Estimation of generalized linear latent variable models

Summary.  Generalized linear latent variable models (GLLVMs), as defined by Bartholomew and Knott, enable modelling of relationships between manifest and latent variables. They extend structural equation modelling techniques, which are powerful tools in the social sciences. However, because of the complexity of the log-likelihood function of a GLLVM, an approximation such as numerical integration must be used for inference. This can limit drastically the number of variables in the model and can lead to biased estimators. We propose a new estimator for the parameters of a GLLVM, based on a Laplace approximation to the likelihood function and which can be computed even for models with a large number of variables. The new estimator can be viewed as an M -estimator, leading to readily available asymptotic properties and correct inference. A simulation study shows its excellent finite sample properties, in particular when compared with a well-established approach such as LISREL. A real data example on the measurement of wealth for the computation of multidimensional inequality is analysed to highlight the importance of the methodology.     

Local dependence estimation using semiparametric archimedean copulas

The authors define a new semiparametric Archimedean copula family which has a flexible dependence structure. The generator of the family is a local interpolation of existing generators. It has locally‐defined dependence parameters. The authors present a penalized constrained least‐squares method to estimate and smooth these parameters. They illustrate the flexibility of their dependence model in a bi‐variate survival example.     

Ethnic Institutions Reconsidered: The Case of Flemish Workers in 19th Century France1

Abstract Traditional perspectives on ethnic institutions tend to consider mainly their role in the preservation of the cultural and social fabric of ethnic communities. Increasing evidence indicates that ethno‐institutional effects are often more varied and complex. France's first industrial‐era immigrants, massively crossing the border from Belgian Flanders during the second half of the 19^th century, are a case in point. Immigrant Flemish workers introduced a new type of institution to the French working class: socialist cooperatives. These would have a long‐term impact not only on the immigrant Flemish community itself, but also on the larger labour movement, on the region, and on the country as a whole. Three elements were important in this process of institutional cross‐fertilization: Belgian workers’ rich institutional repertoire; the coincidence of their settlement with the rise of the French labour movement; and the fact that their institutional innovation was easily transferable.     

Social choice theory in the case of von Neumann-Morgenstern utilities

Part I of this paper offers a novel result in social choice theory by extending Harsanyi's well-known utilitarian theorem into a multi-profile context. Harsanyi was contented with showing that if the individuals' utilities u _i are von Neumann-Morgenstern, and if the given utility u of the social planner is VNM as well, then the Pareto indifference rule implies that u is affine in terms of the u _i. We provide a related conclusion by considering u as functionally dependent on the u _i, through a suitably restricted social welfare functional (u ₁,...,u _n)u=f(u ₁,...,u _n). We claim that this result is more in accordance with contemporary social choice theory than Harsanyi's single-profile theorem is. Besides, harsanyi's initial proof of the latter was faulty. Part II of this paper offers an alternative argument which is intended to be both general and simple enough, contrary to the recent proofs published by Fishburn and others. It finally investigates the affine independence problem on the u _i discussed by Fishburn as a corollary to harsanyi's theorem.The authors are indebted to L. Haddad, A. Sen and two anonymous referees for useful written comments. They also benefited from stimulating remarks in seminars and helpful conversations with their colleagues. The usual caveat of course applies. One of the authors acknowledges partial financial support from the ARI Communication of the C.N.R.S., Paris.     

On the logic of common belief and common knowledge

The paper surveys the currently available axiomatizations of common belief (CB) and common knowledge (CK) by means of modal propositional logics. (Throughout, knowledge — whether individual or common — is defined as true belief.) Section 1 introduces the formal method of axiomatization followed by epistemic logicians, especially the syntax-semantics distinction, and the notion of a soundness and completeness theorem. Section 2 explains the syntactical concepts, while briefly discussing their motivations. Two standard semantic constructions, Kripke structures and neighbourhood structures, are introduced in Sections 3 and 4, respectively. It is recalled that Aumann's partitional model of CK is a particular case of a definition in terms of Kripke structures. The paper also restates the well-known fact that Kripke structures can be regarded as particular cases of neighbourhood structures. Section 3 reviews the soundness and completeness theorems proved w.r.t. the former structures by Fagin, Halpern, Moses and Vardi, as well as related results by Lismont. Section 4 reviews the corresponding theorems derived w.r.t. the latter structures by Lismont and Mongin. A general conclusion of the paper is that the axiomatization of CB does not require as strong systems of individual belief as was originally thought — onlymonotonicity has thusfar proved indispensable. Section 5 explains another consequence of general relevance: despite the infinitary nature of CB, the axiom systems of this paper admit of effective decision procedures, i.e., they aredecidable in the logician's sense.     

Measuring credibility of compensatory preference statements when trade-offs are interval determined

This paper studies how an overall fuzzy preference relation can be constructed in the compensatory context of the simple additive difference model, when imprecision on the trade-offs has to be taken into account. Three credibility indices of preferences are analysed and illustrated by a numerical example. Arguments are presented supporting the use of the third index, for which an interesting transitivity property (which was an open problem) is proved.