scholarly journals The development of a standard procedure for the optimal reliability-feasibility trade-off in Multilevel Linear Models analyses in Psychology and Neuroscience.

2021 ◽  
Author(s):  
Michele Scandola ◽  
Emmanuele Tidoni
Keyword(s):  
Random Effects ◽  
Linear Models ◽  
Standard Procedure ◽  
Random Structure ◽  
Neuroscience Research ◽  
Case Application ◽  
Random Slopes ◽  
Computational Resources ◽  
Multilevel Linear Models ◽  
Best Fit

The use of Multilevel Linear Models (MLMs) is increasing in Psychology and Neuroscience research. A key aspect of MLMs is choosing a random effects structure according to the experimental needs. To date, opposite suggestions are present in the literature, spanning from keeping all random effects, which produces several singularity and convergence issues and often requires high computational resources, to removing random effects until the best fit is found, with the risk of inflating first-type error. However, defining the random structure to fit a non-singular and convergent model is not straightforward. Moreover, the lack of a standard approach may lead the researcher to make decisions that potentially inflate first-type errors and generate distortions in the estimates. To date, how to deal with singular and non-converging models is an ongoing debate.We introduce a new way to control for first-type error inflation during model reduction, namely transforming random slopes in complex random intercepts (CRIs). These are multiple random intercepts that represent the complexity of the factors within a given grouping factor. We demonstrate that CRIs can produce reliable results, require less computational and timing resources, and we provide a straightforward procedure to use CRIs in MLMs reduction. Importantly we outline a few criteria and clear recommendations on how and when scholars should reduce singular and non-converging models.We validated this approach by extensive simulations, a real-case application, and a comprehensive procedure that defines new solutions to avoid overinflated results and potentially standardise the use of MLMs in Psychology and Neuroscience.

scholarly journals Issues with the Random Effects Approach in Meta-Analysis of Sparse Incidence Data

2020 ◽  
Vol 23 (1) ◽  
pp. 1-34
Author(s):  
Elasma Milanzi ◽  
◽  
Matthew Spittal ◽  
Lyle Gurrin ◽  
◽  
...  
Keyword(s):  
Random Effects ◽  
Meta Analysis ◽  
Random Structure ◽  
Random Effects Models ◽  
Incidence Data ◽  
Random Slope ◽  
Effect Measure ◽  
Confidence Interval Coverage ◽  
Random Slopes ◽  
The Impact

The current interest in meta-analysis of count data in which some studies have zero events (sparse data) has led to re-assessment of commonly used meta-analysis methods to establish their validity in such scenarios. The general consensus is that methods which exclude studies with zero events should be avoided. In the family of parametric methods, random effects models come out highly recommended. While acknowledging the strength of this approach, one of its aspects with potentially undesirable impact on the results, is often overlooked. The random effects approach accounts for the variation in the effect measure across studies by using models with random slopes. It has been shown that parameters associated with a random structure risk being estimated with biased unless the distribution of the random effects is correctly specified. In meta-analysis the parameter of interest, average effect measure, is associated with a random structure (random slope). Information on how the effect measure point and precision estimates are affected by misspecification of random effects distribution is still lacking. To fill in the information gap, we used a simulation study to investigate the impact of misspecification of distribution of random effects in this context and provide guidelines in using the random effects approach. Our results indicated that relative bias in the estimated effect measure could be as high as 30% and 95% confidence interval coverage as low as 0%. These results send a clear message that possible effects of misspecification of the distribution of random effects should not be ignored. In light of these findings, we have proposed a sensitivity analysis that also establishes whether a random slope model is necessary.

scholarly journals Retention of the Antibiotic Cefuroxime onto Agricultural and Forest Soils

2021 ◽  
Vol 11 (10) ◽  
pp. 4663
Author(s):  
Raquel Cela-Dablanca ◽  
Carolina Nebot ◽  
Lucia Rodríguez López ◽  
David Ferández-Calviño ◽  
Manuel Arias-Estévez ◽  
...  
Keyword(s):  
Forest Soils ◽  
Linear Models ◽  
Agricultural Soils ◽  
Organic Matter Content ◽  
Matter Content ◽  
Batch Type ◽  
Exchangeable Ca ◽  
Influence Of Ph ◽  
Best Fit ◽  
Soil Colloids

Antibiotics in wastewater, sewage sludge, manures, and slurries constitute a risk for the environment when spread on soils. This work studies the adsorption and desorption of the antibiotic cefuroxime (CFX) in 23 agricultural and forest soils, using batch-type experiments. Our results show that the adsorption values were between 40.75 and 99.57% in the agricultural soils, while the range was lower (from 74.57 to 93.46%) in forest soils. Among the Freundlich, Langmuir, and Linear models, the Freundlich equation shows the best fit for the adsorption results. In addition, agricultural soils with higher pH are the ones that present the highest adsorption. Further confirmation of the influence of pH on adsorption is given by the fact that Freundlich’s KF parameter and the Linear model Kd parameter shows a positive correlation with pH and with the exchangeable Ca and Mg values, which are known to affect the charges of the soil colloids and the formation of cationic bridges between adsorbents and adsorbate. In addition, Freundlich’s n parameter shows a positive and significant correlation with the organic matter content, related to the high adsorption taking place on forest soils despite their pH < 5. Regarding desorption, in most cases, it is lower than 1%, which indicates that CFX is adsorbed in a rather irreversible way onto these soils. Overall, these results can be considered relevant regarding their potential impact on environmental quality and public health.

scholarly journals Gradient boosting for linear mixed models

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Colin Griesbach ◽  
Benjamin Säfken ◽  
Elisabeth Waldmann
Keyword(s):  
Random Effects ◽  
Mixed Models ◽  
Selection Procedure ◽  
Classification Theory ◽  
Gradient Boosting ◽  
Random Structure ◽  
Boosting Algorithm ◽  
The One ◽  
Biased Estimates ◽  
Selection Of

Abstract Gradient boosting from the field of statistical learning is widely known as a powerful framework for estimation and selection of predictor effects in various regression models by adapting concepts from classification theory. Current boosting approaches also offer methods accounting for random effects and thus enable prediction of mixed models for longitudinal and clustered data. However, these approaches include several flaws resulting in unbalanced effect selection with falsely induced shrinkage and a low convergence rate on the one hand and biased estimates of the random effects on the other hand. We therefore propose a new boosting algorithm which explicitly accounts for the random structure by excluding it from the selection procedure, properly correcting the random effects estimates and in addition providing likelihood-based estimation of the random effects variance structure. The new algorithm offers an organic and unbiased fitting approach, which is shown via simulations and data examples.

scholarly journals Identification of Health Expenditures Determinants: A Model to Manage the Economic Burden of Cardiovascular Disease

2021 ◽  
Vol 18 (9) ◽  
pp. 4652
Author(s):  
Fiorella Pia Salvatore ◽  
Alessia Spada ◽  
Francesca Fortunato ◽  
Demetris Vrontis ◽  
Mariantonietta Fiore
Keyword(s):  
Cardiovascular Disease ◽  
Hospital Discharge ◽  
Random Effects ◽  
Economic Burden ◽  
Linear Models ◽  
Health Management ◽  
Model Performance ◽  
Real Data ◽  
Large Set ◽  
Regional Health

The purpose of this paper is to investigate the determinants influencing the costs of cardiovascular disease in the regional health service in Italy’s Apulia region from 2014 to 2016. Data for patients with acute myocardial infarction (AMI), heart failure (HF), and atrial fibrillation (AF) were collected from the hospital discharge registry. Generalized linear models (GLM), and generalized linear mixed models (GLMM) were used to identify the role of random effects in improving the model performance. The study was based on socio-demographic variables and disease-specific variables (diagnosis-related group, hospitalization type, hospital stay, surgery, and economic burden of the hospital discharge form). Firstly, both models indicated an increase in health costs in 2016, and lower spending values for women (p < 0.001) were shown. GLMM indicates a significant increase in health expenditure with increasing age (p < 0.001). Day-hospital has the lowest cost, surgery increases the cost, and AMI is the most expensive pathology, contrary to AF (p < 0.001). Secondly, AIC and BIC assume the lowest values for the GLMM model, indicating the random effects’ relevance in improving the model performance. This study is the first that considers real data to estimate the economic burden of CVD from the regional health service’s perspective. It appears significant for its ability to provide a large set of estimates of the economic burden of CVD, providing information to managers for health management and planning.

Relationship between plasma osmolality and plasma vasopressin in human subjects

1980 ◽  
Vol 238 (4) ◽  
pp. E313-E317 ◽  
Author(s):  
M. Hammer ◽  
J. Ladefoged ◽  
K. Olgaard
Keyword(s):  
Linear Models ◽  
Human Subjects ◽  
Plasma Osmolality ◽  
Metabolic Clearance ◽  
Parabolic Model ◽  
Pronounced Increase ◽  
Plasma Vasopressin ◽  
Log Linear ◽  
The Relationship ◽  
Best Fit

The relationship between plasma osmolality (pOsm) and plasma vasopressin (pAVP) was studied in 13 human subjects during dehydration. The fit of linear, log-linear, parabolic, and exponential models was tested. For all of the data, the nonlinear models had the best fit. However, when individual differences in either gain or threshold were allowed for, the linear models were better than log-linear models. Finally, analyses were made with individual data points. Linear models had the best fit in half of the subjects, whereas for the others the parabolic model gave the best fit. For those subjects investigated in the low range of the osmoregulatory curve, a linear relationship was found, whereas, for those having the most pronounced increase in pOsm, the most significant improvement was found with the parabolic model. This finding indicates that the relationship is not stable during dehydration in the whole range and that hypovolemia probably can influence the secretion rate and/or metabolic clearance rate and thereby the relationship.

scholarly journals Clinical Factors Influencing the Efficacy of Systemic Moxifloxacin in the Therapy of Patients With Generalized Aggressive Periodontitis: A Multilevel Analysis From a Clinical Trial

2015 ◽  
Vol 8 (3) ◽  
pp. 80 ◽  
Author(s):  
Carlos M. Ardila ◽  
Isabel C. Guzmán
Keyword(s):  
Clinical Trial ◽  
Multilevel Analysis ◽  
Linear Models ◽  
Clinical Results ◽  
Aggressive Periodontitis ◽  
Continuous Variables ◽  
Clinical Factors ◽  
Probing Depth ◽  
Clinical Benefits ◽  
Multilevel Linear Models

<p><strong>BACKGROUND:</strong> It has been reported that clinical results of mechanical periodontal treatment could differ between subjects and among different sites of the tooth in the patient. The objective of this multilevel analysis is to investigate clinical factors at subject and sites of the tooth that influence variations in clinical attachment (CAL) increase and probing depth (PD) diminution of adjunctive moxifloxacin (MOX) at six months post-treatment in generalized aggressive periodontitis.</p> <p><strong>METHODS:</strong> This clinical trial included 40 patients randomly distributed to two therapy protocols: scaling and root planing alone or combined with MOX. Multilevel linear models for continuous variables were formulated to evaluate the clinical impact of the hierarchical configuration of periodontal data.</p> <p><strong>RESULTS:</strong> Six months following therapy, the divergences between both protocols were statistically significant in PD diminution and CAL increase, favouring the MOX therapy (p&lt;0.001). Besides, the multilevel analysis revealed that adjunctive MOX at the subject level, non-molar and the interaction non-molar x MOX at the tooth level, interproximal sites and the interaction interproximal sites x MOX at the site level, were statistically significant factors in determining CAL increase and PD diminution.</p> <p><strong>CONCLUSIONS:</strong> The main cause of variability in CAL gain and PD reduction following adjunctive MOX was attributable to the tooth level. Adjunctive MOX and their interactions with non-molar and interproximal sites showed higher clinical benefits at the tooth and site levels which could be essential for PD reduction and CAL gain in generalized aggressive periodontitis subjects.</p>

scholarly journals Generalized linear models with random effects for the description of data with excess zeros

2011 ◽  
Vol 54 (6) ◽  
pp. 661-675
Author(s):  
N. Mielenz ◽  
K. Thamm ◽  
M. Bulang ◽  
J. Spilke
Keyword(s):  
Random Effects ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Linear Models ◽  
Negative Binomial ◽  
Detailed Comparison ◽  
Response Scale ◽  
Explanatory Variables ◽  
Excess Zeros ◽  
Explanatory Factors

Abstract. In this paper count data with excess zeros and repeated observations per subject are evaluated. If the number of values observed for the zero event in the trial substantially exceeds the expected number (derived from the Poisson or from the negative binomial distribution), then there is an excess of zeros. Hurdle and zero-inflated models with random effects are available in order to evaluate this type of data. In this paper both model approaches are presented and are used for the evaluation of the number of visits to the feeder per cow per hour. Finally, for the analysis of the target trait a hurdle model with random effects based on a negative binomial distribution was used. This analysis was derived from a detailed comparison of models and was needed because of a simpler computer implementation. For improved interpretation of the results, the levels of the explanatory factors (for example, the classes of lactation) were not averaged in the link scale, but rather in the response scale. The deciding explanatory variables for the pattern of visiting activities in the 24-hour cycle are the milking and cleaning times at hours 4, 7, 12 and 20. The highly significant differences in the visiting frequencies of cows of the first lactation and those of higher lactations were explained by competition for access to the feeder and thus to the feed.

scholarly journals Estimating Bayes Factors for Linear Models with Random Slopes on Continuous Predictors

2017 ◽  
Author(s):  
Mirko Thalmann ◽  
Marcel Niklaus ◽  
Klaus Oberauer
Keyword(s):  
Bayesian Statistics ◽  
Random Effects ◽  
Mixed Models ◽  
Mixed Effects ◽  
Bayes Factors ◽  
Mixed Effects Models ◽  
Type I ◽  
Frequentist Statistics ◽  
Random Slopes ◽  
Continuous Predictors

Using mixed-effects models and Bayesian statistics has been advocated by statisticians in recent years. Mixed-effects models allow researchers to adequately account for the structure in the data. Bayesian statistics – in contrast to frequentist statistics – can state the evidence in favor of or against an effect of interest. For frequentist statistical methods, it is known that mixed models can lead to serious over-estimation of evidence in favor of an effect (i.e., inflated Type-I error rate) when models fail to include individual differences in the effect sizes of predictors ("random slopes") that are actually present in the data. Here, we show through simulation that the same problem exists for Bayesian mixed models. Yet, at present there is no easy-to-use application that allows for the estimation of Bayes Factors for mixed models with random slopes on continuous predictors. Here, we close this gap by introducing a new R package called BayesRS. We tested its functionality in four simulation studies. They show that BayesRS offers a reliable and valid tool to compute Bayes Factors. BayesRS also allows users to account for correlations between random effects. In a fifth simulation study we show, however, that doing so leads to slight underestimation of the evidence in favor of an actually present effect. We only recommend modeling correlations between random effects when they are of primary interest and when sample size is large enough. BayesRS is available under https://cran.r-project.org/web/packages/BayesRS/, R code for all simulations is available under https://osf.io/nse5x/?view_only=b9a7caccd26a4764a084de3b8d459388

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