Antedependence Models for Longitudinal Data (Chapman & Hall - download pdf or read online

By Dale L. Zimmerman

ISBN-10: 1420064266

ISBN-13: 9781420064261

The 1st e-book devoted to This category of Longitudinal versions even supposing antedependence versions are quite invaluable for modeling longitudinal information that express serial correlation, few books safely disguise those versions. through accumulating effects scattered in the course of the literature, Antedependence versions for Longitudinal information bargains a handy, systematic approach to find out about antedependence versions. Illustrated with various examples, the ebook additionally covers a few very important statistical inference tactics linked to those versions. After describing unstructured and dependent antedependence versions and their houses, the authors speak about casual version identity through uncomplicated precis data and graphical tools. They then current formal likelihood-based systems for regular antedependence versions, together with greatest probability and residual greatest chance estimation of parameters in addition to probability ratio checks and penalized probability version choice standards for the model’s covariance constitution and suggest constitution. The authors additionally evaluate the functionality of antedependence versions to different types established for longitudinal facts. With this publication, readers now not need to seek throughout greatly scattered magazine articles at the topic. The publication presents an intensive therapy of the houses and statistical inference strategies of assorted antedependence types.

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Extra resources for Antedependence Models for Longitudinal Data (Chapman & Hall CRC Monographs on Statistics & Applied Probability)

Example text

Yn be random variables with a positive definite covariance matrix Σ. Let B be any subset of {1 : n} consisting of at most n − 3 elements, and suppose that i, j, k are elements of {1 : n} not in B and such that i = k and j = k. Then σik·B σjk·B . σij·B,k = σij·B − σkk·B Proof. 3. 1 may be used to establish a useful result about partial covariances between PAC(p) variables lagged sufficiently far apart when those variables are regressed on certain subsets of the remaining variables, as developed by the next two lemmas.

However, none of these alternatives are as catchy as the original. There is one unfortunate aspect of the term, however: when it is spoken, hearers often misunderstand it as “anti-dependence” and think it may be either an antonym of dependence, a type of negative dependence, or who knows what. The confusion is usually cleared up by spelling the word for the listener. 2 Antecorrelation and partial antecorrelation Consider again n index-ordered random variables Y1 , Y2 , . . , Yn , but now suppose that their variances exist.

N1 , where φij = −tij . Moreover, the parameters in this last list have useful interpretations: φij is the coefficient corresponding to Yj in the regression of Yi on its predecessors, and δi is the variance of the residual from that same regression. We borrow terminology from time series analysis and refer to the φij ’s as autoregressive coefficients, and to the δi ’s as innovation variances (the i ’s being the innovations). Using this notation, and observing that (φi1 , φi2 , . . 14) may be rewritten as i−1 Yi − μi = φi,i−k (Yi−k − μi−k ) + i , i = 1, .

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Antedependence Models for Longitudinal Data (Chapman & Hall CRC Monographs on Statistics & Applied Probability) by Dale L. Zimmerman

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