Repository logo
 

Optimal designs for linear mixed models.

Simple item page
dc.contributor.advisorHaines, Linda Margaret.
dc.contributor.authorDebusho, Legesse Kassa.
dc.contributor.supervisorHaines, Linda M.
dc.date.accessioned2011-07-21T06:33:03Z
dc.date.available2011-07-21T06:33:03Z
dc.date.created2004
dc.date.issued2004
dc.descriptionThesis (Ph.D.) - University of KwaZulu-Natal, Pietermaritzburg, 2004.
dc.description.abstractThe research of this thesis deals with the derivation of optimum designs for linear mixed models. The problem of constructing optimal designs for linear mixed models is very broad. Thus the thesis is mainly focused on the design theory for random coefficient regression models which are a special case of the linear mixed model. Specifically, the major objective of the thesis is to construct optimal designs for the simple linear and the quadratic regression models with a random intercept algebraically. A second objective is to investigate the nature of optimal designs for the simple linear random coefficient regression model numerically. In all models time is considered as an explanatory variable and its values are assumed to belong the set {a, 1, ... , k}. Two sets of individual designs, designs with non-repeated time points comprising up to k + 1 distinct time points and designs with repeated time points comprising up to k + 1 time points not necessarily distinct, are used in the thesis. In the first case there are 2k+ - 1 individual designs while in the second case there are ( 2 2k k+ 1 ) - 1 such designs. The problems of constructing population designs, which allocate weights to the individual designs in such a way that the information associated with the model parameters is in some sense maximized and the variances associated with the mean responses at a given vector of time points are in some sense minimized, are addressed. In particular D- and V-optimal designs are discussed. A geometric approach is introduced to confirm the global optimality of D- and V-optimal designs for the simple linear regression model with a random intercept. It is shown that for the simple linear regression model with a random intercept these optimal designs are robust to the choice of the variance ratio. A comparison of these optimal designs over the sets of individual designs with repeated and non-repeated points for that model is also made and indicates that the D- and V-optimal iii population designs based on the individual designs with repeated points are more efficient than the corresponding optimal population designs with non-repeated points. Except for the one-point case, D- and V-optimal population designs change with the values of the variance ratio for the quadratic regression model with a random intercept. Further numerical results show that the D-optimal designs for the random coefficient models are dependent on the choice of variance components.en
dc.identifier.urihttp://hdl.handle.net/10413/3221
dc.language.isoenen
dc.subjectRegression Analysis.en
dc.subjectLinear Models (Statistics)en
dc.subjectRandom Variables.en
dc.subjectTheses--Mathematics.en
dc.titleOptimal designs for linear mixed models.en
dc.typeThesisen

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
Debusho_Legesse_Kassa_2004.pdf
Size:
9.68 MB
Format:
Adobe Portable Document Format
Description:
Thesis (PH.D.)-University of Natal, 2004.
Download
License bundle
Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
1.64 KB
Format:
Item-specific license agreed upon to submission
Description:
Download

Collections

Doctoral Degrees (Mathematics and Computer Science Education)