This study explores the relationship between students’ missing responses on a large-scale assessment and their cognitive skill profiles and characteristics. Data from the 48 multiple-choice items on the 2006 Ontario Secondary School Literacy Test (OSSLT), a high school graduation requirement, were analyzed using the item response theory (IRT) three-parameter logistic model and the Reduced Reparameterized Unified Model, a Cognitive Diagnostic Model. Missing responses were analyzed by item and by student. Item-level analyses examined the relationships among item difficulty, item order, literacy skills targeted by the item, the cognitive skills required by the item, the percent of students not answering the item, and other features of the item. Student-level analyses examined the relationships among students’ missing responses, overall performance, cognitive skill mastery profiles, and characteristics such as gender and home language. Most students answered most items: no item was answered by fewer than 98.8% of the students and 95.5% of students had 0 missing responses, 3.2% had 1 missing response, and only 1.3% had more than 1 missing responses). However, whether students responded to items was related to the student’s characteristics, including gender, whether the student had an individual education plan and language spoken at home, and to the item’s characteristics such as item difficulty and the cognitive skills required to answer the item. Unlike in previous studies of large-scale assessments, the missing response rates were not higher for multiple-choice items appearing later in the timed sections. Instead, the first two items in some sections had higher missing response rates. Examination of the student-level missing response rates, however, showed that when students had high numbers of missing responses, these often represented failures to complete a section of the test. Also, if nonresponse was concentrated in items that required particular skills, the accuracy of the estimates for those skills was lower than for other skills. The results of this study have implications for test designers who seek to improve provincial large-scale assessments, and for teachers who seek to help students improve their cognitive skills and develop test taking strategies.

This study explores the relationship between students’ missing responses on a large-scale assessment and their cognitive skill profiles and characteristics. Data from the 48 multiple-choice items on the 2006 Ontario Secondary School Literacy Test (OSSLT), a high school graduation requirement, were analyzed using the item response theory (IRT) three-parameter logistic model and the Reduced Reparameterized Unified Model, a Cognitive Diagnostic Model. Missing responses were analyzed by item and by student. Item-level analyses examined the relationships among item difficulty, item order, literacy skills targeted by the item, the cognitive skills required by the item, the percent of students not answering the item, and other features of the item. Student-level analyses examined the relationships among students’ missing responses, overall performance, cognitive skill mastery profiles, and characteristics such as gender and home language. Most students answered most items: no item was answered by fewer than 98.8% of the students and 95.5% of students had 0 missing responses, 3.2% had 1 missing response, and only 1.3% had more than 1 missing responses). However, whether students responded to items was related to the student’s characteristics, including gender, whether the student had an individual education plan and language spoken at home, and to the item’s characteristics such as item difficulty and the cognitive skills required to answer the item. Unlike in previous studies of large-scale assessments, the missing response rates were not higher for multiple-choice items appearing later in the timed sections. Instead, the first two items in some sections had higher missing response rates. Examination of the student-level missing response rates, however, showed that when students had high numbers of missing responses, these often represented failures to complete a section of the test. Also, if nonresponse was concentrated in items that required particular skills, the accuracy of the estimates for those skills was lower than for other skills. The results of this study have implications for test designers who seek to improve provincial large-scale assessments, and for teachers who seek to help students improve their cognitive skills and develop test taking strategies.

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Cette thèse est consacrée à tester la présence de changements dans les paramètres d'un modèle de régression non-linéaire ainsi que dans un modèle de régression linéaire en très grande dimension. Tout d'abord, nous proposons une méthode basée sur la vraisemblance empirique pour tester la présence de changements dans les paramètres d'un modèle de régression non-linéaire. Sous l'hypothèse nulle, nous prouvons la consistance et la vitesse de convergence des estimateurs des paramètres de régression. La loi asymptotique de la statistique de test sous l'hypothèse nulle nous permet de trouver la valeur critique asymptotique. D'autre part, nous prouvons que la puissance asymptotique de la statistique de test proposée est égale à 1. Le modèle épidémique avec deux points de rupture est également étudié. Ensuite, on s'intéresse à construire les régions de confiance asymptotiques pour la différence entre les paramètres de deux phases d'un modèle non-linéaire avec des regresseurs aléatoires en utilisant la méthode de vraisemblance empirique. On montre que le rapport de la vraisemblance empirique a une distribution asymptotique χ2. La méthode de vraisemblance empirique est également utilisée pour construire les régions de confiance pour la différence entre les paramètres des deux phases d'un modèle non-linéaire avec des variables de réponse manquantes au hasard (Missing At Random (MAR)). Afin de construire les régions de confiance du paramètre en question, on propose trois statistiques de vraisemblance empirique : la vraisemblance empirique basée sur les données cas-complète, la vraisemblance empirique pondérée et la vraisemblance empirique par des valeurs imputées. On prouve que les trois rapports de vraisemblance empirique ont une distribution asymptotique χ2. Un autre but de cette thèse est de tester la présence d'un changement dans les coefficients d'un modèle linéaire en grande dimension, où le nombre des variables du modèle peut augmenter avec la taille de l'échantillon. Ce qui conduit à tester l'hypothèse nulle de non-changement contre l'hypothèse alternative d'un seul changement dans les coefficients de régression. Basée sur les comportements asymptotiques de la statistique de rapport de vraisemblance empirique, on propose une simple statistique de test qui sera utilisée facilement dans la pratique. La normalité asymptotique de la statistique de test proposée sous l'hypothèse nulle est prouvée. Sous l'hypothèse alternative, la statistique de test diverge / In this PHD thesis, we propose a nonparametric method based on the empirical likelihood for detecting the change in the parameters of nonlinear regression models and the change in the coefficient of linear regression models, when the number of model variables may increase as the sample size increases. Firstly, we test the null hypothesis of no-change against the alternative of one change in the regression parameters. Under null hypothesis, the consistency and the convergence rate of the regression parameter estimators are proved. The asymptotic distribution of the test statistic under the null hypothesis is obtained, which allows to find the asymptotic critical value. On the other hand, we prove that the proposed test statistic has the asymptotic power equal to 1. The epidemic model, a particular case of model with two change-points, under the alternative hypothesis, is also studied. Afterwards, we use the empirical likelihood method for constructing the confidence regions for the difference between the parameters of a two-phases nonlinear model with random design. We show that the empirical likelihood ratio has an asymptotic χ2 distribu- tion. Empirical likelihood method is also used to construct the confidence regions for the difference between the parameters of a two-phases nonlinear model with response variables missing at randoms (MAR). In order to construct the confidence regions of the parameter in question, we propose three empirical likelihood statistics : empirical likelihood based on complete-case data, weighted empirical likelihood and empirical likelihood with imputed va- lues. We prove that all three empirical likelihood ratios have asymptotically χ2 distributions. An another aim for this thesis is to test the change in the coefficient of linear regres- sion models for high-dimensional model. This amounts to testing the null hypothesis of no change against the alternative of one change in the regression coefficients. Based on the theoretical asymptotic behaviour of the empirical likelihood ratio statistic, we propose, for a deterministic design, a simpler test statistic, easier to use in practice. The asymptotic normality of the proposed test statistic under the null hypothesis is proved, a result which is different from the χ2 law for a model with a fixed variable number. Under alternative hypothesis, the test statistic diverges