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Karin Stål
-- doctoral thesis --
Identifying Influential Observations in Nonlinear Regression
a focus in parameter estimates and the score test
Abstract
This thesis contributes to influence analysis in nonlinear regression and in particular
the detection of influential observations. The focus is on a regression
model with a known mean function, which is nonlinear in its parameters and
where the function is chosen according to the knowledge about the process
generating the data. The error term in the regression model is assumed to be
additive.
The main goal of this thesis is to work out diagnostic measures for assessing
the influence of observations on various results from a nonlinear regression
analysis. The obtained results comprise diagnostic tools for detecting observations
that, individually or jointly with some other observations, are influential
on the parameter estimates. Moreover, assessing conditional influence, i.e. the
influence of an observation conditional on the deletion of another observation,
is of interest. This can help to identify influential observations which could
be missed due to complex relationships among the observations. Novelties of
the proposed diagnostic tools include the possibility to assess influence of observations
on a specific parameter estimate and to assess influence of multiple
observations.
A further emphasis of this thesis is on the observations' influence on the outcome
of a hypothesis testing procedure based on Rao's score test. An innovative
solution to the problem of visual identification of influential observations
regarding the score test statistic obtained in this thesis is the so called added
parameter plot. As a complement to the added parameter plot, new diagnostic
measures are derived for assessing the influence of single and multiple observations
on the score test statistic.
Keywords: Added parameter plot, differentiation approach, influential observation,
nonlinear regression, score test
ISBN 978-91-7649-115-7