Fast inference for robust nonlinear mixed-effects models.

The interest for nonlinear mixed-effects models comes from application areas as pharmacokinetics, growth curves and HIV viral dynamics. However, the modeling procedure usually leads to many difficulties, as the inclusion of random effects, the estimation process and the model sensitivity to atypical or nonnormal data. The scale mixture of normal distributions include heavy-tailed models, as the Student-t, slash and contaminated normal distributions, and provide competitive alternatives to the usual models, enabling the obtention of robust estimates against outlying observations. Our proposal is to compare two estimation methods in nonlinear mixed-effects models where the random components follow a multivariate scale mixture of normal distributions. For this purpose, a Monte Carlo expectation-maximization algorithm (MCEM) and an efficient likelihood-based approximate method are developed. Results show that the approximate method is much faster and enables a fairly efficient likelihood maximization, although a slightly larger bias may be produced, especially for the fixed-effects parameters. A discussion on the robustness aspects of the proposed models are also provided. Two real nonlinear applications are discussed and a brief simulation study is presented.

Detection of atypical response trajectories in biomedical longitudinal databases.

Many health care professionals and institutions manage longitudinal databases, involving follow-ups for different patients over time. Longitudinal data frequently manifest additional complexities such as high variability, correlated measurements and missing data. Mixed effects models have been widely used to overcome these difficulties. This work proposes the use of linear mixed effects models as a tool that allows to search conceptually different types of anomalies in the data simultaneously.

Individual and Family Determinants for Quality of Life in Parents of Children with Inborn Errors of Metabolism Requiring a Restricted Diet: A Multilevel Analysis Approach.

OBJECTIVE: The objective of this study was to compare the quality of life (QoL) for parents of children with inborn errors of metabolism (IEMs) requiring a restricted diet with French population norms and investigate parental QoL determinants. STUDY DESIGN: This cross-sectional study included mothers and/or fathers of children < 18 years of age affected by IEMs requiring a restricted diet (except phenylketonuria) from January 2015 to December 2017. Parents' QoL was assessed using the World Health Organization Quality of Life BREF questionnaire and compared with age- and sex-matched reference values from the French general population. Linear mixed models were used to examine the effects of demographic, socioeconomic, disease-related, and psychocognitive factors on parental QoL, according to a 2-level regression model considering individuals (parents) nested within families. RESULTS: Of the 1156 parents invited to participate, 785 (68%) were included. Compared with the general population, parents of children with IEMs requiring a restricted diet reported a lower QoL in physical and social relationship domains but a higher QoL in the psychological domain. In the multivariate analysis, characteristics associated with poorer parental QoL included both parent-related factors (being a father, older age, more educated parent, nonworking parent, greater anxiety, seeking more social support, and using less positive thinking and problem-solving coping strategies) and family-related factors (disease complications, increased number of hospital medical providers, child's younger age, single-parent family, and lower family material wealth). CONCLUSION: Parents of children with IEMs requiring a restricted diet reported poorer QoL in physical and social relationship domains than population norms. Psychocognitive factors, beyond disease-specific and family-related characteristics, were the most important determinants influencing parental QoL and may represent essential aspects for interventions. CLINICAL TRIAL REGISTRATION: ClinicalTrials.gov: NCT02552784.

An approach to quantify climate-productivity relationships: an example from a widespread Nothofagus forest.

Unique combinations of geographic and environmental conditions make quantifying the importance of factors that influence forest productivity difficult. I aimed to model the height growth of dominant Nothofagus alpina trees in temperate forests of Chile, as a proxy for forest productivity, by building a dynamic model that accounts for topography, habitat type, and climate conditions. Using stem analysis data of 169 dominant trees sampled throughout south-central Chile (35°50' and 41°30' S), I estimated growth model parameters using a nonlinear mixed-effects framework that takes into account the hierarchical structure of the data. Based on the proposed model, I used a system-dynamics approach to analyze growth rates as a function of topographic, habitat type, and climatic variability. I found that the interaction between aspect, slope, and elevation, as well as the effect of habitat type, play an essential role in determining tree height growth rates of N. alpina. Furthermore, the precipitation in the warmest quarter, precipitation seasonality, and annual mean temperature are critical climatic drivers of forest productivity. Given a forecasted climate condition for the region by 2100, where precipitation seasonality and mean annual temperature increase by 10% and 1°C, respectively, and precipitation in the warmest quarter decreases by 10 mm, I predict a reduction of 1.4 m in height growth of 100-yr-old dominant trees. This study shows that the sensitivity of N. alpina-dominated forests to precipitation and temperature patterns could lead to a reduction of tree height growth rates as a result of climate change, suggesting a decrease in carbon sequestration too. By implementing a system dynamics approach, I provide a new perspective on climate-productivity relationships, bettering the quantitative understanding of forest ecosystem dynamics under climate change. The results highlight that while temperature rising might favor forest growth, the decreasing in both amount and distribution within a year of precipitation can be even more critical to reduce forest productivity.

Mixed-effects models for censored data with autoregressive errors.

Mixed-effects models, with modifications to accommodate censored observations (LMEC/NLMEC), are routinely used to analyze measurements, collected irregularly over time, which are often subject to some upper and lower detection limits. This paper presents a likelihood-based approach for fitting LMEC/NLMEC models with autoregressive of order p dependence of the error term. An EM-type algorithm is developed for computing the maximum likelihood estimates, obtaining as a byproduct the standard errors of the fixed effects and the likelihood value. Moreover, the constraints on the parameter space that arise from the stationarity conditions for the autoregressive parameters in the EM algorithm are handled by a reparameterization scheme, as discussed in Lin and Lee (2007). To examine the performance of the proposed method, we present some simulation studies and analyze a real AIDS case study. The proposed algorithm and methods are implemented in the new R package ARpLMEC.

The essential value of the alternatives of the suboptimal choice procedure is different for pigeons and rats.

Suboptimal choice is the preference for a discriminative alternative with low probability of reinforcement, over a non-discriminative alternative with higher probability of reinforcement. Pigeons consistently prefer the discriminative alternative, whereas rats prefer the non-discriminative; the variables accounting for this difference are not yet clear. The economic concepts related to demand curves have been used to calculate the essential value of different types of reinforcers, so they may be useful to compare the value of the alternatives in the suboptimal choice procedure. The goal of this study was to calculate the essential value of each of the alternatives presented in the suboptimal choice procedure to assess if pigeons (Experiment 1) and rats (Experiment 2) value them differently. In both experiments, the fixed ratio requirement in the initial link was increased throughout sessions in order to obtain the demand curve and calculate the essential value by fitting the exponential-demand model. A Bayesian Linear Mixed-Effects Model indicated that pigeons had higher essential values for the discriminative alternative, whereas rats obtained higher essential values for the non-discriminative alternative. These results suggest that preferences in the suboptimal choice procedure are indeed based on the essential value of the alternatives, and provide a new paradigm to study the variables affecting this phenomenon.

Linear mixed-effects models for the analysis of high-density electromyography with application to diabetic peripheral neuropathy.

This article demonstrates the power and flexibility of linear mixed-effects models (LMEMs) to investigate high-density surface electromyography (HD-sEMG) signals. The potentiality of the model is illustrated by investigating the root mean squared value of HD-sEMG signals in the tibialis anterior muscle of healthy (n = 11) and individuals with diabetic peripheral neuropathy (n = 12). We started by presenting the limitations of traditional approaches by building a linear model with only fixed effects. Then, we showed how the model adequacy could be increased by including random effects, as well as by adding alternative correlation structures. The models were compared with the Akaike information criterion and the Bayesian information criterion, as well as the likelihood ratio test. The results showed that the inclusion of the random effects of intercept and slope, along with an autoregressive moving average correlation structure, is the one that best describes the data (p < 0.01). Furthermore, we demonstrate how the inclusion of additional variance structures can accommodate heterogeneity in the residual analysis and therefore increase model adequacy (p < 0.01). Thus, in conclusion, we suggest that adopting LMEM to repeated measures such as electromyography can provide additional information from the data (e.g. test for alternative correlation structures of the RMS value), and hence provide new insights into HD-sEMG-related work.

Parameterized maximum entropy models predict variability of metabolic scaling across tree communities and populations.

The maximum entropy theory of ecology (METE) applies the concept of "entropy" from information theory to predict macroecological patterns. The energetic predictions of the METE rely on predetermined metabolic scaling from external theories, and this reliance diminishes the testability of the theory. In this work, I build parameterized METE models by treating the metabolic scaling exponent as a free parameter, and I use the maximum-likelihood method to obtain empirically plausible estimates of the exponent. I test the models using the individual tree data from an oak-dominated deciduous forest in the northeastern United States and from a tropical forest in central Panama. My analysis shows that the metabolic scaling exponents predicted from the parameterized METE models deviate from that of the metabolic theory of ecology and exhibit large variation, at both community and population levels. Assemblage and population abundance may act as ecological constraints that regulate the individual-level metabolic scaling behavior. This study provides a novel example of the use of the parameterized METE models to reveal the biological processes of individual organisms. The implication and possible extensions of the parameterized METE models are discussed.

Species richness and functional structure of fish assemblages in three freshwater habitats: effects of environmental factors and management.

In this study, the inverted trophic hypothesis was tested in the freshwater fish communities of a reservoir. The distribution of fish species in three freshwater habitats in the Jurumirim Reservoir, Brazil, was examined using both species richness and the relative proportions of different trophic groups. These groups were used as a proxy for functional structure in an attempt to test the ability of these measures to assess fish diversity. Assemblage structures were first described using non-metric multidimensional scaling (NMDS). The influence of environmental conditions for multiple fish assemblage response variables (richness, total abundance and abundance per trophic group) was tested using generalised linear mixed models (GLMM). The metric typically employed to describe diversity; that is, species richness, was not related to environmental conditions. However, absolute species abundance was relatively well explained with up to 54% of the variation in the observed data accounted for. Differences in the dominance of trophic groups were most apparent in response to the presence of introduced fish species: the iliophagous and piscivorous trophic groups were positively associated, while detritivores and herbivores were negatively associated, with the alien species. This suggests that monitoring functional diversity might be more valuable than species diversity for assessing effects of disturbances and managements policies on the fish community.

Types of Emotion Regulation and Their Associations with Gambling: A Cross-Sectional Study with Disordered and Non-problem Ecuadorian Gamblers.

This cross-sectional study was aimed at investigating the role of emotional regulation in regular gambling in a sample of 197 disordered and non-problem gamblers from Ecuador. Two proxies were used as measures of behavioral signs of generalized emotion dysregulation (UPPS-P emotion-driven impulsivity) and intentional emotion regulation strategies (ERQ), and their associations with gambling cognitions (as measured by the GRCS questionnaire), gambling behavior (SOGS), and comorbid alcohol and drug misuse (MultiCAGE), were explored. For analyses, impulsivity traits, including emotion-driven impulsivity scores, were used as inputs to predict dispositional variables (ERQ strategies and GRCS cognitions), and clinically relevant behavioral outputs, while controlling for gambling severity. Hypotheses were based on previously published work, although the analysis has been improved (using hierarchical linear mixed-effects modelling), and homogenized in covariate control, and decision threshold stringency. Results were as follows: (1) After controlling for relevant covariates, UPPS-P sensation seeking was positively associated with gambling cognitions, whereas positive urgency was positively associated with cognitive biases (interpretative bias, control illusion, and predictive control) but not with other gambling cognitions. (2) Among emotion regulation strategies, reappraisal, but not suppression, was associated with gambling cognitions. (3) Negative urgency was distinctively associated with suppression, but not with reappraisal. And (4), no impulsivity dimensions significantly predicted drug or alcohol misuse, although negative urgency fell just below the decision threshold. These results reinforce the importance of emotion regulation processes in the cognitive and behavioral manifestations of gambling. Most importantly, they suggest a dissociation between the role of model-free dysregulation of negative emotions (as measured by UPPS-P negative urgency), as a key contributor to gambling complication and general psychopathology; and the one of strategic emotion regulation, in fueling gambling-related cognitive distortions.

Dynamics of Caligus rogercresseyi (Boxshall & Bravo, 2000) in farmed Atlantic salmon (Salmo salar) in southern Chile: Are we controlling sea lice?

Caligus rogercresseyi generates the greatest losses in the salmon industry in Chile. The relationship between salmon farming and sea lice is made up of various components: the parasite, host, environment and farming practices, which make it difficult to identify patterns in parasite population dynamics to define prevention and control strategies. The objectives of this study were to analyse and compare the effect of farming, sanitary practices and environmental variables on the abundance of gravid females (GF) and juveniles (JUV) of C. rogercresseyi on Salmo salar in three Salmon Neighborhood Areas (SNAs) in Region 10, south of Chile. Linear mixed-effects models of the negative binomial distribution were used to evaluate the effect of the different explanatory variables on GF and JUV. Productive variables were the key drivers explaining the abundance of GF and JUV. Results suggest that C. rogercresseyi is not controlled and JUV are persistent in the three SNAs, and sanitary practices do not control the dissemination of the parasite among sites. Environmental variables had a low impact on sea lice abundance. There is a need to perform analysis for modelling of parasite population dynamics to improve Integrated Pest Management, including changes in the governance to achieve an effective prevention and control.

Bayesian semiparametric modeling for HIV longitudinal data with censoring and skewness.

In biomedical studies, the analysis of longitudinal data based on Gaussian assumptions is common practice. Nevertheless, more often than not, the observed responses are naturally skewed, rendering the use of symmetric mixed effects models inadequate. In addition, it is also common in clinical assays that the patient's responses are subject to some upper and/or lower quantification limit, depending on the diagnostic assays used for their detection. Furthermore, responses may also often present a nonlinear relation with some covariates, such as time. To address the aforementioned three issues, we consider a Bayesian semiparametric longitudinal censored model based on a combination of splines, wavelets, and the skew-normal distribution. Specifically, we focus on the use of splines to approximate the general mean, wavelets for modeling the individual subject trajectories, and on the skew-normal distribution for modeling the random effects. The newly developed method is illustrated through simulated data and real data concerning AIDS/HIV viral loads.

Error-rate estimation in discriminant analysis of non-linear longitudinal data: A comparison of resampling methods.

Consider longitudinal observations across different subjects such that the underlying distribution is determined by a non-linear mixed-effects model. In this context, we look at the misclassification error rate for allocating future subjects using cross-validation, bootstrap algorithms (parametric bootstrap, leave-one-out, .632 and [Formula: see text]), and bootstrap cross-validation (which combines the first two approaches), and conduct a numerical study to compare the performance of the different methods. The simulation and comparisons in this study are motivated by real observations from a pregnancy study in which one of the main objectives is to predict normal versus abnormal pregnancy outcomes based on information gathered at early stages. Since in this type of studies it is not uncommon to have insufficient data to simultaneously solve the classification problem and estimate the misclassification error rate, we put special attention to situations when only a small sample size is available. We discuss how the misclassification error rate estimates may be affected by the sample size in terms of variability and bias, and examine conditions under which the misclassification error rate estimates perform reasonably well.

Quantile regression in linear mixed models: a stochastic approximation EM approach.

This paper develops a likelihood-based approach to analyze quantile regression (QR) models for continuous longitudinal data via the asymmetric Laplace distribution (ALD). Compared to the conventional mean regression approach, QR can characterize the entire conditional distribution of the outcome variable and is more robust to the presence of outliers and misspecification of the error distribution. Exploiting the nice hierarchical representation of the ALD, our classical approach follows a Stochastic Approximation of the EM (SAEM) algorithm in deriving exact maximum likelihood estimates of the fixed-effects and variance components. We evaluate the finite sample performance of the algorithm and the asymptotic properties of the ML estimates through empirical experiments and applications to two real life datasets. Our empirical results clearly indicate that the SAEM estimates outperforms the estimates obtained via the combination of Gaussian quadrature and non-smooth optimization routines of the Geraci and Bottai (2014) approach in terms of standard errors and mean square error. The proposed SAEM algorithm is implemented in the R package qrLMM().

Extensions to Bayesian generalized linear mixed effects models for household tuberculosis transmission.

Household contact studies, a mainstay of tuberculosis transmission research, often assume that tuberculosis-infected household contacts of an index case were infected within the household. However, strain genotyping has provided evidence against this assumption. Understanding the household versus community infection dynamic is essential for designing interventions. The misattribution of infection sources can also bias household transmission predictor estimates. We present a household-community transmission model that estimates the probability of community infection, that is, the probability that a household contact of an index case was actually infected from a source outside the home and simultaneously estimates transmission predictors. We show through simulation that our method accurately predicts the probability of community infection in several scenarios and that not accounting for community-acquired infection in household contact studies can bias risk factor estimates. Applying the model to data from Vitória, Brazil, produced household risk factor estimates similar to two other standard methods for age and sex. However, our model gave different estimates for sleeping proximity to index case and disease severity score. These results show that estimating both the probability of community infection and household transmission predictors is feasible and that standard tuberculosis transmission models likely underestimate the risk for two important transmission predictors. Copyright © 2017 John Wiley & Sons, Ltd.

Predicting pregnancy outcomes using longitudinal information: a penalized splines mixed-effects model approach.

We propose a semiparametric nonlinear mixed-effects model (SNMM) using penalized splines to classify longitudinal data and improve the prediction of a binary outcome. The work is motivated by a study in which different hormone levels were measured during the early stages of pregnancy, and the challenge is using this information to predict normal versus abnormal pregnancy outcomes. The aim of this paper is to compare models and estimation strategies on the basis of alternative formulations of SNMMs depending on the characteristics of the data set under consideration. For our motivating example, we address the classification problem using a particular case of the SNMM in which the parameter space has a finite dimensional component (fixed effects and variance components) and an infinite dimensional component (unknown function) that need to be estimated. The nonparametric component of the model is estimated using penalized splines. For the parametric component, we compare the advantages of using random effects versus direct modeling of the correlation structure of the errors. Numerical studies show that our approach improves over other existing methods for the analysis of this type of data. Furthermore, the results obtained using our method support the idea that explicit modeling of the serial correlation of the error term improves the prediction accuracy with respect to a model with random effects, but independent errors. Copyright © 2017 John Wiley & Sons, Ltd.

No evidence that elevated CO2 gives tropical lianas an advantage over tropical trees.

Recent studies indicate that lianas are increasing in size and abundance relative to trees in neotropical forests. As a result, forest dynamics and carbon balance may be altered through liana-induced suppression of tree growth and increases in tree mortality. Increasing atmospheric CO2 is hypothesized to be responsible for the increase in neotropical lianas, yet no study has directly compared the relative response of tropical lianas and trees to elevated CO2 . We explicitly tested whether tropical lianas had a larger response to elevated CO2 than co-occurring tropical trees and whether seasonal drought alters the response of either growth form. In two experiments conducted in central Panama, one spanning both wet and dry seasons and one restricted to the dry season, we grew liana (n = 12) and tree (n = 10) species in open-top growth chambers maintained at ambient or twice-ambient CO2 levels. Seedlings of eight individuals (four lianas, four trees) were grown in the ground in each chamber for at least 3 months during each season. We found that both liana and tree seedlings had a significant and positive response to elevated CO2 (in biomass, leaf area, leaf mass per area, and photosynthesis), but that the relative response to elevated CO2 for all variables was not significantly greater for lianas than trees regardless of the season. The lack of differences in the relative response between growth forms does not support the hypothesis that elevated CO2 is responsible for increasing liana size and abundance across the neotropics.

La modelación jerárquica y los efectos de grupo en la predicción del rendimiento académico / The hierarchical modelling and the group effects in the prediction of academic performance

El presente trabajo se realizó con el propósito de mostrar que el grupo es un modificador de la relación entre el rendimiento académico y sus predictores y con ello, fundamentar la necesidad de recurrir a la modelación jerárquica para la predicción del rendimiento. Se aplicaron modelos con coeficientes aleatorios, especialmente apropiados para la circunstancia frecuente de casos agrupados, en la que los supuestos usuales de los modelos lineales ordinarios dejan de ser válidos y los modelos clásicos, inaplicables. Se constató que algunos de los predictores tradicionales tenían relevancia condicionada al grupo, aunque no parecían tener relevancia marginal. Se demostró así que el grupo es un modulador de la relación entre el rendimiento académico y algunos de sus predictores. La consecuencia de mayor trascedencia fue que la asignación de un estudiante a un grupo podía influir considerablemente en su rendimiento académico, independientemente de sus condiciones iniciales

The present paper was aimed at demonstrating that the group acts as a modifier of the relation between the academic performance and its predictors, and at founding the need of resorting to hierarchical modelling to predict this performance. Models with randomized coefficients, specially appropriate for the frequent circumstance of grouped cases, where the suppossed ordinary lineal models are not valid anymore and the classical models are unapplicable, were applied. It was proved that some of the traditonal predictors were relevant according to the group, though they did not seem to have marginal relevancy. This way, it was demonstrated that the group was a modullator of the relation between academic performance and some of its predictors. The most significant consequence was that the assignation of a student to a group may influence considerably on his academic performance, independently of its initial conditions.