Factorial Models (factorial + models)

Distribution by Scientific Domains


Selected Abstracts


Causality and Causal Models: A Conceptual Perspective,

INTERNATIONAL STATISTICAL REVIEW, Issue 3 2006
Benito V. Frosini
Summary This paper aims at displaying a synthetic view of the historical development and the current research concerning causal relationships, starting from the Aristotelian doctrine of causes, following with the main philosophical streams until the middle of the twentieth century, and commenting on the present intensive research work in the statistical domain. The philosophical survey dwells upon various concepts of cause, and some attempts towards picking out spurious causes. Concerning statistical modelling, factorial models and directed acyclic graphs are examined and compared. Special attention is devoted to randomization and pseudo-randomization (for observational studies) in view of avoiding the effect of possible confounders. An outline of the most common problems and pitfalls, encountered in modelling empirical data, closes the paper, with a warning to be very cautious in modelling and inferring conditional independence between variables. Résumé Le but de cet article est d'offrir une vue d'ensemble sur le thème des relations causales, à partir de la doctrine philosophique aristotélique, et ensuite étendues et formalisées dans le champ de l'analyse statistique multivarée. Dans la revue philosophique on analyse plusieurs conceptions de cause, et les essais de reconnâtre les causes "fausses". La partie centrale du travail s'occupe de modèles causals en forme graphique, qui constituent l'instrument électif de plusieurs recherches causales, et met en evidence la différence entre conditionnement et intervention sur une variable. On a dedié une particulière attention aux procédures de randomization dans le but d'éviter de possible confusions. L'article termine en conseillant d'user de la prudence dans la modelage de l'independence conditionnelle et dans son contrôl empirique. [source]


Invariance and factorial models

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 2 2000
P. McCullagh
Two factors having the same set of levels are said to be homologous. This paper aims to extend the domain of factorial models to designs that include homologous factors. In doing so, it is necessary first to identify the characteristic property of those vector spaces that constitute the standard factorial models. We argue here that essentially every interesting statistical model specified by a vector space is necessarily a representation of some algebraic category. Logical consistency of the sort associated with the standard marginality conditions is guaranteed by category representations, but not by group representations. Marginality is thus interpreted as invariance under selection of factor levels (I -representations), and invariance under replication of levels (S -representations). For designs in which each factor occurs once, the representations of the product category coincide with the standard factorial models. For designs that include homologous factors, the set of S -representations is a subset of the I -representations. It is shown that symmetry and quasi-symmetry are representations in both senses, but that not all representations include the constant functions (intercept). The beginnings of an extended algebra for constructing general I -representations is described and illustrated by a diallel cross design. [source]