Mixed Effects Models

2021 ◽  
pp. 209-234
Author(s):  
Justin C. Touchon
Keyword(s):  
Likelihood Ratio ◽  
Data Structures ◽  
Mixed Models ◽  
Repeated Measures ◽  
Generalized Linear Mixed Models ◽  
Statistical Significance ◽  
Linear Mixed Models ◽  
Mixed Effects ◽  
Likelihood Ratio Tests ◽  
Mixed Effects Models

Mixed effects models are powerful techniques for controlling for non-independence of data or repeated measures, and can be harnessed for both normal and non-normal data structures. Chapter 8 teaches readers how to code, assess, interpret, and troubleshoot both linear and generalized linear mixed models using the same RxP dataset which has been used throughout the book, although now it is viewed through a new lens. Readers are taught how to code likelihood ratio tests to calculate statistical significance and how to use multiple packages, such as lme4 and glmmTMB.

scholarly journals Report Quality of Generalized Linear Mixed Models in Psychology: A Systematic Review

2021 ◽  
Vol 12 ◽  
Author(s):  
Roser Bono ◽  
Rafael Alarcón ◽  
María J. Blanca
Keyword(s):  
Systematic Review ◽  
Mixed Models ◽  
Repeated Measures ◽  
Web Of Science ◽  
Generalized Linear Mixed Models ◽  
Linear Mixed Models ◽  
Journal Citation Reports ◽  
Report Quality ◽  
Fixed And Random Effects

Generalized linear mixed models (GLMMs) estimate fixed and random effects and are especially useful when the dependent variable is binary, ordinal, count or quantitative but not normally distributed. They are also useful when the dependent variable involves repeated measures, since GLMMs can model autocorrelation. This study aimed to determine how and how often GLMMs are used in psychology and to summarize how the information about them is presented in published articles. Our focus in this respect was mainly on frequentist models. In order to review studies applying GLMMs in psychology we searched the Web of Science for articles published over the period 2014–2018. A total of 316 empirical articles were selected for trend study from 2014 to 2018. We then conducted a systematic review of 118 GLMM analyses from 80 empirical articles indexed in Journal Citation Reports during 2018 in order to evaluate report quality. Results showed that the use of GLMMs increased over time and that 86.4% of articles were published in first- or second-quartile journals. Although GLMMs have, in recent years, been increasingly used in psychology, most of the important information about them was not stated in the majority of articles. Report quality needs to be improved in line with current recommendations for the use of GLMMs.

On estimating and testing associations between random coefficients from multivariate generalized linear mixed models of longitudinal outcomes

2015 ◽  
Vol 26 (3) ◽  
pp. 1130-1145 ◽  
Author(s):  
Susan K Mikulich-Gilbertson ◽  
Brandie D Wagner ◽  
Paula D Riggs ◽  
Gary O Zerbe
Keyword(s):  
Likelihood Ratio ◽  
Mixed Models ◽  
Generalized Linear Mixed Models ◽  
Mathematical Proof ◽  
Linear Mixed Models ◽  
Delta Method ◽  
Standard Errors ◽  
Ratio Test ◽  
Type I ◽  
Time Lags

Different types of outcomes (e.g. binary, count, continuous) can be simultaneously modeled with multivariate generalized linear mixed models by assuming: (1) same or different link functions, (2) same or different conditional distributions, and (3) conditional independence given random subject effects. Others have used this approach for determining simple associations between subject-specific parameters (e.g. correlations between slopes). We demonstrate how more complex associations (e.g. partial regression coefficients between slopes adjusting for intercepts, time lags of maximum correlation) can be estimated. Reparameterizing the model to directly estimate coefficients allows us to compare standard errors based on the inverse of the Hessian matrix with more usual standard errors approximated by the delta method; a mathematical proof demonstrates their equivalence when the gradient vector approaches zero. Reparameterization also allows us to evaluate significance of coefficients with likelihood ratio tests and to compare this approach with more usual Wald-type t-tests and Fisher’s z transformations. Simulations indicate that the delta method and inverse Hessian standard errors are nearly equivalent and consistently overestimate the true standard error. Only the likelihood ratio test based on the reparameterized model has an acceptable type I error rate and is therefore recommended for testing associations between stochastic parameters. Online supplementary materials include our medical data example, annotated code, and simulation details.

Local Influence to Detect Influential Data Structures for Generalized Linear Mixed Models

Biometrics ◽  
2001 ◽  
Vol 57 (4) ◽  
pp. 1166-1172 ◽  
Author(s):  
Mario J. N. M. Ouwens ◽  
Frans E. S. Tan ◽  
Martijn P. F. Berger
Keyword(s):  
Data Structures ◽  
Mixed Models ◽  
Generalized Linear Mixed Models ◽  
Linear Mixed Models ◽  
Local Influence

scholarly journals High performance implementation of the hierarchical likelihood for generalized linear mixed models: an application to estimate the potassium reference range in massive electronic health records datasets

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Cristian G. Bologa ◽  
Vernon Shane Pankratz ◽  
Mark L. Unruh ◽  
Maria Eleni Roumelioti ◽  
Vallabh Shah ◽  
...  
Keyword(s):  
Real World ◽  
Mixed Models ◽  
Repeated Measures ◽  
High Performance ◽  
Generalized Linear Mixed Models ◽  
Linear Mixed Models ◽  
Care Facility ◽  
Hierarchical Likelihood ◽  
Electronic Health ◽  
Direct Implementation

Abstract Background Converting electronic health record (EHR) entries to useful clinical inferences requires one to address the poor scalability of existing implementations of Generalized Linear Mixed Models (GLMM) for repeated measures. The major computational bottleneck concerns the numerical evaluation of multivariable integrals, which even for the simplest EHR analyses may involve millions of dimensions (one for each patient). The hierarchical likelihood (h-lik) approach to GLMMs is a methodologically rigorous framework for the estimation of GLMMs that is based on the Laplace Approximation (LA), which replaces integration with numerical optimization, and thus scales very well with dimensionality. Methods We present a high-performance, direct implementation of the h-lik for GLMMs in the R package TMB. Using this approach, we examined the relation of repeated serum potassium measurements and survival in the Cerner Real World Data (CRWD) EHR database. Analyzing this data requires the evaluation of an integral in over 3 million dimensions, putting this problem beyond the reach of conventional approaches. We also assessed the scalability and accuracy of LA in smaller samples of 1 and 10% size of the full dataset that were analyzed via the a) original, interconnected Generalized Linear Models (iGLM), approach to h-lik, b) Adaptive Gaussian Hermite (AGH) and c) the gold standard for multivariate integration Markov Chain Monte Carlo (MCMC). Results Random effects estimates generated by the LA were within 10% of the values obtained by the iGLMs, AGH and MCMC techniques. The H-lik approach was 4–30 times faster than AGH and nearly 800 times faster than MCMC. The major clinical inferences in this problem are the establishment of the non-linear relationship between the potassium level and the risk of mortality, as well as estimates of the individual and health care facility sources of variations for mortality risk in CRWD. Conclusions We found that the direct implementation of the h-lik offers a computationally efficient, numerically accurate approach for the analysis of extremely large, real world repeated measures data via the h-lik approach to GLMMs. The clinical inference from our analysis may guide choices of treatment thresholds for treating potassium disorders in the clinic.

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