The General Linear Model and the Generalized Singular Value Decomposition; Some Examples

The general linear model with correlated error variables can be transformed by means of the generalized singular value decomposition to a very simple model (canonical form) where the least squares solution is obvious. The method works also if X and the covariance matrix of the error variables do not have full rank or are nearly rank deficient (rank-k approximation). By backtransformation one obtains the solution for the original model. In this paper we demonstrate the method with some examples

Factor Analysis: Chisquare as Rotation Criterion

The rotation problem in factor analysis consists in finding an orthogonal transformation of the initial factor loadings so that the rotated loadings have a simple structure that can be easily interpreted. The most popular orthogonal transformations are the quartimax and varimax procedure with Kaiser normalization. In this paper we propose the classical chisquare contingency measure as a rotation criterion. We think that this is a very natural and attractive criterion, not only for rotations but also for oblique transformations, that is not to be found in our popular statistical packages up to now

Alternatives to the MCMC method

The Markov Chain Monte Carlo method (MCMC) is often used to generate independent (pseudo) random numbers from a distribution with a density that is known only up to a normalising constant. With the MCMC method it is not necessary to compute the normalising constant (see e.g. Tierney, 1994; Besag, 2000). In this paper we show that the well-known acceptance-rejection algorithm also works with unnormalised densities, and so this algorithm can be used to confirm the results of the MCMC method in simple cases. We present an example with real data

The General Linear Model and the Generalized Singular Value Decomposition

The general linear model with correlated error variables can be transformed by means of the generalized singular value decomposition to a very simple model (canonical form) where the least squares solution is obvious. The method works also if X and the covariance matrix of the error variables do not have full rank or are nearly rank deficient (rank-k approximation). By backtransformation one obtains the solution for the original model

Singulärwert-Zerlegung und Methode der kleinsten Quadrate

The method of least squares is an important instrument to determine the optimal linear estimators in regression models. By means of the singular value decomposition we can find the least squares estimators without differentiation, without solving the normal equations and without assumptions on the rank of the data matrix. Even in case of multicollinearity we can find the simple and natural solutions. The results in the paper are not new, they have been developed mainly in numerical publications, but they are hardly to be found in statistical textbooks

Funerary taphonomy: An overview of goals and methods

Funerary taphonomy has come of age as an important field in osteoarchaeology. Its goal is to reconstruct funerary practices by using taphonomic evidence, including both evidence recorded during excavation (particularly the context and state of articulation of human remains) and evidence observable in subsequent laboratory analysis (such as element representation and traces of burning, animal modification, cut-marks, and fragmentation). This article – intended as a systematic introduction to the field – gives an overview of funerary taphonomy. It first discusses the goals and theoretical questions, and then reviews the wide range of methods available to archaeologists using human remains to investigate funerary behaviour. It finishes with a review of how taphonomists have approached particular issues, such as single burials, commingled multiple depositions, cannibalism, and the cultural reuse of human skeletal parts.This is the final version of the article. It first appeared from Elsevier via http://dx.doi.org/10.1016/j.jasrep.2016.05.03

Fragmentation: the zonation method applied to fragmented human remains from archaeological and forensic contexts

Reproduced with permission of the publisher. Copyright © Oxbow Books and the Association for Environmental Archaeology 2004.Scattered and commingled human and animal remains are commonly encountered on archaeological sites, and this contextual relationship begs the question of whether human and animals were treated in a similar manner before burial. The recording system presented here provides a means by which to confront problems of equifinality - that is, when taphonomic alterations create apparently similar patterns and, therefore, confuse behavioural inferences drawn from them. This method hinges on a standardised representation of the zones on human skeletal elements that allow comparison with those described by Dobney and Rielly (1988) for animal remains. It is anticipated that the anatomical descriptions in combination with the zone drawings presented will aid others to apply the method generally across skeletal assemblages of any date. This system could also be used to aid the curation of museum collections and as a complement to forensic recovery