Estimation and hypothesis testing in mixed linear models

Dissertação apresentada para obtenção do Grau de Doutor em Matemática, Estatística, pela Universidade Nova de Lisboa, faculdade de Ciências e Tecnologia

Modelos Mixtos-Aditivos Generalizados para el Estudio de Fenómenos Biológicos y Sociales Descriptos por Datos Agregados y/o Longitudinales. Generalized Mixed Additive Models for the Study of Biological and Social Phenomenons from Longitudinal and/or Aggregated Data.

Este proyecto propone extender y generalizar los procesos de estimación e inferencia de modelos aditivos generalizados multivariados para variables aleatorias no gaussianas, que describen comportamientos de fenómenos biológicos y sociales y cuyas representaciones originan series longitudinales y datos agregados (clusters). Se genera teniendo como objeto para las aplicaciones inmediatas, el desarrollo de metodología de modelación para la comprensión de procesos biológicos, ambientales y sociales de las áreas de Salud y las Ciencias Sociales, la condicionan la presencia de fenómenos específicos, como el de las enfermedades.Es así que el plan que se propone intenta estrechar la relación entre la Matemática Aplicada, desde un enfoque bajo incertidumbre y las Ciencias Biológicas y Sociales, en general, generando nuevas herramientas para poder analizar y explicar muchos problemas sobre los cuales tienen cada vez mas información experimental y/o observacional.Se propone, en forma secuencial, comenzando por variables aleatorias discretas (Yi, con función de varianza menor que una potencia par del valor esperado E(Y)) generar una clase unificada de modelos aditivos (paramétricos y no paramétricos) generalizados, la cual contenga como casos particulares a los modelos lineales generalizados, no lineales generalizados, los aditivos generalizados, los de media marginales generalizados (enfoques GEE1 -Liang y Zeger, 1986- y GEE2 -Zhao y Prentice, 1990; Zeger y Qaqish, 1992; Yan y Fine, 2004), iniciando una conexión con los modelos lineales mixtos generalizados para variables latentes (GLLAMM, Skrondal y Rabe-Hesketh, 2004), partiendo de estructuras de datos correlacionados. Esto permitirá definir distribuciones condicionales de las respuestas, dadas las covariables y las variables latentes y estimar ecuaciones estructurales para las VL, incluyendo regresiones de VL sobre las covariables y regresiones de VL sobre otras VL y modelos específicos para considerar jerarquías de variación ya reconocidas. Cómo definir modelos que consideren estructuras espaciales o temporales, de manera tal que permitan la presencia de factores jerárquicos, fijos o aleatorios, medidos con error como es el caso de las situaciones que se presentan en las Ciencias Sociales y en Epidemiología, es un desafío a nivel estadístico. Se proyecta esa forma secuencial para la construcción de metodología tanto de estimación como de inferencia, comenzando con variables aleatorias Poisson y Bernoulli, incluyendo los existentes MLG, hasta los actuales modelos generalizados jerárquicos, conextando con los GLLAMM, partiendo de estructuras de datos correlacionados. Esta familia de modelos se generará para estructuras de variables/vectores, covariables y componentes aleatorios jerárquicos que describan fenómenos de las Ciencias Sociales y la Epidemiología.

Approximations of the Fisher information for the construction of efficient experimental designs in nonlinear mixed effects models

Magdeburg, Univ., Fak. für Mathematik, Diss., 2012

Asymptotic analysis of stock price densities and implied volatilities in mixed stochastic models

In this paper, we obtain sharp asymptotic formulas with error estimates for the Mellin con- volution of functions de ned on (0;1), and use these formulas to characterize the asymptotic behavior of marginal distribution densities of stock price processes in mixed stochastic models. Special examples of mixed models are jump-di usion models and stochastic volatility models with jumps. We apply our general results to the Heston model with double exponential jumps, and make a detailed analysis of the asymptotic behavior of the stock price density, the call option pricing function, and the implied volatility in this model. We also obtain similar results for the Heston model with jumps distributed according to the NIG law.

The utility and application of mixed-effects models in second language research

Second language acquisition researchers often face particular challenges when attempting to generalize study findings to the wider learner population. For example, language learners constitute a heterogeneous group, and it is not always clear how a study’s findings may generalize to other individuals who may differ in terms of language background and proficiency, among many other factors. In this paper, we provide an overview of how mixed-effects models can be used to help overcome these and other issues in the field of second language acquisition. We provide an overview of the benefits of mixed-effects models and a practical example of how mixed-effects analyses can be conducted. Mixed-effects models provide second language researchers with a powerful statistical tool in the analysis of a variety of different types of data.

Improved testing inference in mixed linear models

Mixed linear models are commonly used in repeated measures studies. They account for the dependence amongst observations obtained from the same experimental unit. Often, the number of observations is small, and it is thus important to use inference strategies that incorporate small sample corrections. In this paper, we develop modified versions of the likelihood ratio test for fixed effects inference in mixed linear models. In particular, we derive a Bartlett correction to such a test, and also to a test obtained from a modified profile likelihood function. Our results generalize those in [Zucker, D.M., Lieberman, O., Manor, O., 2000. Improved small sample inference in the mixed linear model: Bartlett correction and adjusted likelihood. Journal of the Royal Statistical Society B, 62,827-838] by allowing the parameter of interest to be vector-valued. Additionally, our Bartlett corrections allow for random effects nonlinear covariance matrix structure. We report simulation results which show that the proposed tests display superior finite sample behavior relative to the standard likelihood ratio test. An application is also presented and discussed. (C) 2008 Elsevier B.V. All rights reserved.

Estimation of Parameters in Random Effect Models with Incidence Matrix Uncertainty

Random effect models have been widely applied in many fields of research. However, models with uncertain design matrices for random effects have been little investigated before. In some applications with such problems, an expectation method has been used for simplicity. This method does not include the extra information of uncertainty in the design matrix is not included. The closed solution for this problem is generally difficult to attain. We therefore propose an two-step algorithm for estimating the parameters, especially the variance components in the model. The implementation is based on Monte Carlo approximation and a Newton-Raphson-based EM algorithm. As an example, a simulated genetics dataset was analyzed. The results showed that the proportion of the total variance explained by the random effects was accurately estimated, which was highly underestimated by the expectation method. By introducing heuristic search and optimization methods, the algorithm can possibly be developed to infer the 'model-based' best design matrix and the corresponding best estimates.

A class of mixed integrable models

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Parameterized Link Functions in Generalized Linear Random Effect Models: a Case Study on Breast Cancer Treatment

In non-linear random effects some attention has been very recently devoted to the analysis ofsuitable transformation of the response variables separately (Taylor 1996) or not (Oberg and Davidian 2000) from the transformations of the covariates and, as far as we know, no investigation has been carried out on the choice of link function in such models. In our study we consider the use of a random effect model when a parameterized family of links (Aranda-Ordaz 1981, Prentice 1996, Pregibon 1980, Stukel 1988 and Czado 1997) is introduced. We point out the advantages and the drawbacks associated with the choice of this data-driven kind of modeling. Difficulties in the interpretation of regression parameters, and therefore in understanding the influence of covariates, as well as problems related to loss of efficiency of estimates and overfitting, are discussed. A case study on radiotherapy usage in breast cancer treatment is discussed.

Changes in soil organic carbon storage under different agricultural management systems in the Southwest Amazon Region of Brazil

The Cerrado and Amazon regions of Brazil are probably the largest agricultural frontier of the world, and Could be a sink or source for C depending on the net effect of land use change and subsequent management on soil organic C pools. We evaluated the effects of agricultural management systems on soil organic C (SOC) stocks in the Brazilian states of Rondonia and Mato Grosso, and derived regional specific factors for soil C stock change associated with different management systems. We used 50 observations (data points) in this study, including 42 dealing with annual cropping practices and 8 dealing with perennial cropping, and analyzed the data in linear mixed-effect models. No tillage (NT) systems in Cerrado areas increased SOC Storage by 1.08 +/- 0.06 relative to SOC stocks under native conditions, while SOC storage increased by a modest factor of 1.01 +/- 0.17 in Cerradao and Amazon Forest conditions. Full tillage (FT) had negative effect on SOC storage relative to NT, decreasing SOC stocks by a factor of 0.94 +/- 0.04. but did not significantly reduce SOC stocks relative to native levels when adopted in the Cerrado region. Perennial cropping had a minimal impact on SOC stocks, estimated at a factor Value of 0.98 +/- 0.14, suggesting these systems maintain about 98% of the SOC stock found under native vegetation. The results Suggest that NT adoption may be increasing SOC with land use change from native vegetation to cropland management in the Cerrado region of Brazil. (C) 2009 Elsevier B.V. All rights reserved.

Relationship between median nerve somatosensory evoked potentials and spinal cord injury levels in patients with quadriplegia

Study design: Cross-sectional study. Objectives: To observe if there is a relationship between the level of injury by the American Spinal Cord Injury Association (ASIA) and cortical somatosensory evoked potential (SSEP) recordings of the median nerve in patients with quadriplegia. Setting: Rehabilitation Outpatient Clinic at the university hospital in Brazil. Methods: Fourteen individuals with quadriplegia and 8 healthy individuals were evaluated. Electrophysiological assessment of the median nerve was performed by evoked potential equipment. The injury level was obtained by ASIA. N(9), N(13) and N(20) were analyzed based on the presence or absence of responses. The parameters used for analyzing these responses were the latency and the amplitude. Data were analyzed using mixed-effect models. Results: N(9) responses were found in all patients with quadriplegia with a similar latency and amplitude observed in healthy individuals; N(13) responses were not found in any patients with quadriplegia. N(20) responses were not found in C5 patients with quadriplegia but it was present in C6 and C7 patients. Their latencies were similar to healthy individuals (P > 0.05) but the amplitudes were decreased (P < 0.05). Conclusion: This study suggests that the SSEP responses depend on the injury level, considering that the individuals with C6 and C7 injury levels, both complete and incomplete, presented SSEP recordings in the cortical area. It also showed a relationship between the level of spinal cord injury assessed by ASIA and the median nerve SSEP responses, through the latency and amplitude recordings. Spinal Cord (2009) 47, 372-378; doi:10.1038/sc.2008.147; published online 20 January 2009

The association between air pollution and blood pressure in traffic controllers in Santo Andre, Sao Paulo, Brazil

Background: Urban air pollutants are associated with cardiovascular events. Traffic controllers are at high risk for pollution exposure during outdoor work shifts. Objective: The purpose of this study was to evaluate the relationship between air pollution and systemic blood pressure in traffic controllers during their work shifts. Methods: This cross-sectional study enrolled 19 male traffic controllers from Santo Andre city (Sao Paulo, Brazil) who were 30-60 years old and exposed to ambient air during outdoor work shifts. Systolic and diastolic blood pressure readings were measured every 15 min by an Ambulatory Arterial Blood Pressure Monitoring device. Hourly measurements (lags of 0-5 h) and the moving averages (2-5 h) of particulate matter (PM(10)), ozone (O(3)) ambient concentrations and the acquired daily minimum temperature and humidity means from the Sao Paulo State Environmental Agency were correlated with both systolic and diastolic blood pressures. Statistical methods included descriptive analysis and linear mixed effect models adjusted for temperature, humidity, work periods and time of day. Results: Interquartile increases of PM(10) (33 mu g/m(3)) and O(3) (49 mu g/m(3)) levels were associated with increases in all arterial pressure parameters, ranging from 1.06 to 2.53 mmHg. PM(10) concentration was associated with early effects (lag 0), mainly on systolic blood pressure. However, O(3) was weakly associated most consistently with diastolic blood pressure and with late cumulative effects. Conclusions: Santo Andre traffic controllers presented higher blood pressure readings while working their outdoor shifts during periods of exposure to ambient pollutant fluctuations. However, PM(10) and O(3) induced cardiovascular effects demonstrated different time courses and end-point behaviors and probably acted through different mechanisms. (C) 2011 Elsevier Inc. All rights reserved.

Impact of academic exposure on health status of university students

OBJECTIVE: To assess the impact of academic life on health status of university students. METHODS: Longitudinal study including 154 undergraduate students from the Universidade de Aveiro, Portugal, with at least two years of follow-up observations. Sociodemographic and behavioral characteristics were collected using questionnaires. Students' weight, height, blood pressure, serum glucose, serum lipids and serum homocysteine levels were measured. Regression analysis was performed using linear mixed-effect models, allowing for random effects at the participant level. RESULTS: A higher rate of dyslipidemia (44.0% vs. 28.6%), overweight (16.3% vs. 12.5%) and smoking (19.3% vs. 0.0%) was found among students exposed to the academic life when compared to freshmen. Physical inactivity was about 80%. Total cholesterol, high density lipoprotein-cholesterol (HDL-C), triglycerides, systolic blood pressure, and physical activity levels were significantly associated with gender (p<0.001). Academic exposure was associated with increased low density lipoprotein-cholesterol (LDL-C) levels (about 1.12 times), and marginally with total cholesterol levels (p=0.041). CONCLUSIONS: High education level does not seem to have a protective effect favoring a healthier lifestyle and being enrolled in health-related areas does not seem either to positively affect students' behaviors. Increased risk factors for non-transmissible diseases in university students raise concerns about their well-being. These results should support the implementation of health promotion and prevention programs at universities.