Simulations Monte Carlo et tests de score sur les matrices nulles : approche par inférence exacte

Authors: Ly, Boucar
Advisor: Rivest, Louis-Paul
Abstract: This document proposes tools of simulation of null matrices based on the conditional law of a presence-absence matrix knowing its sufficient statistics. These tools are based on logistic regression and, moreover, they take into account the heterogeneity of the sites and also the interaction that can exist between the variables that define this heterogeneity. In this work, we have treated the case where the variables that characterize the heterogeneity of the sites are binary and there are more than two. Thus, two tools have been put in place, namely the logistic regression algorithm with interaction between the two site variables and the one without interaction between the site variables. From a simulation study on10 000 presence-absence matrices, we were able not only to describe the properties of the implemented algorithms, but also to compare these algorithms with other null matrix simulation algorithms. These comparisons showed that the score tests with the logistic regression based algorithms with or without interaction between the site variables give acceptable results regardless of the impactof the site variables. On the other hand, the ’fixed-fixed’ algorithm, when the site variables have alternate effects, becomes vulnerable to type I errors. With the algorithm based on the independence model, the results obtained are not reliable because the test is very vulnerable to type I errors. For the Peres-Neto algorithm, the score test is very conservative but itimproves with the alternate effect site variables. Finally, these different algorithms were used to simulate null matrices from a real dataset. This enabled us to compare the structure of the matrices simulated by the different algorithms with respect to that of the observed matrix.
Document Type: Mémoire de maîtrise
Issue Date: 2019
Open Access Date: 24 January 2020
Grantor: Université Laval
Collection:Thèses et mémoires

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