الفهرس 
Introductionيوجد فقط 14 صفحة متاحة للعرض العام
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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.