A simple approach for the analysis of generalizea linear mixed models

Linear mixed model (LMM) approaches have been widely applied in many areas of research data analysis because they offer great flexibility for different data structures and linear model systems. In this study, emphasis is placed on comparing the properties of two LMM approaches: restricted maximum likelihood (REML) and minimum norm quadratic unbiased estimation (MINQUE) with and without resampling techniques being included. Bias, testing power, Type I error, and computing time were compared between REML and MINQUE approaches with and without Jackknife technique based on 500 simulated data sets. Results showed that MINQUE and REML methods performed equally regarding bias, Type I error, and power. Jackknife-based MINQUE and REML greatly improved power compared to non-Jackknife based linear mixed model approaches. Results also showed that MINQUE is more time-saving compared to REML, especially with the use of resampling techniques and large data set analysis. Results from the actual cotton data analysis were in agreement with our simulated results. Therefore, Jackknife-based MINQUE approaches could be recommended to achieve desirable power with reduced time for a large data analysis and model simulations.

This chapter describes the facilities for estimation of variance components and analysis of linear mixed models using the method of residual maximum likelihood (REML), sometimes also known as restricted maximum likelihood. The REML algorithm estimates the treatment effects and variance components in a linear mixed model: that is, a linear model with both fixed and random effects. Like regression, REML can be used to analyse unbalanced data sets; but, unlike regression, it can also account for more than one source of variation in the data, providing an estimate of the variance components associated with the random terms in the model.

In Chapter 3, regression-based methods to analyse longitudinal data are introduced. Linear mixed models analysis and linear GEE mixed model analysis are explained in detail, while the adjustment for covariance method is explained in less detail. It is shown that the different regression-based methods adjust for the correlated observations within the subject in a different way; linear mixed model analysis by allowing different regression coefficients for different subjects (i.e. random intercept and random slope(s)), GEE analysis by estimating directly the correlation between the repeated observations within the subject by assuming a priori a certain correlation structure. It is explained that a linear mixed model analysis with only a random intercept is basically the same as a linear GEE analysis with an exchangeable correlation structure. In this chapter, special attention is given to the interpretation of the regression coefficient, which is a weighted average of the between-subjects relationship and the within-subjects relationship. All methods are accompanied by extensive real-life data examples.

This paper proves that in mixed linear model, the analysis of variance estimation (ANOVAE), the minimum norm quadratic unbiased estimation (MINQUE), the spectral decomposition estimation (SDE) and the restricted maximum likelihood estimation (RMLE) of variance components are the same under some conditions. Based on this result, we construct a linear Bayes estimation (LBE) for the parameter vector consisting of variance components and establish its superiorities. Numerical computations and an illustration show that the LBE is comparable to Lindley's approximation, Tierney and Kadane's approximation and the usual Bayes estimation (UBE) obtained by the MCMC method and easy to use as well.

Computer simulation was used to compare minimum variance quadratic estimation (MIVQUE), minimum norm quadratic unbiased estimation (MINQUE), restricted maximum likelihood (REML), maximum likelihood (ML), and Henderson's Method 3 (HM3) on the basis of variance among estimates, mean square error (MSE), bias and probability of nearness for estimation of both individual variance components and three ratios of variance components. The investigation also compared three procedures for dealing with negative estimates and included the use of both individual observations and plot means as the experimental unit of the analysis. The structure of data simulated (field design, mating designs, genetic architecture and imbalance) represented typical analysis problems in quantitative forest genetics. Results of comparing the estimation techniques demonstrated that: estimates of probability of nearness did not discriminate among techniques; bias was discriminatory among procedures for dealing with negative estimates but not among estimation techniques (except ML); sampling variance among estimates was discriminatory among procedures for dealing with negative estimates, estimation techniques and unit of observation; and MSE provided no additional information to variance of the estimates. HM3 and REML were the closest competitors under these criteria; however, REML demonstrated greater robustness to imbalance. Of the three negative estimate procedures, two are of practical significance and guidelines for their application are presented. Estimates from individual observations were always preferable to those from plot means over the experimental levels of this study.

Summary - A method is described for the simultaneous estimation of variance components due to several genetic and environmental effects from unbalanced data by restricted maximum likelihood (REML). Estimates are obtained by evaluating the likelihood explicitly and using standard, derivative-free optimization procedures to locate its maximum. The model of analysis considered is the so-called Animal Model which includes the additive genetic merit of animals as a random effect, and incorporates all information on relationships between animals. Furthermore, random effects in addition to animals’ additive genetic effects, such as maternal genetic, dominance or permanent environmental effects are taken into account. Emphasis is placed entirely upon univariate analyses. Simulation is employed to investigate the efficacy of three different maximization techniques and the scope for approximation of sampling errors. Computations are illustrated with a numerical example. variance components - restricted maximum likelihood - animal model - additional random effects - derivative - free approach

Research has demonstrated erosion of empathy in students during medical education. Particularly, U.S. studies have demonstrated empathy declines during clinical training in the third and fourth year of traditional medical programs. Yet, studies conducted outside the U.S. have not confirmed this trend. Timing and extent of patient interactions have been identified as empathy-protective factors. The need to examine empathy within different learning contexts has been noted, as has the need for longitudinal and time-series research designs to analyze trajectories. Between fall 2010 and spring 2019, we assessed empathy longitudinally among six student cohorts (N = 493) at a U.S. medical school, where patient interaction occurs early and throughout an integrated curriculum. Empathy levels of students in each cohort were assessed at five time points utilizing the Jefferson Scale of Physician Empathy-Student version. We hypothesized empathy levels will not degrade by program end, and trajectories will not show patterns of decline in Years Three and Four. Analysis of Variance (ANOVA) and Linear Mixed Model (LMM) analyses were used to analyze differences at baseline and changes in empathy trajectories. ANOVA analyses revealed statistically significant differences at baseline by class cohort (F(5, 487) = [23.28], p < 0.001). LMM analyses indicated empathy was either significantly higher or not different at the end of the program (F(19, 1676) = [13.97], p < 0.001). Empathy trajectories varied among cohorts; yet, none resulted in an overall empathy decline by the end of the program. Findings demonstrate empathy in U.S. medical students can be unchanged or higher by the end of medical education. Outcomes are consistent with reports of non-declining medical student empathy outside the U.S. and support the notion of context-specificity. Results further support recent research, suggesting decreases in empathy during training can stabilize or increase by program end. These findings have important implications for future empathy research context and design considerations, as well as program planning.

Association mapping is an alternative to mapping in a biparental population. A key to successful association mapping is to avoid spurious associations by controlling for population structure. Confirming the marker/trait association in an independent population is necessary for the implementation of the marker in other genetic studies. Two independent soybean populations consisting of advanced breeding lines representing the diversity within maturity groups 00, 0, and I were screened in multi-site, replicated field trials to discover molecular markers associated with iron deficiency chlorosis (IDC), a major yield-limiting factor in soybean. Lines with extreme phenotypes were initially screened to identify simple sequence repeat (SSR) markers putatively associated with the IDC. Marker data collected from all lines were used to control for population structure and kinship relationships. Single factor analysis of variance (SFA) and mixed linear model (MLM) analyses were used to discover marker/trait associations. The MLM analyses, which include population structure, kinship or both factors, reduced the number of markers significantly associated with IDC by 50% compared with SFA. With the MLM approach, three markers were found to be associated with IDC in the first population. Two of these markers, Satt114 and Satt239, were also found to be associated with IDC in the second confirmation population. For both populations, those lines with the tolerance allele at both these two marker loci had significantly lower IDC scores than lines with one or no tolerant alleles.

On the effect of ignoring correlation in the covariates when fitting linear mixed models

McFadden, BA, Walker, AJ, Cintineo, HP, Bozzini, BN, Sanders, DJ, Chandler, AJ, and Arent, SM. Sex differences in physiological responses to a National Collegiate Athletic Association Division I soccer season. J Strength Cond Res 38(11): 1891-1899, 2024-Identifying physiological changes that occur in response to workload demands can help to elucidate athlete management and recovery strategies. The purpose of this study was to compare the physical and physiological demands between men and women throughout the course of a collegiate soccer season. Men ( N = 23) and women ( N = 26) soccer players participated in blood draws before preseason (T1) and every 4 weeks thereafter (T2-T4). Workload was determined at all practices and games via heart rate and global positioning satellite monitoring systems. Repeated measures multivariate analysis of variance and linear mixed models were used to assess workload and biomarker responses throughout the season ( p < 0.05). Both teams experienced the highest workloads during the first 4 weeks of the season ( p < 0.05), which was followed by several biomarker perturbations. Sex-by-Time interactions were observed for total cortisol, growth hormone, insulin-like growth factor-1, thyroxine, thyroid-stimulating hormone, vitamin D, and omega 3 fatty acid index ( p < 0.05). Additional Sex effects were observed for free and total testosterone, estrogen, prolactin, sex-hormone binding globulin, creatine kinase, and iron levels ( p < 0.05). Women soccer players experienced further Time effects for free cortisol, iron, ferritin, and percent transferrin saturation ( p < 0.05). Male soccer players experienced additional Time effects for total testosterone, estrogen, creatine kinase, interleukin-6, triiodothyronine, and ferritin ( p < 0.05). Despite similar patterns of change in workloads, differential fluctuations in physiological markers were observed between the sexes. Understanding sex differences in response to comparable workloads may enhance exercise prescriptions for better athlete management plans. Additional strategies to increase iron may be warranted in female athletes.

This paper presents a Bayesian analysis of linear mixed models for quantile regression using a modified Cholesky decomposition for the covariance matrix of random effects and an asymmetric Laplace distribution for the error distribution. We consider several novel Bayesian shrinkage approaches for both fixed and random effects in a linear mixed quantile model using extended penalties. To improve mixing of the Markov chains, a simple and efficient partially collapsed Gibbs sampling algorithm is developed for posterior inference. We also extend the framework to a Bayesian mixed expectile model and develop a Metropolis–Hastings acceptance–rejection (MHAR) algorithm using proposal densities based on iteratively weighted least squares estimation. The proposed approach is then illustrated via both simulated and real data examples. Results indicate that the proposed approach performs very well in comparison to the other approaches.

A genetic model was proposed to simultaneously investigate genetic effects of both polygenes and several single genes for quantitative traits of diploid plants and animals. Mixed linear model approaches were employed for statistical analysis. Based on two mating designs, a full diallel cross and a modified diallel cross including F(2), Monte Carlo simulations were conducted to evaluate the unbiasedness and efficiency of the estimation of generalized least squares (GLS) and ordinary least squares (OLS) for fixed effects and of minimum norm quadratic unbiased estimation (MINQUE) and Henderson III for variance components. Estimates of MINQUE (1) were unbiased and efficient in both reduced and full genetic models. Henderson III could have a large bias when used to analyze the full genetic model. Simulation results also showed that GLS and OLS were good methods to estimate fixed effects in the genetic models. Data on Drosophila melanogaster from Gilbert were used as a worked example to demonstrate the parameter estimation.

A simulation study was conducted to assess Type I error and statistical power of linear mixed models, generalized linear mixed models, and linear quantile mixed models for the analysis of longitudinal cytometry by time-of-flight data. Findings indicate that, while generalized linear mixed models have superior statistical power, they also suffer from inflated Type I error rates. Linear mixed models can have substantially lower statistical power than the other methods at larger effect sizes. While linear quantile mixed models have slightly lower statistical power at smaller effect sizes, they have intermediate statistical power at larger effect sizes and good Type I error control. Taken altogether, these results generally recommend the use of linear quantile mixed models for longitudinal datasets such as for cytometry by time-of-flight data, although linear mixed models may be slightly more useful at small effect sizes and sample sizes.

BackgroundFunctional decline associated with dementia, including in Alzheimer’s disease (AD), is not uniform across individuals, and respective heterogeneity is not yet fully explained. Such heterogeneity may in part be related to genetic variability among individuals. In this study, we investigated whether the SNP rs6859 in nectin cell adhesion molecule 2 (NECTIN2) gene (a major risk factor for AD) influences trajectories of cognitive decline in older participants from the Alzheimer’s Disease Neuroimaging Initiative (ADNI).MethodsWe retrospectively analyzed records on 1310 participants from the ADNI database for the multivariate analysis. We used longitudinal measures of Mini-Mental State Examination (MMSE) scores in participants, who were cognitively normal, or having AD, or other cognitive deficits to investigate the trajectories of cognitive changes. Multiple linear regression, linear mixed models and latent class analyses were conducted to investigate the association of the SNP rs6859 with MMSE.ResultsThe regression coefficient per one allele dose of the SNP rs6859 was independently associated with MMSE in both cross-sectional (-2.23, p < 0.01) and linear mixed models (-2.26, p < 0.01) analyses. The latent class model with three distinct subgroups (class 1: stable and gradual decline, class 2: intermediate and late decline, and class 3: lowest and irregular) performed best in the posterior classification, 42.67% (n = 559), 21.45% (n = 281), 35.88% (n = 470) were classified as class 1, class 2, and class 3. In the heterogeneous linear mixed model, the regression coefficient per one allele dose of rs6859 – A risk allele was significantly associated with MMSE class 1 and class 2 memberships and related decline; Class 1 (-2.28, 95% CI: -4.05, -0.50, p < 0.05), Class 2 (-5.56, 95% CI: -9.61, -1.51, p < 0.01) and Class 3 (-0.37, 95% CI: -1.62, 0.87, p = 0.55).ConclusionsThis study found statistical evidence supporting the classification of three latent subclass groups representing complex MMSE trajectories in the ADNI cohort. The SNP rs6859 can be suggested as a candidate genetic predictor of variation in modeling MMSE trajectory, as well as for identifying latent classes with higher baseline MMSE. Functional studies may help further elucidate this relationship.

Genetic variation in environmental sensitivity (ES) among breeds underscores the importance of accounting for genotype-by-environment (G×E) interactions in breeding programmes. This is especially true for countries where there is a large variation in location production systems and environmental conditions and where farms use crossbreeding. We present a systematic framework for assessing G×E by combining genomic reconstruction of an individual animal's breed composition with characterisation of production environment diversity, using factor analysis of mixed data (FAMD) and linear mixed models. Data from 288 farms in Ethiopia were analysed as a case study, which included weekly performance records, household parameters, daily meteorological data, and genotypes from 780 crossbred cows. To test G×E, the following context parameters were considered: agroecological zone (AEZ), market proximity, and farm size. Results showed that the best performances for milk yield (MY), age at first calving (AFC), and calf BW were generally observed on large, urban farms. However, MY, number of services per conception (NSC), and AFC improved with increasing exotic ancestry up to about 60%, beyond which these traits levelled off or declined. Antagonistic relationships among performance traits and their interactions with breed composition were also observed. While MY, calf BW, and AFC generally improved with increasing exotic ancestry, NSC was negatively affected by some ancestral breeds. Specifically, Holsteins exhibited consistently high NSC (3.52-4.66±1.12) across all AEZ and market proximities, highlighting a limitation of their use in crossbreeding strategies with respect to fertility. Our study demonstrates that breed-by-environment interactions can be assessed using field data and genotypes collected from crossbred animals in highly diverse production systems. However, the study design is inevitably unbalanced for breed composition, which limits the ability to assess the performance of breed combinations not well represented in the studied population.