Modelling complex longitudinal survey data

Abstract

Modelling methods for longitudinal complex survey data are investigated in this thesis. An empirical investigation using longitudinal survey data is conducted. Variance effects of clustering are identified and results indicate that clustering impacts may be stronger for longitudinal studies than for cross-sectional studies. Earlier empirical evidence that those impacts could be less the more complex the analysis, which may sometimes be used to justify ignoring the complex sampling scheme in longitudinal analysis, is thus contradicted. A theoretical discussion is provided in order to support the major empirical results. The considered longitudinal regression modelling methods are reviewed in the complex survey context. The adoption of covariance structure models for longitudinal survey data is emphasised in this dissertation as this approach includes a wide range of modelling techniques and has application in the social sciences. A weighted estimation procedure (Sw), which considers covariates, is proposed for estimating the population covariance matrix ~. Further developments on variance estimation methods for t considering the complex survey approach are accomplished by adopting a Taylor expansion technique in order to extend asymptotically distribution-free (ADF) methods. By adopting Sw, modifications to point estimation methods, such as unweighted (ULS) and generalised least squares (GLS), for a vector parameter are also proposed. A pseudo maximum likelihood (PML) for covariance structure models is also derived via maximisation of the pseudo log likelihood function. The behaviour of the proposed estimation procedures are assessed by simulation. ADF variance estimation methodology for GLS point estimators is extended. A method for estimating the asymptotic covariance matrix of the PML point estimator is proposed under the complex survey data approach. Some extensions to model fitting statistics when working with longitudinal data in a complex survey design framework are developed. We propose modifying the Wald goodness of fit test in the context of models for covariance structures, which is shown to be equivalent to modifying the scaled test statistics. Furthermore, we also propose a modification for the Wald significance test for nested hypothesis. Goodness of fit indices are also modified in order be utilised in the complex survey data context. An additional simulation study is adopted for evaluating the proposed variance estimation methods.

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