The Impact of Covariance Misspecification in Multivariate Gaussian Mixtures on Estimation and Inference: An Application to Longitudinal Modeling

Multivariate Gaussian mixtures are a class of models that provide a flexible parametric approach for the representation of heterogeneous multivariate outcomes. When the outcome is a vector of repeated measurements taken on the same subject, there is often inherent dependence between observations. However, a common covariance assumption is conditional independence---that is, given the mixture component label, the outcomes for subjects are independent. In this paper, we study, through asymptotic bias calculations and simulation, the impact of covariance misspecification in multivariate Gaussian mixtures. Although maximum likelihood estimators of regression and mixing probability parameters are not consistent under misspecification, they have little asymptotic bias when mixture components are well-separated or if the assumed correlation is close to the truth even when the covariance is misspecified. We also present a robust standard error estimator and show that it outperforms conventional estimators in simulations and can indicate the model is misspecified. Body mass index data from a national longitudinal study is used to demonstrate the effects of misspecification on potential inferences made in practice

Condiciones para la evaluación formativa del aprendizaje en el área de Comunicación del nivel secundaria en la modalidad no presencial

El proceso de evaluación formativa requiere de ciertas condiciones para ejecutarla; es decir, aquellas situaciones, aspectos o circunstancias que dependen del docente y del estudiante, con el fin de mejorar y lograr efectividad en los aprendizajes. La pregunta de investigación es: ¿Cuáles son las condiciones para desarrollar la evaluación formativa del aprendizaje en el área de Comunicación del nivel secundaria en la modalidad no presencial en una institución educativa pública del distrito de Independencia de Lima? Y como objetivo general: describir las condiciones para el desarrollo de la evaluación formativa del aprendizaje en el área de Comunicación del nivel secundaria en la modalidad no presencial en una institución educativa pública del distrito de Independencia. La investigación es cualitativa, nivel exploratorio y utilizó el método de estudio de caso único. Para recoger información se aplicó la entrevista semiestructurada individual a siete docentes del área de Comunicación de una institución educativa pública de Lima. El análisis de datos comprendió procesos de codificación y categorización y se aplicó la suma categórica. Se destaca en los resultados que para las docentes entrevistadas la evaluación formativa exige cuidar algunas situaciones o condiciones que favorezcan su uso. Entre las condiciones que ellas reconocen se tiene la planificación que les permite ajustar los procesos de enseñanza y aprendizaje a las características, necesidades y demandas de aprendizajes de los estudiantes; la selección adecuada de técnicas e instrumentos de evaluación para recoger información, así como prever y ejecutar el proceso de retroalimentación para identificar fortalezas y dificultades en el aprendizaje de los estudiantes. Además, ellas reconocen la importancia de la participación activa y el compromiso de los estudiantes en ese proceso, porque les permitirá tomar decisiones oportunas; así como asumir compromisos con la mejora de su propio aprendizaje.The process of formative assessment requires certain conditions under which to be applied; that is, those situations, aspects or circumstances that depend on the teacher and the student, which aim at improving and achieving effectiveness in learning. The research question is: What are the conditions under which to develop formative assessment of the learning process in the area of Communication at high school level in (online) distance courses in a public school in the district of Independencia in Lima? And the main objective is: to describe the conditions that promote the development of formative assessment of the learning process in the area of Communication at high school level in (online) distance courses in a public school in the district of Independencia. This is qualitative research, at an exploratory level and the single case study method was used. Individual semi structured interviews were used to gather information from seven schoolteachers in the area of communication in a public school in Lima. The analysis of the data included coding and categorizing processes and, the coproduct (categorical sum) was used. From the findings, it is highlighted that for the interviewed teachers, formative assessment demands taking care of certain situation or conditions which boost its use. Among these, teachers pointed out planning, which allows them to adjust the teaching and learning processes to the characteristics, needs and demands of their students; the appropriate selection of assessment techniques and instruments to gather information, and: moreover, foreseeing and carrying out the feedback process to identify strengths and weaknesses in the students’ learning process. Furthermore, teachers acknowledge the importance of active participation and students’ commitment in the process since this will let learners take timely decisions, as well as take on new responsibilities in the improvement of their own learning process

Classification of longitudinal data through a semiparametric mixed-effects model based on lasso-type estimators

We propose a classification method for longitudinal data. The Bayes classifier is classically used to determine a classification rule where the underlying density in each class needs to be well modeled and estimated. This work is motivated by a real dataset of hormone levels measured at the early stages of pregnancy that can be used to predict normal versus abnormal pregnancy outcomes. The proposed model, which is a semiparametric linear mixed-effects model (SLMM), is a particular case of the semiparametric nonlinear mixed-effects class of models (SNMM) in which finite dimensional (fixed effects and variance components) and infinite dimensional (an unknown function) parameters have to be estimated. In SNMM’s maximum likelihood estimation is performed iteratively alternating parametric and nonparametric procedures. However, if one can make the assumption that the random effects and the unknown function interact in a linear way, more efficient estimation methods can be used. Our contribution is the proposal of a unified estimation procedure based on a penalized EM-type algorithm. The Expectation and Maximization steps are explicit. In this latter step, the unknown function is estimated in a nonparametric fashion using a lasso-type procedure. A simulation study and an application on real data are performed.The authors are grateful to two anonymous referees and an Associate Editor for their insightful comments and valuable suggestions, which led to substantial improvements in the presentation of this work. Ana Arribas–Gil was supported by projects MTM2010-17323 and ECO2011-25706, Spain. Rolando de la Cruz was supported by project FONDECYT 1120739, grant ANILLO ACT–87, and grant FONDAP 15130011, Chile. Cristian Meza was supported by projects FONDECYT 11090024 and 1141256, and grant ANILLO ACT–1112, CONICYT-PIA, Chile

Model-based clustering of longitudinal data

A new family of mixture models for the model-based clustering of longitudinal data is introduced. The covariance structures of eight members of this new family of models are given and the associated maximum likelihood estimates for the parameters are derived via expectation-maximization (EM) algorithms. The Bayesian information criterion is used for model selection and a convergence criterion based on Aitken’s acceleration is used to determine convergence of these EM algorithms. This new family of models is applied to yeast sporulation time course data, where the models give good clustering performance. Further constraints are then imposed on the decomposition to allow a deeper investigation of correlation structure of the yeast data. These constraints greatly extend this new family of models, with the addition of many parsimonious models.Higher Education Authorit

Joint Bayesian weight and height postnatal growth model to study the effects of maternal smoking during pregnancy

International audienceGrowth models used for describing the dynamics of body weight and height generally consider each trait independently. We proposed modeling height and weight trajectories jointly with a nonlinear heteroscedastic mixed model based on the Jenss-Bayley growth function with correlated individual random effects and using Bayesian inference techniques. Simulations showed that our model provides good estimates of the growth parameters. We illustrated how it can be used to assess the associations between maternal smoking during pregnancy, an early-life factor potentially involved in prenatal programming of obesity, and children's growth from birth to 5 years of age. We used real data from the EDEN study, a large French mother-child cohort study with a high number of height and weight measurements (a total of approximately 30 000 measurements for each of the 2 traits across the 1666 children). Our results supported the existence of a relationship between maternal smoking during pregnancy and growth from birth to 5 years of age. Children from mothers who smoked throughout pregnancy were shown to display a higher body mass index from the first few months of life onwards compared to children from nonsmokers. At 5 years of age, their mean body mass index was 0.21 kg/m2 higher than unexposed children. It was mainly explained by the fact that these children tended to be smaller at birth but rapidly exceeded the weight of children from nonsmokers postnatally