Suchergebnisse

For modelling the effect of crossed, fixed factors on the response variable in balanced designs with nested stratifications, a generalized linear mixed model is proposed. This model is based on a set of quasi‐likelihood assumptions which imply quadratic variance functions. From these variance functions, deviances are obtained to quantify the variation per stratification. The effects of the fixed factors will be tested, an dispersion components will be estimated. The practical use of the model is illustrated by reanalysing a soldering failures problem.

In this paper a review will be given of some methods available for modelling relationships between categorical response variables and explanatory variables. These methods are all classed under the name polytomous logistic regression (PLR). Models for PLR will be presented and compared; model parameters will be tested and estimated by weighted least squares and by likelihood. Usually, software is needed for computation, and available statistical software is reported.An industrial problem is solved to some extent as an example to illustrate the use of PLR. The paper is concluded by a discussion on the various PLR‐methods and some topics that need a further study are mentioned.

From the literature on nonparametric rank tests, limiting distributions of Wilcoxon's test tor symmetry and ot Friedman's test for treatment effect are known for observations that are classified in blocks. It is assumed that there is no interaction between blocks and treatments. In the case of fixed blocks this assumption is quite reasonable, in the case of random blocks it is not, as the presence of a random interaction does not make testing for treatment effect superfluous. For classified, categorical data in random blocks the limiting distribution will be derived in this paper of Wilcoxon's rank test in a model which includes a random interaction between blocks and treatments.An illustration is given by some data from a judgement comparison experiment for the image quality of Video Long Play discs.

AbstractThe analysis of count response data from designed experiments is well–known for independent response variables having the Poisson distribution. For experimental designs where responses are dependent, no general results seem to be available. An example of this type of design is the split–plot design, where sub–plot responses are essentially dependent within whole plots.In this paper, a model will be proposed for split–plot count data and a separate analysis for whole plot and sub–plot data will be presented. It is interesting to note, that the same model is used in the quite different context of consumer buying behaviour. It is derived by Goodhardt, Ehrenberg and Chatfield and it was called the 'Dirichlet model', as the Dirichlet multinomial distribution, together with the negative binomial distribution, build up the model.

AbstractThe beta–binomial distribution is reported in literature as a useful generalization of the binomial in case of heterogeneous binomial sampling. An extra model parameter is introduced to accommodate for extra–binomial variation. Some additions to results already available will be given by presenting approximate F–tests for factorial designs, where the response variable is of 0–1 type and sampling is heterogeneous binomial. These tests can be used when sample sizes are large and equal and some degrees of freedom are left from replicates or negligible interactions to estimate the extra model parameter.

Abstract  When observations from a normal distribution can only be obtained indirectly by counting the number of subjects responding to a previously chosen dose, parameter estimates can be obtained by using probit analysis. Well‐known is the maximum likelihood technique of parameter estimation, less known is the approach by weighted least squares. The latter approach is followed to compare the parameters of several normal distributions by testing their equality, in analogy with the analysis of variance. A practical situation gave rise to this study and it is worked out at the end of the paper.

Wer von uns weiß heute noch, dass dieser "Sokrates der 18. Jahrhunderts", der nach 1728 nur 57 1/3 Jahre lebte, ebenso sehr als Algebraist und Handelsmann anerkannt und hoch geschätzt war? So rundet das Leben dieses körperlich und sozial benachteiligten Juden gleichzeitig ein gewichtiges Kapitel der Geschichte Brandenburgs Preußens. – Und zwar zu einer Zeit, als dies kleine Königtum noch immer an den Folgen des Dreißigjährigen Krieges krankte und dem Bankrott nahe war. Somit kamen viele ökonomische, historische, politische Tatsachen ins Spiel, die an diesem Geschehen beteiligt waren, als der 14jährige aus seiner Vaterstadt Dessau 1743 seinem Lehrer, dem gerade ernannten Oberrabbiner Brandenburgs, ins Ausland, nach Berlin, folgte. Dies zu einer Zeit, wo seit 1740 die Juden im Lande des Philosophenkönigs Friedrich II durch die schmähliche Neuabfassung des Judenreglements unter entwürdigenden Bedingungen existierten. Trotzdem war und wurde dies ein ungewöhnlich günstiger Zeitpunkt in der Geschichte Brandenburgs. Denn die Hauptstadt verfügte, trotz aller physischen und sozialen Nachteile, über ein sehr reges intellektuelles Klima, hauptsächlich dank des Einflusses der Hugenottischen Immigranten.