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Hinton Dissertation Final.pdf (840.69 KB)

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Contributions to Discriminant Analysis of Cross-Sectional and Longitudinal Data with Applications

Hinton, Alice M
http://rave.ohiolink.edu/etdc/view?acc_num=osu1390479004

Abstract Details

2014, Doctor of Philosophy, Ohio State University, Biostatistics.
There are a variety of methods available to classify an object into one of two populations. Here, the method of discriminant analysis is considered in the cross-sectional and the longitudinal setting with a structured multivariate normal model. The generalized likelihood ratio change detection algorithm is also investigated as an alternative to methods based on discriminant analysis in the longitudinal setting. Traditionally, discriminant functions are developed to classify a new observation from a cross-sectional dataset into a population. An error is made when the observation is incorrectly classified. In the literature, several parametric and empirical methods of estimating these misclassification probabilities have been proposed. The performance of six parametric and three empirical misclassification probability estimators are compared. It is found that the parametric methods, which rely on an assumption of normality, generally outperform the empirical methods when a linear discriminant function is used for classification and the data originate from normal populations. The preferred parametric method depends on the size of the training dataset and the parameters of the populations, particularly the distance between the means. The empirical methods are preferred only when the two populations are well separated and the variances are significantly different. The ideas of discriminant analysis are used to develop a classifier for a multivariate longitudinal dataset in which a change in both mean and variance occurs at an unknown time. Conditional distributions involving a patterned covariance matrix accounting for the correlations between the variables as well as the correlations present across time are then utilized to develop a discriminant function. After a training dataset is used to provide estimates for each of the parameters needed to specify the discriminant function, the classifier can be sequentially applied as observations are accumulated to identify the time at which the change occurs. The generalized likelihood ratio change detection algorithm is an alternative to the classifier based on the discriminant function. The algorithm assumes a known direction but unknown magnitude of change in the mean and no change in the variance. The probability of the algorithm detecting a change at a time greater than a specified time point is theoretically derived and approximated using simulation. The robustness of the algorithm to correlation in the data is also investigated and it is found to be robust only to small longitudinal correlations. Both the method based on the discriminant function as well as the generalized likelihood ratio change detection algorithm are applied to a multivariate longitudinal dataset composed of patients with lupus nephritis. The method based on the discriminant function uses the data as a training dataset resulting in a classifier which can be used to monitor a new lupus patient for renal inflammation. The generalized likelihood ratio change detection algorithm provides an alternative method of monitoring a new patient. A comparison of these two methods reveals that the classifier based on the discriminant function performs similarly to the generalized ratio change detection algorithm applied to transformed data obtained by removing the autocorrelations.
Haikady Nagaraja (Advisor)
Biostatistics

Recommended Citations

Citations

  • Hinton, A. M. (2014). Contributions to Discriminant Analysis of Cross-Sectional and Longitudinal Data with Applications [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1390479004

    APA Style (7th edition)

  • Hinton, Alice. Contributions to Discriminant Analysis of Cross-Sectional and Longitudinal Data with Applications. 2014. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1390479004.

    MLA Style (8th edition)

  • Hinton, Alice. "Contributions to Discriminant Analysis of Cross-Sectional and Longitudinal Data with Applications." Doctoral dissertation, Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1390479004

    Chicago Manual of Style (17th edition)

osu1390479004
341
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This open access ETD is published by The Ohio State University and OhioLINK.