UBC Theses and Dissertations
Longitudinal analysis for binary and count data Graham, Jinko
Longitudinal data sets consist of repeated observations of an outcome over time, and a corresponding set of covariates for each of many subjects. In many fields, multivariate analysis-of-variance is commonly used to analyse longitudinal data. Such an analysis is appropriate when responses for each subject are multivariate Gaussian with a common covariance matrix for all subjects. In many cases, however, the longitudinal response cannot be transformed to satisfy these assumptions. An alternate analysis might rely on specification of an appropriate likelihood to obtain estimates of regression parameters and their standard errors. Unfortunately, the correlation structure in the data for each subject may not be well understood, making such parametric modelling difficult. This thesis discusses two methods for the analysis of longitudinal data which require only minimal assumptions about the true correlation structure in the data for each subject to yield consistent estimates of regression parameters and their standard errors. The first method is based on the use of a "working" likelihood and extends the results of Zeger, Liang and Self (Biometrika, 1985) to the case of time-dependent covariates. The second method, first presented by Liang and Zeger (Biometrika, 1986), is based on quasi-likelihood theory. This method uses generalized estimating equations to arrive at consistent estimates of the regression coefficients and their standard errors, and can be applied to any longitudinal response with univariate marginal distributions for which the quasi-likelihood formulation is sensible. This includes Gaussian, Poisson, binomial (bernoulli), gamma, and inverse Gaussian distributions. Both methods are extensively illustrated using the results from an experiment on hummingbird learning. These methods enable much more information to be extracted from the hummingbird data set than a more traditional analysis-of-variance, and therefore provide useful and powerful tools for researchers in this subject area.
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