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New residuals in multivariate bilinear models

testing hypotheses, diagnosing models and validating model assumptions

Seid Hamid, Jemila (2005). New residuals in multivariate bilinear models. Diss. (sammanfattning/summary) Uppsala : Sveriges lantbruksuniv., Acta Universitatis agriculturae Sueciae, 1652-6880 ; 2005:83
ISBN 91-576-6982-1
[Doctoral thesis]

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Abstract

New residuals taking the bilinear structure into account are defined for the Extended Growth Curve Model. It is shown that the ordinary residuals are defined by projecting the observation matrix on the space orthogonal to the one generated by the design matrices which turn out to be the sum of two tensor product spaces. The space on which the ordinary residuals are defined is then decomposed into four orthogonal spaces and new residuals are defined by projecting the observation matrix on the resulting four spaces. The information contained in them is used to check the adequacy of the model and to check if there are extreme observations. Tests are proposed for the Growth and Extended Growth Curve models which turn out to be functions of appropriate residuals. It is shown that the distributions of the tests under the null hypotheses are independent of the unknown covariance matrix. The distributions are difficult to find, however, two suggestions are made to tackle this problem. We consider a conditional approach and discuss why it is appropriate in our situation. Moreover, it is shown that the distribution of the conditional test under the null and alternative hypotheses can be written as sums of independent central and non-central chi-square random variables, respectively. However, the exact distributions, which are available as an infinite series, are too complicated to be used in practice and approximations are needed. We use Satterthwaite's approximation to find the critical point. Under the alternative, an approximation similar to that of Satterthwaite is provided for obtaining an approximate power. However, our approach is different and new ideas are utilized to get the approximation. Numerical examples are given to illustrate the results.

Authors/Creators:Seid Hamid, Jemila
Title:New residuals in multivariate bilinear models
Subtitle:testing hypotheses, diagnosing models and validating model assumptions
Year of publishing :August 2005
Volume:2005:83
Number of Pages:46
Papers/manuscripts:
NumberReferences
ALLI. Seid Hamid, J. & von Rosen (2005). Residuals in the extended growth curve model. (Accepted by Scand. J. Statist.) II. Seid Hamid, J. & von Rosen (2005b). Hypothesis testing via residuals in two GMANOVA models. Report 2005:4, Centre of Biostochastics, SLU, Sweden. III. Seid Hamid, J. & von Rosen (2005c). An approximate critical point for a test in the growth curve model: A conditional approach. Report 2005:5, Centre of Biostochastics, SLU, Sweden.
Place of Publication:Uppsala
ISBN for printed version:91-576-6982-1
ISSN:1652-6880
Language:English
Publication Type:Doctoral thesis
Full Text Status:Public
Agris subject categories.:X Agricola extesions > X10 Mathematics and statistics
Subjects:Not in use, please see Agris categories
Agrovoc terms:statistical methods, mathematical models
Keywords:ancillary statistics, conditional test, decomposition of linear spaces, estimated likelihood, extended growth curve model, growth curve model, restricted likelihood, Satterthwaite approximation, tensor product of linear spaces
URN:NBN:urn:nbn:se:slu:epsilon-722
Permanent URL:
http://urn.kb.se/resolve?urn=urn:nbn:se:slu:epsilon-722
ID Code:909
Department:?? 4072 ??
Deposited By: Jemila Seid Hamid
Deposited On:05 Sep 2005 00:00
Metadata Last Modified:02 Dec 2014 10:08

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