scholarly journals Fixed effect variance and the estimation of the heritability: Issues and solutions

2017 ◽  
Author(s):  
Pierre de Villemereuil ◽  
Michael B. Morrissey ◽  
Shinichi Nakagawa ◽  
Holger Schielzeth
Keyword(s):  
Fixed Effects ◽  
Linear Models ◽  
Phenotypic Selection ◽  
Mixed Effects ◽  
Mixed Effects Models ◽  
Phenotypic Variance ◽  
Biologically Relevant ◽  
Complex Models ◽  
Variance Parameters ◽  
Variance Explained

AbstractLinear mixed effects models are frequently used for estimating quantitative genetic parameters, including the heritability, of traits of interest. Heritability is an important metric, because it acts as a filter that determines how efficiently phenotypic selection translates into evolutionary change. As a quantity of biological interest, it is important that the denominator, the phenotypic variance, actually reflects the amount of phenotypic variance in the relevant ecological stetting. The current practice of quantifying heritability from mixed effects models frequently deprives the heritability of variance explained by fixed effects (often leading to upward-bias) and it has been suggested to omit fixed effects when estimating heritabilities. We advocate an alternative option of fitting complex models incorporating all relevant effects, while including the variance explained by fixed effects into the estimation of heritabilities. The approach is easily implemented (an example is provided) and allows corrections for the estimation of heritability, such as the exclusion of variance arising from experimental design effects while still including all biologically relevant sources of variation. We explore the complications arising depending on the nature of the covariates included as fixed effects (e.g. biological or experimental origin, characteristics of biological covariates). Furthermore, we discuss fixed effects in non-linear and generalized linear models when fixed effects. In these cases, the variance parameters depend on the location of the intercept and hence on the scaling of the fixed effects. Integration over the biologically relevant range of fixed effects offers a preferred solution in those situations.

Mixed effects models for fish growth

2010 ◽  
Vol 67 (2) ◽  
pp. 269-277 ◽  
Author(s):  
Sanford Weisberg ◽  
George Spangler ◽  
Laurie S. Richmond
Keyword(s):  
Species Interactions ◽  
Fixed Effects ◽  
Management Practices ◽  
Linear Models ◽  
Growth Increment ◽  
Mixed Effects ◽  
Fish Growth ◽  
Mixed Effects Models ◽  
External Conditions ◽  
The Individual

Fish growth in a particular year has both intrinsic and environmental components. Intrinsic growth can depend on both the age and size of the fish and on particular characteristics of the individual fish. The environmental component is the influence of external conditions such as food supply on the growth increment. In this article, we present mixed-effects models as an alternative to fixed-effects linear models for incremental fish growth used previously in the literature and show how these models overcome many of the shortcomings of the fixed-effects approach. In addition, widely available software allows for fitting these models and for elaboration of them to learn about the effects of additional factors such as temperature, species interactions, management practices, the introduction of an invasive species, or other known environmental variables. Finally, we provide a connection with the more usual modeling of size-attained data through the use of growth functions such as the von Bertalanffy.

scholarly journals Including random effects in statistical models in ecology: fewer than five levels?

2021 ◽  
Author(s):  
Dylan G.E. Gomes
Keyword(s):  
Random Effects ◽  
Fixed Effects ◽  
Linear Models ◽  
Random Effect ◽  
Mixed Effects ◽  
Parameter Estimates ◽  
Type I ◽  
Type I Errors ◽  
Ecological Sites ◽  
Generalized Linear Mixed Effects

AbstractAs generalized linear mixed-effects models (GLMMs) have become a widespread tool in ecology, the need to guide the use of such tools is increasingly important. One common guideline is that one needs at least five levels of a random effect. Having such few levels makes the estimation of the variance of random effects terms (such as ecological sites, individuals, or populations) difficult, but it need not muddy one’s ability to estimate fixed effects terms – which are often of primary interest in ecology. Here, I simulate ecological datasets and fit simple models and show that having too few random effects terms does not influence the parameter estimates or uncertainty around those estimates for fixed effects terms. Thus, it should be acceptable to use fewer levels of random effects if one is not interested in making inference about the random effects terms (i.e. they are ‘nuisance’ parameters used to group non-independent data). I also use simulations to assess the potential for pseudoreplication in (generalized) linear models (LMs), when random effects are explicitly ignored and find that LMs do not show increased type-I errors compared to their mixed-effects model counterparts. Instead, LM uncertainty (and p values) appears to be more conservative in an analysis with a real ecological dataset presented here. These results challenge the view that it is never appropriate to model random effects terms with fewer than five levels – specifically when inference is not being made for the random effects, but suggest that in simple cases LMs might be robust to ignored random effects terms. Given the widespread accessibility of GLMMs in ecology and evolution, future simulation studies and further assessments of these statistical methods are necessary to understand the consequences of both violating and blindly following simple guidelines.

scholarly journals The influence of study characteristics on coordinate-based fMRI meta-analyses

2017 ◽  
Author(s):  
Han Bossier ◽  
Ruth Seurinck ◽  
Simone Kühn ◽  
Tobias Banaschewski ◽  
Gareth J. Barker ◽  
...  
Keyword(s):  
Random Effects ◽  
Fixed Effects ◽  
Meta Analysis ◽  
Group Analysis ◽  
Likelihood Estimation ◽  
Ordinary Least Squares ◽  
Mixed Effects ◽  
Mixed Effects Models ◽  
Activation Likelihood Estimation ◽  
Meta Analyses

AbstractGiven the increasing amount of neuroimaging studies, there is a growing need to summarize published results. Coordinate-based meta-analyses use the locations of statistically significant local maxima with possibly the associated effect sizes to aggregate studies. In this paper, we investigate the influence of key characteristics of a coordinate-based meta-analysis on (1) the balance between false and true positives and (2) the reliability of the outcome from a coordinate-based meta-analysis. More particularly, we consider the influence of the chosen group level model at the study level (fixed effects, ordinary least squares or mixed effects models), the type of coordinate-based meta-analysis (Activation Likelihood Estimation, fixed effects and random effects meta-analysis) and the amount of studies included in the analysis (10, 20 or 35). To do this, we apply a resampling scheme on a large dataset (N = 1400) to create a test condition and compare this with an independent evaluation condition. The test condition corresponds to subsampling participants into studies and combine these using meta-analyses. The evaluation condition corresponds to a high-powered group analysis. We observe the best performance when using mixed effects models in individual studies combined with a random effects meta-analysis. This effect increases with the number of studies included in the meta-analysis. We also show that the popular Activation Likelihood Estimation procedure is a valid alternative, though the results depend on the chosen threshold for significance. Furthermore, this method requires at least 20 to 35 studies. Finally, we discuss the differences, interpretations and limitations of our results.

Effect of Application of Probiotics Based on Mixed Effects Models

2013 ◽  
Vol 631-632 ◽  
pp. 545-549
Author(s):  
Ya Ling Xu ◽  
Wei Wei Sui ◽  
Jun Jian Qiao
Keyword(s):  
Fixed Effects ◽  
Mixed Effects ◽  
Hebei Province ◽  
Mixed Effects Models ◽  
Linear Mixed Effects Model ◽  
Linear Mixed Effects ◽  
Independent Variables ◽  
Spss Software ◽  
Shed Light

In order to explore the effect of application of J-4 micro ecological preparation, based on the data from the experiment in the farm of Yixian County, Hebei Province, the research group established a linear mixed effects model , with time as independent variables, age and different formulations as the fixed effects, using spss software for analysis and solving, the results indicate that the model has the extremely good fitting and forecasting effect and method1 is the optimal ratio. The results will shed light on the further study of the role of probiotics .

An imputation approach for fitting two-part mixed effects models for longitudinal semi-continuous data

2020 ◽  
Vol 29 (11) ◽  
pp. 3351-3361
Author(s):  
Hyoyoung Choo-Wosoba ◽  
Debamita Kundu ◽  
Paul S Albert
Keyword(s):  
Random Effects ◽  
Fixed Effects ◽  
Clinical Trial Data ◽  
Mixed Effects ◽  
Mixed Effects Models ◽  
Unbiased Estimation ◽  
Continuous Components ◽  
Wide Range ◽  
Parameter Values ◽  
Imputation Approach

Two-part mixed effects models are often used for analyzing longitudinal data with many zeros. Typically, these models are formulated with binary and continuous components separately with random effects that are correlated between the two components. Researchers have developed maximum-likelihood and Bayesian approaches for fitting these models that often require using particular software packages or very specialized software. We propose an imputation approach that will allow practitioners to separately use standard linear and generalized linear mixed models to estimate the fixed effects for two-part mixed effects models with complex random effects structures. An approximation to the conditional distribution of positive measurements given an individual’s pattern of non-zero measurements is proposed that can be easily estimated and then imputed from. We show that for a wide range of parameter values, the imputation approach results in nearly unbiased estimation and can be implemented with standard software. We illustrate the proposed imputation approach for the analysis of longitudinal clinical trial data with many zeros.

scholarly journals Analyzing ingrowth using zero-inflated negative binomial models

Silva Fennica ◽  
2020 ◽  
Vol 54 (4) ◽  
Author(s):  
Juha Lappi ◽  
Timo Pukkala
Keyword(s):  
Fixed Effects ◽  
Negative Binomial ◽  
Basal Area ◽  
National Forest Inventory ◽  
Mixed Effects ◽  
Low Fertility ◽  
Mixed Effects Models ◽  
Permanent Sample Plots ◽  
Temperature Sum ◽  
Stand Basal Area

Ingrowth is an important element of stand dynamics in several silvicultural systems, especially in continuous cover forestry. Earlier predictive models for ingrowth in Finnish forests are few and not based on up-to-date statistical methods. Ingrowth is here defined as the number of trees over 1.3 m entering a plot. This study developed new ingrowth models for Scots pine ( L.), (Picea abies (L.) H. Karst.) and birch ( Roth and Ehrh.) using data from the permanent sample plots of the Finnish national forest inventory. The data were over-dispersed compared to a Poisson process and had many zeros. Therefore, a zero-inflated negative binomial model was used. The total and species-specific stand basal areas, temperature sum and fertility class were used as predictors in the ingrowth models. Both fixed-effects and mixed-effects models were fitted. The mixed-effects model versions included random plot effects. The mixed-effects models had larger likelihoods but provided biased predictions. Also censored prediction was considered where only a certain maximum number of ingrowth trees were accepted for a plot. The models predicted most pine ingrowth in pine-dominated stands on sub-xeric and xeric sites where stand basal area was low. The predicted amount of spruce ingrowth was maximized when the basal area of spruce was 13 m ha. Increasing temperature sum increased spruce ingrowth. Predicted birch ingrowth decreased with increasing stand basal area and towards low fertility classes. An admixture of pine increased the predicted amount of spruce ingrowth.Pinus sylvestrisNorway spruceBetula pendulaB. pubescens2–1

Fitting Growth Model Using Nonlinear Regression with Random Parameters

2011 ◽  
Vol 480-481 ◽  
pp. 1308-1312
Author(s):  
Yao Xiang Li ◽  
Li Chun Jiang
Keyword(s):  
Random Effects ◽  
Repeated Measures ◽  
Fixed Effects ◽  
Model Building ◽  
Mixed Effects ◽  
Mixed Effects Models ◽  
Ratio Test ◽  
Nonlinear Mixed Effects ◽  
Nonlinear Mixed Effects Models ◽  
Mixed Effect

Mixed Effect models are flexible models to analyze grouped data including longitudinal data, repeated measures data, and multivariate multilevel data. One of the most common applications is nonlinear growth data. The Chapman-Richards model was fitted using nonlinear mixed-effects modeling approach. Nonlinear mixed-effects models involve both fixed effects and random effects. The process of model building for nonlinear mixed-effects models is to determine which parameters should be random effects and which should be purely fixed effects, as well as procedures for determining random effects variance-covariance matrices (e.g. diagonal matrices) to reduce the number of the parameters in the model. Information criterion statistics (AIC, BIC and Likelihood ratio test) are used for comparing different structures of the random effects components. These methods are illustrated using the nonlinear mixed-effects methods in S-Plus software.

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