Maximum Likelihood Estimation for Multivariate t Nonlinear Mixed Model with Censoring Information
碩士 === 逢甲大學 === 統計學系 === 105 === In biomedical studies and clinical trials, multivariate longitudinal data have several inherent features: (i) more than one series of response variables are repeatedly collected at irregularly occasions over a period of time; (ii) censored measuremens often occur in...
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| Format: | Others |
| Language: | zh-TW |
| Published: |
2017
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| Online Access: | http://ndltd.ncl.edu.tw/handle/93782993725025615114 |
| Summary: | 碩士 === 逢甲大學 === 統計學系 === 105 === In biomedical studies and clinical trials, multivariate longitudinal data have several inherent features: (i) more than one series of response variables are repeatedly collected at irregularly occasions over a period of time; (ii) censored measuremens often occur in the data due to limitations of the measuring technology; (iii) outliers or heavy-tailed noises are possibly embodied within multiple response variables; and (iv) the longitudinal profile usually exhibits nonlinear growth patterns. In this thesis, we propose the multivariate t nonlinear mixed model with censored responses (MtNLMMC) for a joint analysis of multivariate longitudinal data with potential outliers and censored measurements. A flexible ECME algorithm is provided to obtain maximum likelihood estimates of the model parameters and the expected information matrix to approximate the asymptotic variance-covariance matrix of fixed effects. We present real-data examples to illustrate the proposed methodology. Simulation studies are conducted to compare the performance of MtNLMMC with orther existing approaches in terms of the estimated results and model selection among different degrees of freedom and censored proportions, and the correlations between individual random effects and bivariate responses.
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