الفهرس | يوجد فقط 14 صفحة متاحة للعرض العام |
المستخلص longitudinal data or repeated measures data arise in many areas as diverse as agri- culture, biology, economics, manufacturing, and geophysics. Multivariate nonlinear mixed-e¤ects models (MNLMM) have received increasing use because of their exibil- ity for analyzing multi-outcome longitudinal data following possibly nonlinear pro les with underlying multivariate normality assumptions for the random e¤ects and with- insubject errors. However, such normality assumption might not o¤er robust inference if the data, even after being transformed, particularly exhibit skewness. In our thesis, the researcher proposes a multivariate skew normal-nonlinear mixed model or a multivariate skew normal independent-nonlinear mixed e¤ect models con- structed by assuming a multivariate skew normal distribution or a multivariate skew normal independent distribution for the random e¤ects and a multivariate normal distribution or a multivariate normal independent distribution for the random errors. The proposed model is called the multivariate skew normal- nonlinear mixed e¤ects model (MSN-NLMM) and the multivariate skew normal independent- nonlinear mixed- e¤ects model (MSNI-NLMM), allowing for analyzing multi-outcome longitudinal data exhibiting nonlinear growth patterns. To describe the autocorrelation possibly ex- isting among irregularly observed measures, the researcher consider an uncorrelated (UNC) structure, a continuous-type autoregressive model with order1 (AR(1)), and the damped exponential correlation dependence structures for the within-subject errors. When tting the MNLMM, it is rather di¢ cult to exactly evaluate the observed log-likelihood function in a closed-form expression, because it involves complicated multiple integrals. To address this issue, the corresponding approximations of the observed log-likelihood function under the three algorithms are proposed. These al- gorithmic schemes include the penalized nonlinear least squares coupled to the multi- variate linear mixed-e¤ects (PNLS-MLME) procedure, Laplacian approximation, the pseudo-data expectation conditional maximization (ECM) algorithm. We illustrate an e¢ cient expectation conditional maximization algorithm coupled with the rst-order Taylor approximation for maximizing the complete pseudo-data likelihood function with real data from HIV/AIDS studies. In light of the criteria which are the maximized log-likelihood (lmax), the Akaike information criterion (AIC; Akaike, 1973) and Bayesian information criterion (BIC; Schwarz, 1978) and with UNC, AR(1) and DEC dependence structures for the within-subject errors, the best model is the multivariate skew slash-nonlinear mixed e¤ect models (MSS-NLMM) with DEC dependence. Also, a simulation study is conducted to assess the performance of the proposed models. Bias and mean squared errors are used to evaluate the performance of the estimates via the proposed model. The simulation study shows that the pro- posed approximate ML estimates based on the EM algorithm provide good asymptotic properties. To achieve the purpose of this study, the thesis consists of six chapters as follow: Chapter 1: An introduction includes a background on longitudinal data and mixed e¤ects models in addition to the aims of the study. Chapter 2: Mixed e¤ects models which discuss both linear and nonlinear mixed e¤ects models. Chapter 3: Multivariate skew normal nonlinear mixed models in terms of the proposed methods. Chapter 4: Multivariate skew normal/independent nonlinear mixed models in terms of the proposed methods. Chapter 5: Application and simulation study : ACTG 315 data. Chapter 6: Conclusion and future work. |