Two-Level Time Series Modelling With Autocorrelated Error Terms
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Date
2018-07
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UNIVERSITY OF ILORIN
Abstract
The multilevel models, viewed as linear mixed-effects models, have been adapted as a standard method of conducting analyses in repeated measure data. This mixed model may still violate some of the assumptions, such as random error independence and homogeneity of variance, thereby leading to model misspecification. However, the literature has not adequately addressed these challenges. To this end, this work was motivated to examining the effects of the violation of these assumptions and their impacts on both standard and correlated modelling techniques. The objectives of this study were to: (i) investigate the consequences of violation of non-autocorrelation assumption on the parameter estimates in two-level time series modelling techniques; (ii) examine the asymptotic behaviour of two-level time series modelling techniques when the assumption of non-autocorrelated error terms is not met; (iii) determine the robustness of two-level correlated time series modelling technique to misspecification of the true dependency structure between observations; and (iv) validate the modelling techniques on suitable real-life data sets.
Data were simulated by injecting different levels of autocorrelation at varying sample sizes. The data generated were of first-order autoregressive errors with specified parameters. The maximum likelihood and Bayes estimation methods were used to estimate the parameters. The sensitivity of model fit criteria and the robustness of the mixed effect estimates of the two-level time series models for violations of non-autocorrelation assumptions were examined. The components of the covariance structure for the first-level model were mis-specified to determine their effects on parameter estimation. The measures of performance used were mean square error, bias, and variance. A real-life data set was used to validate the modelling techniques.
The findings of the study were that:
i. violating non-autocorrelated errors assumption affected the accuracy of the parameter estimates of both standard and correlated modelling techniques, however, the severity of this bias depends on the degree to which errors are autocorrelated, but adding the autocorrelation parameter improved the fit to the data under correlated model;
ii. though REML exhibited less bias when compared with MLE, however sensitivity of both level sample sizes to a non-autocorrelation violation is not consistent
iii. misspecifying the within-subject covariance structure has a negative effect on the parameter estimates; and
iv. with the observed variance-covariance matrices, there is low levels of inferential accuracy of mixed effect estimates and increase sample sizes at both levels has no effect on the bias rate.
The study concluded that violation of model assumptions has significant effects on the accuracy of the model parameter estimates regardless of sample sizes, while a correlated model provided a better fit. The study recommended that autocorrelation should be tested for, and if found should be modelled appropriately. This study, therefore, provides additional knowledge concerning the performance of two-level time series modelling techniques when a non-autocorrelation assumption is violated.
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Two-Level Time Series Modelling, Autocorrelated Error Terms