP. 1

Michaelmas 2009This thesis is dedicated to the late

Event history analysis seems ideally suited for the analysis of World Fertility Survey (WFS) data, which consists of full birth histories and related information. However, it has not been much used for this purpose, and most analyses of WFS data have consisted of tabulations of standard fertility rates, and regressions with children ever born as the dependent variable, both of which have disadvantages. We suggest that this is because event history analysis has practical drawbacks for WFS data, even though, in principle, it provides a superior analytic framework. These are the many partial dates, the computational burden of discrete-time event history analysis, the need to take account of five clocks at once (age, period, cohort, time since last event, and parity), and the difficulty of interpreting the coefficients. We propose a modeling strategy for the event history analysis of WFS data which aims to overcome these problems, and we apply it to the previously unanalyzed WFS data from...

ABSTRACT. – A rule for choosing among nested models is presented, taking into account that the usual model selection procedure is a sequence of tests, followed by estimation of the parameters that remain in the model. We take a decision theoretical approach and formulate the loss functions and the rules from a Bayesian point of view. The rule resembles a Neyman-Pearson type test but it takes into consideration the estimation loss across different candidate models and reports an estimate together with an associated loss, taking into account the uncertainty in the selection. The method is compared with other existing procedures and illustrated by examples. Choix de modèles à partir de critères d’estimation RÉSUMÉ. – Nous développons une méthode de sélection de modèles pour des modèles emboités. L’apport de cette méthode est prendre en compte l’usage courant en sélection de modèle, qui est d’appliquer une suite de tests et d’effectuer ensuite l’estimation des paramètres restants. Nous reprenons cette démarche d’un point de vue décisionnel, en introduisant des fonctions de coût adéquates et en définissant les estimateurs de Bayes associés. La règle de décision est similaire à celle de Neyman-Pearson mais elle prend en compte les coûts respectifs des différents modèles et propose un estimateur en sus d’un modèle, en intégrant l’incertitude liée au choix du modèle. Nous comparons cette nouvelle méthode avec les techniques existantes et l’illustrons sur des exemples standards. * C. GOUTIS; Ch. P. ROBERT: CREST-INSEE. Constantinos Goutis died tragically in a scubadiving accident on July 21, 1996, near Seattle. He was then 33 and a visiting

Research article Bias and heteroscedastic memory error in self-reported health behavior: an investigation using covariance structure analysis