Nonlinear mixed-effects models and nonparametric inference: a method based on bootstrap for the analysis of non-normal repeated measures data in biostatistical practice

[spa] En la presente investigacion se presenta un "taller" de análisis avanzado de datos en el contexto de los modelos mixtos, con matrices estructuradas de varianzas-covarianzas de los efectos aleatorios y/o de los residuos. El ajuste de dichos modelos ha permitiedo poner de manifiesto ciertas preocupaciones por la sensibilidad de las inferencias respecto de las suposiciones del modelo, especialmente cuando no cumplen las hipótesis habituales sobre normalidad de residuos y de factores aleatorios. El propósito principal del trabajo ha sido el estudio de la validez del empleo de modelos mixtos no lineales para analizar datos de medidas repetidas y discutir la robustez del enfoque inferencial paramétrico basado en la aproximación propuesta por Lindstrom y Bates (1990), y proponer y evaluar posibles alternativas al mismo, basadas en la metodología bootstrap. Se discute además el mejor procedimiento para generar las muestras bootstrap a partir de datos longitudinales bajo modelos mixtos, y se realiza una adaptación de la metodología bootstrap a métodos de ajuste en dos etapas, como STS (Standard two-stage) y GTS (Global two-stage). Los resultados de simulación confirman que la aproximación paramétrica basada en la hipótesis de normalidad no es fiable cuando la distribución de la variable estudiada se aparta seriamente de la normal. En concreto, los intervalos de confianza aproximados basados en una aproximación lineal, y en general en los resultados asintóticos de la máxima verosimilitud, no son robustos frente a la desviación de la hipótesis de normalidad de los datos, incluso para tamaños muéstrales relativamente grandes. El método "bootstrap" proporciona un estimador de los parámetros, en términos de amplitud del intervalo y de su cobertura relativamente más adecuado que el método clásico, basado en la hipótesis de normalidad de la variable estudiada

Impact of incorrect assumptions on the covariance structure of random effects and/or residuals in nonlinear mixed models for repeated measures data

In this paper we analyse, using Monte Carlo simulation, the possible consequences of incorrect assumptions on the true structure of the random effects covariance matrix and the true correlation pattern of residuals, over the performance of an estimation method for nonlinear mixed models. The procedure under study is the well known linearization method due to Lindstrom and Bates (1990), implemented in the nlme library of S-Plus and R. Its performance is studied in terms of bias, mean square error (MSE), and true coverage of the associated asymptotic confidence intervals. Ignoring other criteria like the convenience of avoiding over parameterised models, it seems worst to erroneously assume some structure than do not assume any structure when this would be adequate

On the consequences of misspecifing assumptions concerning residuals distribution in a repeated measures and nonlinear mixed modelling context

In this paper we describe the results of a simulation study performed to elucidate the robustness of the Lindstrom and Bates (1990) approximation method under non-normality of the residuals, under different situations. Concerning the fixed effects, the observed coverage probabilities and the true bias and mean square error values, show that some aspects of this inferential approach are not completely reliable. When the true distribution of the residuals is asymmetrical, the true coverage is markedly lower than the nominal one. The best results are obtained for the skew normal distribution, and not for the normal distribution. On the other hand, the results are partially reversed concerning the random effects. Soybean genotypes data are used to illustrate the methods and to motivate the simulation scenario

Impact of incorrect assumptions on the covariance structure of random effects and/or residuals in nonlinear mixed models for repeated measures data

In this paper we analyse, using Monte Carlo simulation, the possible consequences of incorrect assumptions on the true structure of the random effects covariance matrix and the true correlation pattern of residuals, over the performance of an estimation method for nonlinear mixed models. The procedure under study is the well known linearization method due to Lindstrom and Bates (1990), implemented in the nlme library of S-Plus and R. Its performance is studied in terms of bias, mean square error (MSE), and true coverage of the associated asymptotic confidence intervals. Ignoring other criteria like the convenience of avoiding over parameterised models, it seems worst to erroneously assume some structure than do not assume any structure when this would be adequate

On the consequences of misspecifing assumptions concerning residuals distribution in a repeated measures and nonlinear mixed modelling context

In this paper we describe the results of a simulation study performed to elucidate the robustness of the Lindstrom and Bates (1990) approximation method under non-normality of the residuals, under different situations. Concerning the fixed effects, the observed coverage probabilities and the true bias and mean square error values, show that some aspects of this inferential approach are not completely reliable. When the true distribution of the residuals is asymmetrical, the true coverage is markedly lower than the nominal one. The best results are obtained for the skew normal distribution, and not for the normal distribution. On the other hand, the results are partially reversed concerning the random effects. Soybean genotypes data are used to illustrate the methods and to motivate the simulation scenario

Évaluation par approche statistique de l’impact des changements climatiques sur les ressources en eau : application au périmètre du Gharb (Maroc)

Afin d’évaluer l’impact des changements climatiques sur les ressources en eau, nous réalisons dans ce travail une analyse statistique spatio-temporelle de certaines variables climatiques du bilan hydrique. En effet, pour comprendre les variations climatiques ayant eu lieu dans le passé, l’analyse statistique doit se faire sur des séries chronologiques de données représentatives aussi bien sur le plan spatial que temporel. Toutefois, ces séries de données présentent souvent des lacunes dans les mesures et des irrégularités qui entravent leur utilisation directe. Pour cela, l’analyse statistique adoptée dans cette étude s’est appuyée sur trois étapes : i) le comblement des données manquantes par deux méthodes d’imputation, à savoir la méthode d’imputation multivariée par des équations enchainées (MICE) et la méthode des k plus proches voisins (k-NN); ii) la détection des changements significatifs ayant eu lieu dans le passé dans les séries chronologiques. Les dates de ces changements sont marquées par des ruptures au niveau de la moyenne des variables climatiques étudiées. Ces ruptures ont été validées par trois tests statistiques (Pettitt, Buishand et homogénéité normale SNH); iii) l’investigation de tendances potentielles dans les données climatiques par les tests statistiques (Sen et Mann-Kendall) ainsi que par une projection future. Comme application, nous avons traité les données climatiques pour les périodes 1974-2016 et 2021-2050 issues de cinq stations météorologiques du périmètre du Gharb situé au nord du Maroc. Les résultats obtenus montrent que la méthode d’imputation de MICE est la plus performante pour toutes les stations. Pour les tendances, les séries de températures, d’évapotranspiration potentielle et du déficit hydrique présentaient des tendances significatives à la hausse sur tous les pas de temps. Tandis que pour les séries de précipitations, les tendances étaient non significatives. Les projections à l’horizon 2021-2050 ont fait ressortir que nous pourrions assister à un léger décalage de la saison la plus pluvieuse de l’année et l’effet du réchauffement serait plus important en allant de l’ouest vers l’est du périmètre du Gharb en raison de l’effet de continentalité.In order to evaluate the climate change impact on water resources, we carry out in this work, a spatio-temporal statistical analysis of some water balance variables. In order to understand past climate variations, a statistical analysis must be made for representative time series both temporally and spatially. These data sets, however, often have irregularities and gaps in the measurements which hinder their direct use. For this reason, the statistical analysis used in this study was based on three steps: i) filling gaps of missing data using two imputation methods, namely multiple imputation by chained equations (MICE) and the k-nearest neighbour method (k-NN); ii) the detection within time series of significant changes that occurred in the past. Dates of these changes are characterized by breaks at the level of the mean of the studied climate variables. These breaks were confirmed by three statistical tests (Pettitt, Buishand, and Normal Homogeneity SNH); iii) the investigation of potential climate data trends by using statistical tests (Sen and Mann-Kendall) as well as with a projection technique for the future. As an application, we processed climate data from five weather stations in the Gharb perimeter, located in northern Morocco, for the periods 1974-2016 and 2021-2050. The results obtained showed that MICE imputation is the most efficient for all stations. For trends, while the series of temperatures, potential evapotranspiration, and water deficit showed significant upward trends over all time steps, the trends were non-significant for the precipitation series. The projections for 2021-2050 showed that we could witness a slight shift in the wettest season of the year and that the effect of warming would be greater from west to east in the Gharb perimeter due to the effect of continentality

Assessment of performance of the regional climate model (RegCM4.6) to simulate winter rainfall in the north of Morocco: The case of Tangier-Tétouan-Al-Hociema Region

We examine the performance of the regional climate model RegCM v4.6 to simulate spatial variability of precipitation in the northwestern region of Morocco during the winter of 2009–2010. Simulations cover 24 months from 2009 to 2010 with 30 km as a horizontal grid. We use NCEP reanalysis as forcing data and for better comparison of results, observed precipitations derived from CRU, CHIRPS, and CMORPH data. Results indicate that, on the whole, the RegCM4 model represents appropriate regional aspects of rainfall over the study area but underestimates precipitations over mountainous and Mediterranean regions of the study area (Case of Tangier-Tétouan-Al-Hociema Region) which is probably due to poor representation of orography in the Model and some aspects of local Mediterranean climate. Projected precipitations are also examined in this work in comparison with the reference period of 1970–2005, with simulations performed by RegCM 4.6 regional model for the period 2023–2099 under scenarios RCP4.5 and RCP8.5, forced by HadGEM2-ES General Circulation Model. Results show a decrease in precipitations mean for (2023–2099) for both RCP4.5 and RCP8.5 scenarios over the study area in comparison with the historical period (1970–2005), with a significant decrease under RCP8.5 scenarios. This work proves that the RegCM v4.6 model can be used for regional climate prediction, particularly for the spatial distribution of precipitation, but for sectorial applications and impact studies, the Model outputs should be bias corrected