Sequential regression techniques with application to the individual sprint in track cycling

Moffatt, JL

Abstract

The research work described in this thesis is concerned with processes comprising a sequence
of stages, where states and actions taken during each stage influence the outcome at the end of
the process. Statistical analysis of such processes using standard approaches can be
problematic due to the potentially large number of covariates that are influential, especially
towards the end of the process. Therefore, three alternative statistical techniques of increasing
complexity were developed. These techniques are all based on a sequential approach, in
which logistic regression models are developed at consecutive stages. These techniques were
applied to the individual sprint event in track cycling and all successfully gave insight into
beneficial tactics for each stage of the race.
The first technique involves considering for each model only covariates related to the current
and previous stages. As such, a sequence of overlapping models is created. This approach
successfully enabled stable and easy to interpret models to be created. However, the joint
effect of applying tactics at different stages of the individual sprint could not be determined.
The sequential logistic regression technique overcame this limitation by using the score (the
logistic transformation of the probability of outcome) from the model developed at the
previous stage as a covariate in the succeeding model. As such, all prior information can be
incorporated into each model. However this score is estimated with uncertainty, which can
cause the model parameter estimates to be biased. Furthermore, the effects of this intrinsic
measurement error were found to propagate through stages, particularly in terms of the
relative importance of prior and current states and actions. The novel third technique therefore
combines the sequential logistic regression approach with measurement error techniques to
account for error in the score.

• Thesis Type: Thesis
• Deposit Date: Jul 30, 2021
• Award Date: Jul 1, 2012