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.

Using empirical Bayes predictors from generalized linear mixed models to test and visualize associations among longitudinal outcomes

2018 ◽  
Vol 28 (5) ◽  
pp. 1399-1411 ◽  
Author(s):  
Susan K Mikulich-Gilbertson ◽  
Brandie D Wagner ◽  
Gary K Grunwald ◽  
Paula D Riggs ◽  
Gary O Zerbe
Keyword(s):  
Random Effects ◽  
Mixed Models ◽  
Empirical Bayes ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Maximum Likelihood Estimates ◽  
Parameter Estimates ◽  
P Values ◽  
Association Analyses ◽  
Second Stage

Medical research is often designed to investigate changes in a collection of response variables that are measured repeatedly on the same subjects. The multivariate generalized linear mixed model (MGLMM) can be used to evaluate random coefficient associations (e.g. simple correlations, partial regression coefficients) among outcomes that may be non-normal and differently distributed by specifying a multivariate normal distribution for their random effects and then evaluating the latent relationship between them. Empirical Bayes predictors are readily available for each subject from any mixed model and are observable and hence, plotable. Here, we evaluate whether second-stage association analyses of empirical Bayes predictors from a MGLMM, provide a good approximation and visual representation of these latent association analyses using medical examples and simulations. Additionally, we compare these results with association analyses of empirical Bayes predictors generated from separate mixed models for each outcome, a procedure that could circumvent computational problems that arise when the dimension of the joint covariance matrix of random effects is large and prohibits estimation of latent associations. As has been shown in other analytic contexts, the p-values for all second-stage coefficients that were determined by naively assuming normality of empirical Bayes predictors provide a good approximation to p-values determined via permutation analysis. Analyzing outcomes that are interrelated with separate models in the first stage and then associating the resulting empirical Bayes predictors in a second stage results in different mean and covariance parameter estimates from the maximum likelihood estimates generated by a MGLMM. The potential for erroneous inference from using results from these separate models increases as the magnitude of the association among the outcomes increases. Thus if computable, scatterplots of the conditionally independent empirical Bayes predictors from a MGLMM are always preferable to scatterplots of empirical Bayes predictors generated by separate models, unless the true association between outcomes is zero.

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 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 Mixed Models as a Tool for Comparing Groups of Time Series in Plant Sciences

Plants ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 362
Author(s):  
Ioannis Spyroglou ◽  
Jan Skalák ◽  
Veronika Balakhonova ◽  
Zuzana Benedikty ◽  
Alexandros G. Rigas ◽  
...  
Keyword(s):  
Time Series ◽  
Random Effects ◽  
Mixed Models ◽  
Mixed Model ◽  
Repeated Measurements ◽  
Time Series Models ◽  
Additional Time ◽  
Biotic Stresses ◽  
Viable Solution ◽  
Long Time

Plants adapt to continual changes in environmental conditions throughout their life spans. High-throughput phenotyping methods have been developed to noninvasively monitor the physiological responses to abiotic/biotic stresses on a scale spanning a long time, covering most of the vegetative and reproductive stages. However, some of the physiological events comprise almost immediate and very fast responses towards the changing environment which might be overlooked in long-term observations. Additionally, there are certain technical difficulties and restrictions in analyzing phenotyping data, especially when dealing with repeated measurements. In this study, a method for comparing means at different time points using generalized linear mixed models combined with classical time series models is presented. As an example, we use multiple chlorophyll time series measurements from different genotypes. The use of additional time series models as random effects is essential as the residuals of the initial mixed model may contain autocorrelations that bias the result. The nature of mixed models offers a viable solution as these can incorporate time series models for residuals as random effects. The results from analyzing chlorophyll content time series show that the autocorrelation is successfully eliminated from the residuals and incorporated into the final model. This allows the use of statistical inference.

Analysis of aggregation, a worked example: numbers of ticks on red grouse chicks

Parasitology ◽  
2001 ◽  
Vol 122 (5) ◽  
pp. 563-569 ◽  
Author(s):  
D. A. ELSTON ◽  
R. MOSS ◽  
T. BOULINIER ◽  
C. ARROWSMITH ◽  
X. LAMBIN
Keyword(s):  
Random Effects ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Negative Binomial ◽  
Generalized Linear Mixed Model ◽  
Red Grouse ◽  
Worked Example ◽  
Fixed And Random Effects ◽  
Individual Effects ◽  
Lagopus Lagopus Scoticus

The statistical aggregation of parasites among hosts is often described empirically by the negative binomial (Poisson-gamma) distribution. Alternatively, the Poisson-lognormal model can be used. This has the advantage that it can be fitted as a generalized linear mixed model, thereby quantifying the sources of aggregation in terms of both fixed and random effects. We give a worked example, assigning aggregation in the distribution of sheep ticksIxodes ricinuson red grouseLagopus lagopus scoticuschicks to temporal (year), spatial (altitude and location), brood and individual effects. Apparent aggregation among random individuals in random broods fell 8-fold when spatial and temporal effects had been accounted for.

scholarly journals The Impact of Misspecified Random Effect Distribution in a Weibull Regression Mixed Model

Stats ◽  
2018 ◽  
Vol 1 (1) ◽  
pp. 48-76
Author(s):  
Freddy Hernández ◽  
Viviana Giampaoli
Keyword(s):  
Weibull Distribution ◽  
Random Effects ◽  
Mixed Models ◽  
Fixed Effects ◽  
Mixed Model ◽  
Random Effect ◽  
Estimation Procedure ◽  
Weibull Regression ◽  
Two Parameters ◽  
The Impact

Mixed models are useful tools for analyzing clustered and longitudinal data. These models assume that random effects are normally distributed. However, this may be unrealistic or restrictive when representing information of the data. Several papers have been published to quantify the impacts of misspecification of the shape of the random effects in mixed models. Notably, these studies primarily concentrated their efforts on models with response variables that have normal, logistic and Poisson distributions, and the results were not conclusive. As such, we investigated the misspecification of the shape of the random effects in a Weibull regression mixed model with random intercepts in the two parameters of the Weibull distribution. Through an extensive simulation study considering six random effect distributions and assuming normality for the random effects in the estimation procedure, we found an impact of misspecification on the estimations of the fixed effects associated with the second parameter σ of the Weibull distribution. Additionally, the variance components of the model were also affected by the misspecification.

Maximum likelihood estimates of incorrect Markov models for time series and the derivation of AIC

1980 ◽  
Vol 17 (01) ◽  
pp. 59-72 ◽  
Author(s):  
Yosihiko Ogata
Keyword(s):  
Time Series ◽  
Asymptotic Behavior ◽  
Maximum Likelihood ◽  
Markov Models ◽  
Maximum Likelihood Estimators ◽  
Information Criterion ◽  
Parametric Family ◽  
Autoregressive Models ◽  
Maximum Likelihood Estimates ◽  
True Distribution

The asymptotic behavior of the maximum likelihood estimators of Markov models or autoregressive models are given when the true distribution is not a member of the assumed parametric family. The derivation of Akaike's Information Criterion is reviewed for this case.

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