scholarly journals Explicit Maximum Likelihood Estimates from Balanced Data in the Mixed Model of the Analysis of Variance

1980 ◽  
Vol 8 (4) ◽  
pp. 811-819 ◽  
Author(s):  
Ted H. Szatrowski ◽  
John J. Miller
Keyword(s):  
Maximum Likelihood ◽  
Analysis Of Variance ◽  
Mixed Model ◽  
Maximum Likelihood Estimates

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.

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 Linkage analysis with an alternative formulation for the mixed model of inheritance: the finite polygenic mixed model.

Genetics ◽  
1995 ◽  
Vol 141 (4) ◽  
pp. 1651-1656
Author(s):  
C Stricker ◽  
R L Fernando ◽  
R C Elston
Keyword(s):  
Maximum Likelihood ◽  
Linkage Analysis ◽  
Mixed Model ◽  
Efficient Algorithms ◽  
Maximum Likelihood Estimates ◽  
Alternative Formulation

Abstract This paper presents an extension of the finite polygenic mixed model of Fernando et al. (1994) to linkage analysis. The finite polygenic mixed model, extended for linkage analysis, leads to a likelihood that can be calculated using efficient algorithms developed for oligogenic models. For comparison, linkage analysis of 5 simulated 4021-member pedigrees was performed using the usual mixed model of inheritance, approximated by Hasstedt (1982), and the finite polygenic mixed model extended for linkage analysis presented here. Maximum likelihood estimates of the finite polygenic mixed model could be inferred to be closer to the simulated values in these pedigrees.

scholarly journals Maximum Likelihood Analysis of Rare Binary Traits Under Different Modes of Inheritance

Genetics ◽  
1996 ◽  
Vol 143 (4) ◽  
pp. 1819-1829 ◽  
Author(s):  
G Thaller ◽  
L Dempfle ◽  
I Hoeschele
Keyword(s):  
Maximum Likelihood ◽  
Mixed Model ◽  
Major Gene ◽  
Likelihood Ratio Statistic ◽  
Information Criterion ◽  
Genetic Models ◽  
Parameter Estimates ◽  
Gene Effects ◽  
Binary Traits ◽  
Deterministic Algorithms

Abstract Maximum likelihood methodology was applied to determine the mode of inheritance of rare binary traits with data structures typical for swine populations. The genetic models considered included a monogenic, a digenic, a polygenic, and three mixed polygenic and major gene models. The main emphasis was on the detection of major genes acting on a polygenic background. Deterministic algorithms were employed to integrate and maximize likelihoods. A simulation study was conducted to evaluate model selection and parameter estimation. Three designs were simulated that differed in the number of sires/number of dams within sires (10/10, 30/30, 100/30). Major gene effects of at least one SD of the liability were detected with satisfactory power under the mixed model of inheritance, except for the smallest design. Parameter estimates were empirically unbiased with acceptable standard errors, except for the smallest design, and allowed to distinguish clearly between the genetic models. Distributions of the likelihood ratio statistic were evaluated empirically, because asymptotic theory did not hold. For each simulation model, the Average Information Criterion was computed for all models of analysis. The model with the smallest value was chosen as the best model and was equal to the true model in almost every case studied.

scholarly journals Directional Selection and the Site-Frequency Spectrum

Genetics ◽  
2001 ◽  
Vol 159 (4) ◽  
pp. 1779-1788 ◽  
Author(s):  
Carlos D Bustamante ◽  
John Wakeley ◽  
Stanley Sawyer ◽  
Daniel L Hartl
Keyword(s):  
Maximum Likelihood ◽  
High Power ◽  
Negative Selection ◽  
Likelihood Estimation ◽  
Directional Selection ◽  
Likelihood Ratio Tests ◽  
Maximum Likelihood Estimates ◽  
Likelihood Methods ◽  
Ancestral States ◽  
Asymptotic Variances

Abstract In this article we explore statistical properties of the maximum-likelihood estimates (MLEs) of the selection and mutation parameters in a Poisson random field population genetics model of directional selection at DNA sites. We derive the asymptotic variances and covariance of the MLEs and explore the power of the likelihood ratio tests (LRT) of neutrality for varying levels of mutation and selection as well as the robustness of the LRT to deviations from the assumption of free recombination among sites. We also discuss the coverage of confidence intervals on the basis of two standard-likelihood methods. We find that the LRT has high power to detect deviations from neutrality and that the maximum-likelihood estimation performs very well when the ancestral states of all mutations in the sample are known. When the ancestral states are not known, the test has high power to detect deviations from neutrality for negative selection but not for positive selection. We also find that the LRT is not robust to deviations from the assumption of independence among sites.

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