Because both validity and reliability indices are a function of the scores on a given administration of a measure, their values can often vary across samples. It is a common mistake to say that a test is reliable when in fact it is not the test that is reliable but the scores on the test that are reliable. In 1998, vacha-haase proposed a fixed-effects meta-analytic method for evaluating reliability that is similar to validity generalization studies called reliability generalization (rg). This study was conducted to evaluate alternative analysis strategies for the meta-analysis method of reliability generalization when the reliability estimates are not statistically independent. Five approaches for handling the violation of independence were implemented: ignoring the violation and treating each observation as independent, calculating one mean or median from each study, randomly selecting only one observation per study, or using a mixed effects model. This Monte Carlo study included five factors in the method. These factors were (a) the coefficient alpha, (b) sample size in the primary studies, (c) number of primary studies in the rg study, (d) number of reliability estimates from each, and (e) the degree of violation of independence where the strength of the dependence is related to the number of reliability indices (i.e. coefficient alpha) derived from a simulated set of examines and the magnitude of the correlation between the journal studies (with intra-class correlation icc = 0, .0l , .30, and .90). These factors were used to simulate samples under known and controlled population conditions. In general, the results suggested that the type of treatment does not have a noticeable impact on the accuracy of the reliability results but that researchers should be cautious when the intra-class correlation is relatively large. In addition, the simulations in this study resulted in very poor confidence band coverage. This research suggested that RG meta-analysis methods are appropriate for describing the overall average reliability of a measure or construct but the RG researcher should be careful in regards to the construction of confidence intervals.

Au cours de cette thèse nous nous sommes intéressés à la problématique du démélange hyperspectral en milieux urbains. En particulier nous nous sommes penchés sur la prise en compte du phénomène de variabilité intra-classe dans les méthodes de démélange. La mise en évidence de la variabilité intra-classe a été le point de départ de cette étude. Nous avons ainsi constaté que ce phénomène était non-négligeable dans les milieux urbains et qu'il devait être pris en compte. En nous basant sur des modèles de mélange existants dans la littérature nous avons développé deux nouveaux modèles de mélange prenant en compte cette variabilité intra-classe. Le premier est un modèle de mélange linéaire. Le second est un modèle linéaire-quadratique qui permet de prendre en compte les réflexions multiples sur les bâtiments. Dans un premier temps nous ne nous sommes intéressés qu'au cas des modèles linéaires. Comme aucune méthode de la littérature ne permet d'effectuer le démélange à partir de nos modèles de mélange nous avons développé deux méthodes UP-NMF et IP-NMF. UP-NMF est une adaptation de la méthode NMF à notre modèle de mélange. Pour rendre compte de la notion de classes de matériaux purs une contrainte sur l'inertie des classes a été ajoutée à UP-NMF pour obtenir IP-NMF. Les premiers tests ont été effectués sur données semi-synthétiques et ont permis de déterminer l'impact de l'initialisation de ces méthodes sur leurs performances et de fixer le paramètre d'inertie. Les performances de UP-NMF et IP-NMF ont été comparées à celles des méthodes standards de démélange. Les seconds tests ont été effectués sur une portion d'image de Toulouse. Dans cette partie nous avons mis en évidence que, contrairement à des méthodes standards, les résultats de IP-NMF étaient peu sensibles à une erreur sur l'estimation du nombre de classes pures. Finalement nous avons développé une méthode de démélange linéaire-quadratique, LQIP-NMF, en nous basant sur le modèle que nous avons mis en place. Les tests de LQIP-NMF ont montré qu'en cas de trop forte variabilité intra-classe les effets de non-linéarité étaient de second ordre et qu'il ne semblait pas pertinent de les prendre en compte. / This work is devoted to unmixing for urban areas. We particularly focused on the impact of intra-class variability on unmixing. We first described the results of a study highlighting intra-class variability assessed in real images. It appeared that this phenomenon was significant and had to be included in the mixing models. Based on the state of the art we developed 2 new mixing models dealing with intra-class variability. The first one is a linear one. The second one is a linear-quadratic one which allows to consider multiple scattering effects on buildings. First only the linear mixing model was considered. Currently it does not exist any unmixing method able to deal with this new model. So two methods were developed, UP-NMF and IP-NMF. UP-NMF is a new unmixing method based on an extension of the standard NMF. To overcome UP-NMF limitations an extended method is proposed, IP-NMF, which limit the spreading of each class by adding an inertia constraint in the cost function. These methods were firstly tested on a semi-synthetic data set. These tests allowed us to study the impact of the initialisation on our methods performance and also to fix the inertia parameter. We also compared the results of UP-NMF and IP-NMF to the results obtained with standard methods. The second tests were performed on an image taken above Toulouse. It appeared that IP-NMF is less sensitive to an error in the estimation of classes number than standard methods. Finally we developed a linear-quadratic method, LQIP-NMF, dealing with the non-linear mixing model previously described. In cases of high intra-class variability, the quadratic terms are drowned in the large variability of materials. So it seems that it is not relevant to taking into account these non-linearities.

This research aims to identify and evaluate the systemic factors which may be related to decrease in Grade 6 learner’s achievement in Mozambique between 2000 and 2007, looking for possible changes in Educational Effectiveness over that period. SACMEQ III learner results from Grade 6 Reading and Mathematics showed an overall mean decrease from 2000 to 2007. The main research question addressed in this study is: What are the systemic contextual factors associated with decrease in achievement in Reading and Mathematics between 2000 and 2007 in Mozambique? The conceptual framework underpinning this research presents the education system in terms of inputs, processes and outputs (Howie, 2002). Hierarchical Linear Models, based on trend design approach (Nilsen, & Gustafsson, 2014) was used to assess the variation in learner achievement decrease associated with changes in schools inputs and processes. The findings suggest that school-level factors linked to inputs and antecedents have a strong effect on the decrease in learner’s achievement, compared to the processes and practices. Moreover, learners’ background factors, specifically parent’s education and use of language of instruction at home, seem to be the crucial factors associated with learner achievement decrease. When school level variables related to parent’s education, use of language of instruction at home, are included in the model, the amount of variation accounted for, showed an increase (from 23.5 % to 37.7 %,). One can argue that the variation accounted for variables such as parents’ education, whilst use of language of instruction could be indicative of changes in learner’s intake composition between 2000 and 2007. Implications of these findings on the assumptions for large scale assessment studies in developing countries, such as Mozambique, are key issues. For instance, a question could be raised about the “trend” assumption of large scale assessment: To what extent can the trend level of achievement be measured where the learner’s intake composition is changing over the time? In the SACMEQ studies a stronger longitudinal design is needed to investigate how both school and intake factors influence achievement. / Thesis (PhD)--University of Pretoria, 2017. / Science, Mathematics and Technology Education / PhD / Unrestricted

Le travail présenté dans cette thèse a pour objectif de proposer un algorithme de classification supervisée d’images texturées basée sur la modélisation multivariée de champs texturaux. Inspiré des algorithmes de classification dits à « Sac de Mots Visuels » (SMV), nous proposons une extension originale au cas des descripteurs paramétriques issus de la modélisation multivariée des coefficients des sous-bandes d’une décomposition en ondelettes. Différentes contributions majeures de cette thèse peuvent être mises en avant. La première concerne l’introduction d’une loi a priori intrinsèque à l’espace des descripteurs par la définition d’une loi gaussienne concentrée. Cette dernière étant caractérisée par un barycentre ¯_ et une varianceσ2, nous proposons un algorithme d’estimation de ces deux quantités. Nous proposons notamment une application au cas des modèles multivariés SIRV ( Spherically Invariant Random Vector ), en séparant le problème complexe d’estimationdu barycentre comme la résolution de deux problèmes d’estimation plus simples ( un sur la partie gaussienne et un surle multiplieur ). Afin de prendre en compte la diversité naturelle des images texturées ( contraste, orientation, . . . ), nousproposons une extension au cas des modèles de mélanges permettant ainsi de construire le dictionnaire d’apprentissage.Enfin, nous validons cet algorithme de classification sur diverses bases de données d’images texturées et montrons de bonnes performances de classification vis-à-vis d’autres algorithmes de la littérature. / The prime objective of this thesis is to propose an unsupervised classification algorithm of textured images based on multivariate stochastic models. Inspired from classification algorithm named "Bag of Words" (BoW), we propose an original extension to parametric descriptors issued from the multivariate modeling of wavelet subband coefficients. Some major contributions of this thesis can be outlined. The first one concerns the introduction of an intrinsic prior on the parameter space by defining a Gaussian concentrated distribution. This latter being characterized by a centroid ¯_ and a variance _2,we propose an estimation algorithm for those two quantities. Next, we propose an application to the multivariate SIRV (Spherically Invariant Random Vector) model, by resolving the difficult centroid estimation problem as the solution of two simpler ones (one for the Gaussian part and one for the multiplier part). To handle with the intra-class diversity of texture images (scene enlightenment, orientation . . . ), we propose an extension to mixture models allowing the construction of the training dictionary. Finally, we validate this classification algorithm on various texture image databases and show interesting classification performances compared to other state-of-the-art algorithms.

The field of statistics is becoming increasingly more important as the amount of data in the world grows. This thesis studies the Growth Curve model in multivariate statistics which is a model that is not widely used. One difference compared with the linear model is that the Maximum Likelihood Estimators are more complicated. That makes it more difficult to use and to interpret which may be a reason for its not so widespread use. From this perspective this thesis will compare the traditional mean estimator for the Growth Curve model with the unweighted mean estimator. The unweighted mean estimator is simpler than the regular MLE. It will be proven that the unweighted estimator is in fact the MLE under certain conditions and examples when this occurs will be discussed. In a more general setting this thesis will present conditions when the un-weighted estimator has a smaller covariance matrix than the MLEs and also present confidence intervals and hypothesis testing based on these inequalities.