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A statistical analysis of sequences of roadside vegetation condition ratings using Markov chains

Brown, Suzanne (2000) A statistical analysis of sequences of roadside vegetation condition ratings using Markov chains. Honours thesis, Murdoch University.

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This thesis explores the modelling and analysis of sequences of ratings using Markov chains. The ratings, collected by Main roads WA, are the assessments of the roadside vegetation condition of consecutive road segments made by six different people. Our objective was to model the autodependence structure of the ratings. This enables standard errors of the proportions of the five possible ratings to be determined and provides insights useful for the collection of future ratings.

The autodependence of the observations in the sequences is captured using the matrix of transition probabilities for a Markov chain. These are the probabilities of the next segment of the road having a particular rating conditional on the rating of the current segment of road being known. The optimal parametrization for this matrix was then obtained using maximum likelihood estimation. We found that no simplifications to the matrix provided an adequate fit to the data.

The transition matrices revealed that raters stay with the same rating as for the previous road segment approximately sixty percent of the time.

The standard error and the sampling distribution of these proportions were estimated by simulation and the distributions were found to be approximately normal. The standard errors were also calculated using a mathematical approximation, but these only showed quasi agreement with the simulated values. The estimates were least satisfactory for ratings with small proportions in the Markov chain.

It was found that sequential sampling is about a quarter as efficient as random sampling when standard errors from each are compared.

Finally, statistical testing revealed significant differences between the transition probabilities for the urban and rural land use categories.

Publication Type: Thesis (Honours)
Murdoch Affiliation: School of Mathematical and Physical Sciences
Notes: Note to the author: If you would like to make your thesis openly available on Murdoch University Library's Research Repository, please contact: Thank you.
Supervisor: Taplin, Ross
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