Aperçu

Résumé (français)

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Résumé (anglais)

Multilevel models, also referred as hierarchical or mixed models, are statistical models that analyze a population with hierarchical structure. In a multilevel data structure, units of observations are randomly sampled from populations at different levels simultaneously. Multilevel analyses provide researchers with powerful tools to investigate phenomena with greater precision than that provided by other techniques. What is significant about such multiple sampling is that the model parameters at each level of analysis could be estimated. Renjun Ma and Bent Jorgensen (2007) obtained an optimal estimating function for the regression parameters of the generalized linear mixed models (GLMM) based on the Tweedie exponential dispersion model distributions, allowing an efficient common fitting algorithm for the whole class using the best linear unbiased predictor of random effects. The first objective of my thesis is to apply the this GLMM to Canada large forest fire data which involving both cluster and spatial data analysis. When using standard multilevel modeling for data from complex surveys involving stratification and clustering, unequal selection probabilities at some stage of sampling, if we ignore the sampling designs, the verity estimator may be biased and inconsistent. Sampling weights are often used to take account of the sampling designs. Our second objective is to extend the unbiased and consistent estimating function to complex survey data. We developed different strategies using regular or resealed weights calculated from different sampling designs. Simulation studies are conducted to test the estimator performance.