scholarly journals Accounting for Estimation Uncertainty and Shrinkage in Bayesian Within-Subject Intervals: A Comment on Nathoo, Kilshaw, and Masson (2018)

2018 ◽  
Author(s):  
Daniel W. Heck
Keyword(s):  
Maximum Likelihood ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Mathematical Psychology ◽  
Maximum Likelihood Estimates ◽  
Psychonomic Bulletin ◽  
Estimation Uncertainty ◽  
Mean Differences ◽  
Highest Density Interval ◽  
Fully Bayesian

To facilitate the interpretation of systematic mean differences in within-subject designs, Nathoo, Kilshaw, and Masson (2018, Journal of Mathematical Psychology, 86, 1-9) proposed a Bayesian within-subject highest-density interval (HDI). However, their approach rests on independent maximum-likelihood estimates for the random effects which do not take estimation uncertainty and shrinkage into account. I propose an extension of Nathoo et al.'s method using a fully Bayesian, two-step approach. First, posterior samples are drawn for the linear mixed model. Second, the within-subject HDI is computed repeatedly based on the posterior samples, thereby accounting for estimation uncertainty and shrinkage. After marginalizing over the posterior distribution, the two-step approach results in a Bayesian within-subject HDI with a width similar to that of the classical within-subject confidence interval proposed by Loftus and Masson (1994, Psychonomic Bulletin & Review, 1, 476-490).

scholarly journals Maximum likelihood estimation based on Newton–Raphson iteration for the bivariate random effects model in test accuracy meta-analysis

2019 ◽  
Vol 29 (4) ◽  
pp. 1197-1211
Author(s):  
Brian H Willis ◽  
Mohammed Baragilly ◽  
Dyuti Coomar
Keyword(s):  
Maximum Likelihood ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Meta Analysis ◽  
Maximum Likelihood Estimates ◽  
Global Maximum ◽  
Test Accuracy ◽  
Generalised Linear Mixed Model ◽  
Newton Raphson ◽  
Raphson Iteration

A bivariate generalised linear mixed model is often used for meta-analysis of test accuracy studies. The model is complex and requires five parameters to be estimated. As there is no closed form for the likelihood function for the model, maximum likelihood estimates for the parameters have to be obtained numerically. Although generic functions have emerged which may estimate the parameters in these models, they remain opaque to many. From first principles we demonstrate how the maximum likelihood estimates for the parameters may be obtained using two methods based on Newton–Raphson iteration. The first uses the profile likelihood and the second uses the Observed Fisher Information. As convergence may depend on the proximity of the initial estimates to the global maximum, each algorithm includes a method for obtaining robust initial estimates. A simulation study was used to evaluate the algorithms and compare their performance with the generic generalised linear mixed model function glmer from the lme4 package in R before applying them to two meta-analyses from the literature. In general, the two algorithms had higher convergence rates and coverage probabilities than glmer. Based on its performance characteristics the method of profiling is recommended for fitting the bivariate generalised linear mixed model for meta-analysis.

scholarly journals Response transformations for random effect and variance component models

2020 ◽  
pp. 1471082X2096691
Author(s):  
Amani Almohaimeed ◽  
Jochen Einbeck
Keyword(s):  
Maximum Likelihood ◽  
Random Effects ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Random Effect ◽  
Statistical Technique ◽  
Response Distribution ◽  
Level Data ◽  
Variance Component Models ◽  
Response Transformation

Random effect models have been popularly used as a mainstream statistical technique over several decades; and the same can be said for response transformation models such as the Box–Cox transformation. The latter aims at ensuring that the assumptions of normality and of homoscedasticity of the response distribution are fulfilled, which are essential conditions for inference based on a linear model or a linear mixed model. However, methodology for response transformation and simultaneous inclusion of random effects has been developed and implemented only scarcely, and is so far restricted to Gaussian random effects. We develop such methodology, thereby not requiring parametric assumptions on the distribution of the random effects. This is achieved by extending the ‘Nonparametric Maximum Likelihood’ towards a ‘Nonparametric profile maximum likelihood’ technique, allowing to deal with overdispersion as well as two-level data scenarios.

scholarly journals PSVIII-10 Effects of enzyme supplementation in corn distiller’s dried grains with solubles (DDGS) diets on growth performance in broilers: a meta-analysis

2020 ◽  
Vol 98 (Supplement_3) ◽  
pp. 211-211
Author(s):  
Jae-Cheol Jang ◽  
Zhikai Zeng ◽  
Pedro E Urriola ◽  
Gerald C Shurson
Keyword(s):  
Growth Performance ◽  
Fixed Effects ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Meta Analysis ◽  
Growth Responses ◽  
Exogenous Enzymes ◽  
The Mean ◽  
Enzyme Supplementation ◽  
Mean Differences

Abstract The objective of this study was to conduct a meta-analysis to quantitatively summarize the growth responses of broilers fed cDDGS and the efficacy of various types of dietary enzyme supplementation. A total of 12 publications with 69 observations were included in the database. Individual observations were analyzed using a multivariable linear mixed model. The mean differences (MD) of BWG, FI, and gain efficiency (G/F) were calculated by subtracting either the enzyme response in corn-soybean meal (CSB) or CSB+cDDGS based diets to the control, and was expressed as a percentage (MD = (enzyme – control)/control ×100%). A type of exogenous enzymes (xylanase; protease; carbohydrases; cocktail = proteases + carbohydrases), and feeding phase (starter = d 0 to d 21; finisher = d 21 to d 42 or 49; overall = d 0 to d 42 or more) were included as fixed effects. Dietary enzyme inclusion showed significant improvement on BWG (3.19%, P < 0.01) and G/F (5.69%, P < 0.01) in broilers fed cDDGS diet. However, no significant enzyme responses were observed in broilers fed CSB diet on growth performance. Broilers fed cDDGS diet had increased (P < 0.01) BWG with the addition of protease (3.32 %) and cocktail (3.27 %), whereas addition of xylanased improved (P < 0.01) G/F by (3.56 %) and carbohydrases (1.90 %). Broilers fed cDDGS diet with enzyme supplementation showed greater improvement in BWG (3.71 %, P < 0.01) and G/F (3.78 %, P < 0.01) at finisher phase compared with starter phase. Likewise, Broilers fed CSB diet with enzyme supplementation increased BWG (9.40 %, P < 0.01) and G/F (3.11 %, P < 0.01) at finisher phase. In conclusion, supplementation of xylanase and carbohydrases in cDDGS diet improved G/F, and the enzyme response can be maximized when fed during the finisher phase diet compared with the starter phase diet.

scholarly journals Linear Mixed Models

2022 ◽  
pp. 141-170
Author(s):  
Osval Antonio Montesinos López ◽  
Abelardo Montesinos López ◽  
Jose Crossa
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Mixed Models ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Linear Mixed Models ◽  
Prediction Performance ◽  
Environment Interaction ◽  
Model Framework ◽  
Genotype Environment Interaction

AbstractThe linear mixed model framework is explained in detail in this chapter. We explore three methods of parameter estimation (maximum likelihood, EM algorithm, and REML) and illustrate how genomic-enabled predictions are performed under this framework. We illustrate the use of linear mixed models by using the predictor several components such as environments, genotypes, and genotype × environment interaction. Also, the linear mixed model is illustrated under a multi-trait framework that is important in the prediction performance when the degree of correlation between traits is moderate or large. We illustrate the use of single-trait and multi-trait linear mixed models and provide the R codes for performing the analyses.

Asymptotic Optimality of Restricted Maximum Likelihood Estimates for the Mixed Model

1979 ◽  
Vol 28 (1-4) ◽  
pp. 125-142 ◽  
Author(s):  
Kalyan Das
Keyword(s):  
Maximum Likelihood ◽  
Conceptual Design ◽  
Analysis Of Variance ◽  
Variance Components ◽  
Mixed Model ◽  
Asymptotic Optimality ◽  
Restricted Maximum Likelihood ◽  
Maximum Likelihood Estimates ◽  
Asymptotically Normal ◽  
Reasonable Sense

In this paper we study the asymptotic optimality of the restricted maximum likelihood estimates of variance components in the mixed model of analysis of variance. Using conceptual design sequences of Miller (1977), under slightly stronger conditions, we show that the restricted maximum likelihood estimates are not only asymptotically normal, but also asymptotically equivalent to the maximum likelihood estimates in a reasonable sense.

On the use of a penalized quasilikelihood information criterion for generalized linear mixed models

Biometrika ◽  
2020 ◽  
Author(s):  
Francis K C Hui
Keyword(s):  
Maximum Likelihood ◽  
Random Effects ◽  
Mixed Models ◽  
Mixed Model ◽  
Computation Time ◽  
Information Criterion ◽  
Information Criteria ◽  
Maximum Likelihood Estimates ◽  
Model Complexity ◽  
Fixed And Random Effects

Summary Information criteria are commonly used for joint fixed and random effects selection in mixed models. While information criteria are straightforward to implement, a major difficulty in applying them is that they are typically based on maximum likelihood estimates, but calculating such estimates for one candidate mixed model, let alone multiple models, presents a major computational challenge. To overcome this hurdle, we study penalized quasilikelihood estimation and use it as the basis for performing fast joint selection. Under a general framework, we show that penalized quasilikelihood estimation produces consistent estimates of the true parameters. We then propose a new penalized quasilikelihood information criterion whose distinguishing feature is the way it accounts for model complexity in the random effects, since penalized quasilikelihood estimation effectively treats the random effects as fixed. We demonstrate that the criterion asymptotically identifies the true set of important fixed and random effects. Simulations show that the quasilikelihood information criterion performs competitively with and sometimes better than common maximum likelihood information criteria for joint selection, while offering substantial reductions in computation time.

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