Beyond fight or flight: The protective role of pre-pandemic meditation practice against anxiety and perceived stress.

The COVID-19 pandemic generated distinct mental health challenges, characterised by stress and anxiety due to its unpredictable duration and continuous threat. This study examined the role of meditation practice on anxiety symptoms and perceived stress, considering co-variables such as self-compassion, acceptance, awareness, brooding, lockdown duration, and sociodemographic characteristics. The study used a longitudinal design and data were collected through online surveys from April 2020 to January 2021 (at four different time points) and included 238 participants from Portugal (165 had prior experience with meditation practices, 73 were non-meditators) with a mean age of 43.08 years (SD = 10.96). Linear mixed models revealed that over time, during the lockdown, the non-meditators group demonstrated a greater increase of anxiety symptoms (ß = -0.226, SE = 0.06, p = 0.006) and perceived stress (ß = -0.20, SE = 0.06, p = 0.004), whereas the meditators group showed non-significant (p > 0.05) variations in anxiety and stress symptoms during the same period of time. The effect of meditation on anxiety symptoms was moderated by sex, days of lockdown, self-compassion, and acceptance. The effect of meditation on perceived stress was moderated by sex, years of education, days of lockdown, and levels of awareness. Additionally, the study explored the potential predictive effect of different meditation session lengths, indicating that longer meditation practices offered greater protection against an increase in anxiety symptoms. These findings highlight the importance of cultivating self-regulation skills and investing in preventive mental health strategies to promote well-being and autonomy. Mental health professionals should prioritise educating communities on evidence-based practices like meditation and compassion exercises to enhance overall health.

The Benefits of Permutation-Based Genome-Wide Association Studies.

Linear mixed models (LMMs) are a commonly used method for genome-wide association studies (GWAS) that aim to detect associations between genetic markers and phenotypic measurements in a population of individuals while accounting for population structure and cryptic relatedness. In a standard GWAS, hundreds of thousands to millions of statistical tests are performed, requiring control for multiple hypothesis testing. Typically, static corrections that penalize the number of tests performed are used to control for the family-wise error rate, which is the probability of making at least one false positive. However, it has been shown that in practice this threshold is too conservative for normally distributed phenotypes and not stringent enough for non-normally distributed phenotypes. Therefore, permutation-based LMM approaches have recently been proposed to provide a more realistic threshold that takes phenotypic distributions into account. In this work, we will discuss the advantages of permutation-based GWAS approaches, including new simulations and results from a re-analysis of all publicly available Arabidopsis thaliana phenotypes from the AraPheno database.

Joint models reveal genetic architecture of pubertal stage transitions and their association with BMI in admixed Chilean population.

Early or late pubertal onset can lead to disease in adulthood, including cancer, obesity, type 2 diabetes, metabolic disorders, bone fractures, and psychopathologies. Thus, knowing the age at which puberty is attained is crucial as it can serve as a risk factor for future diseases. Pubertal development is divided into five stages of sexual maturation in boys and girls according to the standardized Tanner scale. We performed genome-wide association studies (GWAS) on the "Growth and Obesity Chilean Cohort Study" cohort composed of admixed children with mainly European and Native American ancestry. Using joint models that integrate time-to-event data with longitudinal trajectories of body mass index (BMI), we identified genetic variants associated with phenotypic transitions between pairs of Tanner stages. We identified $42$ novel significant associations, most of them in boys. The GWAS on Tanner $3\rightarrow 4$ transition in boys captured an association peak around the growth-related genes LARS2 and LIMD1 genes, the former of which causes ovarian dysfunction when mutated. The associated variants are expression and splicing Quantitative Trait Loci regulating gene expression and alternative splicing in multiple tissues. Further, higher individual Native American genetic ancestry proportions predicted a significantly earlier puberty onset in boys but not in girls. Finally, the joint models identified a longitudinal BMI parameter significantly associated with several Tanner stages' transitions, confirming the association of BMI with pubertal timing.

Model selection of GLMMs in the analysis of count data in single-case studies: A Monte Carlo simulation.

Generalized linear mixed models (GLMMs) have great potential to deal with count data in single-case experimental designs (SCEDs). However, applied researchers have faced challenges in making various statistical decisions when using such advanced statistical techniques in their own research. This study focused on a critical issue by investigating the selection of an appropriate distribution to handle different types of count data in SCEDs due to overdispersion and/or zero-inflation. To achieve this, I proposed two model selection frameworks, one based on calculating information criteria (AIC and BIC) and another based on utilizing a multistage-model selection procedure. Four data scenarios were simulated including Poisson, negative binominal (NB), zero-inflated Poisson (ZIP), and zero-inflated negative binomial (ZINB). The same set of models (i.e., Poisson, NB, ZIP, and ZINB) were fitted for each scenario. In the simulation, I evaluated 10 model selection strategies within the two frameworks by assessing the model selection bias and its consequences on the accuracy of the treatment effect estimates and inferential statistics. Based on the simulation results and previous work, I provide recommendations regarding which model selection methods should be adopted in different scenarios. The implications, limitations, and future research directions are also discussed.

Exploring the Interplay between the Hologenome and Complex Traits in Bovine and Porcine Animals Using Genome-Wide Association Analysis.

Genome-wide association studies (GWAS) significantly enhance our ability to identify trait-associated genomic variants by considering the host genome. Moreover, the hologenome refers to the host organism's collective genetic material and its associated microbiome. In this study, we utilized the hologenome framework, called Hologenome-wide association studies (HWAS), to dissect the architecture of complex traits, including milk yield, methane emissions, rumen physiology in cattle, and gut microbial composition in pigs. We employed four statistical models: (1) GWAS, (2) Microbial GWAS (M-GWAS), (3) HWAS-CG (hologenome interaction estimated using COvariance between Random Effects Genome-based restricted maximum likelihood (CORE-GREML)), and (4) HWAS-H (hologenome interaction estimated using the Hadamard product method). We applied Bonferroni correction to interpret the significant associations in the complex traits. The GWAS and M-GWAS detected one and sixteen significant SNPs for milk yield traits, respectively, whereas the HWAS-CG and HWAS-H each identified eight SNPs. Moreover, HWAS-CG revealed four, and the remaining models identified three SNPs each for methane emissions traits. The GWAS and HWAS-CG detected one and three SNPs for rumen physiology traits, respectively. For the pigs' gut microbial composition traits, the GWAS, M-GWAS, HWAS-CG, and HWAS-H identified 14, 16, 13, and 12 SNPs, respectively. We further explored these associations through SNP annotation and by analyzing biological processes and functional pathways. Additionally, we integrated our GWA results with expression quantitative trait locus (eQTL) data using transcriptome-wide association studies (TWAS) and summary-based Mendelian randomization (SMR) methods for a more comprehensive understanding of SNP-trait associations. Our study revealed hologenomic variability in agriculturally important traits, enhancing our understanding of host-microbiome interactions.

The perspective of the logarithmic field sprayer technology.

A logarithmic sprayer was suggested about 70 years ago, but it has not yet been seriously used in research and development, and subsequent registration of plant protection products. Logarithmic sprayers have resorted to mere demonstration experiments to show end users and others how plant protection products work. Fitting dose-response curves in field experiments, however, generates much essential information, e.g., extraction of various effective field rate levels (e.g., ED20, ED50, and ED80). One of the reasons for it rarely being used in the registration of plant protection products is that the dose-response curve regression was hitherto difficult to fit; the registration requirement solely focuses on analyses of variance. Another alleged obstacle is that the logarithmic plots have systematically, not randomly distributed field rates. This paper goes through some of the problems of how to non-randomly analyze field rates by taking autocorrelation into account to make the logarithmic sprayer palatable as registration documentation by assessing efficacy, selectivity, environmental side effects, general toxicity of plant protection products, and cost-effectiveness. The development in precision agriculture, drone technology, and automation of data capture and subsequent analysis could make the logarithmic sprayer a cost-effective alternative to numerous ANOVA experiments with very few fixed field rates to aid the precision spraying of pesticides and thus reduce unnecessary environmental side effects. © 2024 Society of Chemical Industry.

Ice phenology interactions with water and air temperatures in high mountain lakes.

Ice phenology is of great importance for the thermal structure of lakes and ponds and the biology of lake species. Under the current climate change conditions, ice-cover duration has been reduced by an advance in ice-off, and a delay in ice-on, and future projections foresee this trend as continuing. Here, we describe the current ice phenology of Pyrenean high mountain lakes and ponds, including ice-cover duration and ice-on and ice-off dates. We used mixed models to identify the variables that explained the observed patterns, extrapolated them across all water bodies in the mountain range, and related the seasonality of air and water temperatures with ice phenology using structural equation models. Ice phenology was obtained from the temperature series of 85 lakes and ponds for fourteen years, including 2001 to 2004 and 2009 to 2019. We discovered that high autumn precipitation was related to earlier ice-on dates, and that earlier ice-off dates were associated with higher following-summer water temperatures. We found a greater predictability of ice-off dates and ice-cover duration than ice-on dates. Altitude was the most important variable explaining the variation in ice phenology, followed by latitude, which was related to climatic differences among the northern and southern slopes of the mountain range. The lake area was significant for ice-on dates and ice-cover duration. The interannual variability in air temperature and radiation was remarkable for the ice-off date and ice-cover duration but not for the ice-on date. In contrast, wind speed was related to an earlier ice-off date and shorter ice-cover duration. All the measured lakes and ponds froze in winter during the studied period, a feature maintained in the extrapolation to the whole set of water bodies.

Linear modeling of zonal level crop production in Ethiopia.

Accounting for zonal-level variations and identifying factors that have linear effects on crop production help to make better decisions and plan new policies for effective crop production and food security. The main objective of this study is to identify potential subsets of covariates and estimate their linear effects on crop production. A linear mixed effects model (random--intercept) is used on agricultural sample survey data for Meher seasons from 2012/13 to 2019/20 to explore and identify the best variance-covariance structure for the longitudinal data on 90 zones with eight repeated observations and different sampling weights. The minimum, mean, and maximum crop production by farmers across the country are 1.616, 8.693, and 147.843 quintals, respectively, and about 98 % of farmers produced less than 25 quintals. There is a small rate of increase in mean and median crop production by farmers across the years, and the variability between zones is highest in the year 2019/20 and in the Somali region. The histogram, kernel density, and P-P plots suggested a common logarithm transformation on the crop production variable. Results from the data exploration and variance-covariance structure selection methods suggested a heterogeneous compound symmetry (CSH) structure. Covariates region, year, proportion of farmers who practice pure-agriculture and other-agriculture types, proportion of farmers who use any type of fertilizer, farmer's age, area used, farmer association crop production, indigenous seed used, improved seed used, UREA fertilizer used, other fertilizers used, and percentage of crop damaged are significant in linearly explaining/affecting log crop production, and among these area used, farmers association crop production, UREA fertilizer used, and indigenous seed used have relatively highest effect on log crop production. Zones Wolayita, North-Shewa (Am), West-Arsi, West-Welega, Dawro, and Guji are top/good performers while zones Southwest-Shewa, Waghimra, Guraghe, South-Omo, Keffa, North-Wello, South-Wello, and Eastern Tigray are bottom/poor performers in crop production. Model assumptions and influence diagnostics results suggested the linearity of the model and normality of random effects and residuals are not violated, even though some zones have influences on either model parameters, precisions of estimates of these parameters, and predicted values.

A cautionary tale on the effects of different covariance structures in linear mixed effects modeling of fMRI data.

With the steadily increasing abundance of longitudinal neuroimaging studies with large sample sizes and multiple repeated measures, questions arise regarding the appropriate modeling of variance and covariance. The current study examined the influence of standard classes of variance-covariance structures in linear mixed effects (LME) modeling of fMRI data from patients with pediatric mild traumatic brain injury (pmTBI; N = 181) and healthy controls (N = 162). During two visits, participants performed a cognitive control fMRI paradigm that compared congruent and incongruent stimuli. The hemodynamic response function was parsed into peak and late peak phases. Data were analyzed with a 4-way (GROUP×VISIT×CONGRUENCY×PHASE) LME using AFNI's 3dLME and compound symmetry (CS), autoregressive process of order 1 (AR1), and unstructured (UN) variance-covariance matrices. Voxel-wise results dramatically varied both within the cognitive control network (UN>CS for CONGRUENCY effect) and broader brain regions (CS>UN for GROUP:VISIT) depending on the variance-covariance matrix that was selected. Additional testing indicated that both model fit and estimated standard error were superior for the UN matrix, likely as a result of the modeling of individual terms. In summary, current findings suggest that the interpretation of results from complex designs is highly dependent on the selection of the variance-covariance structure using LME modeling.

An evaluation of computational methods for aggregate data meta-analyses of diagnostic test accuracy studies.

BACKGROUND: A Generalized Linear Mixed Model (GLMM) is recommended to meta-analyze diagnostic test accuracy studies (DTAs) based on aggregate or individual participant data. Since a GLMM does not have a closed-form likelihood function or parameter solutions, computational methods are conventionally used to approximate the likelihoods and obtain parameter estimates. The most commonly used computational methods are the Iteratively Reweighted Least Squares (IRLS), the Laplace approximation (LA), and the Adaptive Gauss-Hermite quadrature (AGHQ). Despite being widely used, it has not been clear how these computational methods compare and perform in the context of an aggregate data meta-analysis (ADMA) of DTAs. METHODS: We compared and evaluated the performance of three commonly used computational methods for GLMM - the IRLS, the LA, and the AGHQ, via a comprehensive simulation study and real-life data examples, in the context of an ADMA of DTAs. By varying several parameters in our simulations, we assessed the performance of the three methods in terms of bias, root mean squared error, confidence interval (CI) width, coverage of the 95% CI, convergence rate, and computational speed. RESULTS: For most of the scenarios, especially when the meta-analytic data were not sparse (i.e., there were no or negligible studies with perfect diagnosis), the three computational methods were comparable for the estimation of sensitivity and specificity. However, the LA had the largest bias and root mean squared error for pooled sensitivity and specificity when the meta-analytic data were sparse. Moreover, the AGHQ took a longer computational time to converge relative to the other two methods, although it had the best convergence rate. CONCLUSIONS: We recommend practitioners and researchers carefully choose an appropriate computational algorithm when fitting a GLMM to an ADMA of DTAs. We do not recommend the LA for sparse meta-analytic data sets. However, either the AGHQ or the IRLS can be used regardless of the characteristics of the meta-analytic data.

The effectiveness of an online short-format Recovery College model: a co-learning model to support mental health.

BACKGROUND: Our societies are facing mental health challenges, which have been compounded by the Covid-19. This event led people to isolate themselves and to stop seeking the help they needed. In response to this situation, the Health and Recovery Learning Center, applying the Recovery College (RC) model, modified its training program to a shorter online format. This study examines the effectiveness of a single RC training course delivered in a shortened online format to a diverse population at risk of mental health deterioration in the context of Covid-19. METHODS: This quasi-experimental study used a one-group pretest-posttest design with repeated measures. Three hundred and fifteen (n = 315) learners agreed to take part in the study and completed questionnaires on wellbeing, anxiety, resilience, self-management, empowerment and stigmatizing attitudes and behaviors. RESULTS: Analyses of variance using a linear mixed models revealed that attending a RC training course had, over time, a statistically significant effect on wellbeing (p = 0.004), anxiety (p < 0.001), self-esteem/self-efficacy (p = 0.005), disclosure/help-seeking (p < 0.001) and a slight effect on resilience (p = 0.019) and optimism/control over the future (p = 0.01). CONCLUSIONS: This study is the first to measure participation in a single online short-format RC training course, with a diversity of learners and a large sample. These results support the hypothesis that an online short-format training course can reduce psychological distress and increase self-efficacy and help-seeking. TRIAL REGISTRATION: This study was previously approved by two certified ethics committees: Comité d'éthique de la recherche du CIUSSS EMTL, which acted as the committee responsible for the multicenter study, reference number MP-12-2021-2421, and Comité d'éthique avec les êtres humains de l'UQTR, reference number CER-20-270-07.01.

Novel non-linear models for clinical trial analysis with longitudinal data: A tutorial using SAS for both frequentist and Bayesian methods.

Longitudinal data from clinical trials are commonly analyzed using mixed models for repeated measures (MMRM) when the time variable is categorical or linear mixed-effects models (ie, random effects model) when the time variable is continuous. In these models, statistical inference is typically based on the absolute difference in the adjusted mean change (for categorical time) or the rate of change (for continuous time). Previously, we proposed a novel approach: modeling the percentage reduction in disease progression associated with the treatment relative to the placebo decline using proportional models. This concept of proportionality provides an innovative and flexible method for simultaneously modeling different cohorts, multivariate endpoints, and jointly modeling continuous and survival endpoints. Through simulated data, we demonstrate the implementation of these models using SAS procedures in both frequentist and Bayesian approaches. Additionally, we introduce a novel method for implementing MMRM models (ie, analysis of response profile) using the nlmixed procedure.

Negative variance components and intercept-slope correlations greater than one in magnitude: How do such "non-regular" random intercept and slope models arise, and what should be done when they do?

Statistical models with random intercepts and slopes (RIAS models) are commonly used to analyze longitudinal data. Fitting such models sometimes results in negative estimates of variance components or estimates on parameter space boundaries. This can be an unlucky chance occurrence, but can also occur because certain marginal distributions are mathematically identical to those from RIAS models with negative intercept and/or slope variance components and/or intercept-slope correlations greater than one in magnitude. We term such parameters "pseudo-variances" and "pseudo-correlations," and the models "non-regular." We use eigenvalue theory to explore how and when such non-regular RIAS models arise, showing: (i) A small number of measurements, short follow-up, and large residual variance increase the parameter space for which data (with a positive semidefinite marginal variance-covariance matrix) are compatible with non-regular RIAS models. (ii) Non-regular RIAS models can arise from model misspecification, when non-linearity in fixed effects is ignored or when random effects are omitted. (iii) A non-regular RIAS model can sometimes be interpreted as a regular linear mixed model with one or more additional random effects, which may not be identifiable from the data. (iv) Particular parameterizations of non-regular RIAS models have no generality for all possible numbers of measurements over time. Because of this lack of generality, we conclude that non-regular RIAS models can only be regarded as plausible data-generating mechanisms in some situations. Nevertheless, fitting a non-regular RIAS model can be acceptable, allowing unbiased inference on fixed effects where commonly recommended alternatives such as dropping the random slope result in bias.

Measurement error models with zero inflation and multiple sources of zeros, with applications to hard zeros.

We consider measurement error models for two variables observed repeatedly and subject to measurement error. One variable is continuous, while the other variable is a mixture of continuous and zero measurements. This second variable has two sources of zeros. The first source is episodic zeros, wherein some of the measurements for an individual may be zero and others positive. The second source is hard zeros, i.e., some individuals will always report zero. An example is the consumption of alcohol from alcoholic beverages: some individuals consume alcoholic beverages episodically, while others never consume alcoholic beverages. However, with a small number of repeat measurements from individuals, it is not possible to determine those who are episodic zeros and those who are hard zeros. We develop a new measurement error model for this problem, and use Bayesian methods to fit it. Simulations and data analyses are used to illustrate our methods. Extensions to parametric models and survival analysis are discussed briefly.

Lifestyle-related factors in late midlife as predictors of frailty from late midlife into old age: a longitudinal birth cohort study.

BACKGROUND: Few studies have examined longitudinal changes in lifestyle-related factors and frailty. METHODS: We examined the association between individual lifestyle factors (exercise, diet, sleep, alcohol, smoking and body composition), their sum at baseline, their change over the 17-year follow-up and the rate of change in frailty index values using linear mixed models in a cohort of 2,000 participants aged 57-69 years at baseline. RESULTS: A higher number of healthy lifestyle-related factors at baseline was associated with lower levels of frailty but not with its rate of change from late midlife into old age. Participants who stopped exercising regularly (adjusted ß × Time = 0.19, 95%CI = 0.10, 0.27) and who began experiencing sleeping difficulties (adjusted ß × Time = 0.20, 95%CI = 0.10, 0.31) experienced more rapid increases in frailty from late midlife into old age. Conversely, those whose sleep improved (adjusted ß × Time = -0.10, 95%CI = -0.23, -0.01) showed a slower increase in frailty from late midlife onwards. Participants letting go of lifestyle-related factors (decline by 3+ factors vs. no change) became more frail faster from late midlife into old age (adjusted ß × Time = 0.16, 95% CI = 0.01, 0.30). CONCLUSIONS: Lifestyle-related differences in frailty were already evident in late midlife and persisted into old age. Adopting one new healthy lifestyle-related factor had a small impact on a slightly less steeply increasing level of frailty. Maintaining regular exercise and sleeping habits may help prevent more rapid increases in frailty.

The effective sample size in Bayesian information criterion for level-specific fixed and random-effect selection in a two-level nested model.

Popular statistical software provides the Bayesian information criterion (BIC) for multi-level models or linear mixed models. However, it has been observed that the combination of statistical literature and software documentation has led to discrepancies in the formulas of the BIC and uncertainties as to the proper use of the BIC in selecting a multi-level model with respect to level-specific fixed and random effects. These discrepancies and uncertainties result from different specifications of sample size in the BIC's penalty term for multi-level models. In this study, we derive the BIC's penalty term for level-specific fixed- and random-effect selection in a two-level nested design. In this new version of BIC, called BIC E 1 , this penalty term is decomposed into two parts if the random-effect variance-covariance matrix has full rank: (a) a term with the log of average sample size per cluster and (b) the total number of parameters times the log of the total number of clusters. Furthermore, we derive the new version of BIC, called BIC E 2 , in the presence of redundant random effects. We show that the derived formulae, BIC E 1 and BIC E 2 , adhere to empirical values via numerical demonstration and that BIC E ( E indicating either E 1 or E 2 ) is the best global selection criterion, as it performs at least as well as BIC with the total sample size and BIC with the number of clusters across various multi-level conditions through a simulation study. In addition, the use of BIC E 1 is illustrated with a textbook example dataset.

FieldSimR: an R package for simulating plot data in multi-environment field trials.

This paper presents a general framework for simulating plot data in multi-environment field trials with one or more traits. The framework is embedded within the R package FieldSimR, whose core function generates plot errors that capture global field trend, local plot variation, and extraneous variation at a user-defined ratio. FieldSimR's capacity to simulate realistic plot data makes it a flexible and powerful tool for a wide range of improvement processes in plant breeding, such as the optimisation of experimental designs and statistical analyses of multi-environment field trials. FieldSimR provides crucial functionality that is currently missing in other software for simulating plant breeding programmes and is available on CRAN. The paper includes an example simulation of field trials that evaluate 100 maize hybrids for two traits in three environments. To demonstrate FieldSimR's value as an optimisation tool, the simulated data set is then used to compare several popular spatial models for their ability to accurately predict the hybrids' genetic values and reliably estimate the variance parameters of interest. FieldSimR has broader applications to simulating data in other agricultural trials, such as glasshouse experiments.

Mixed models for repetitive measurements: the basics.

Linear mixed models are regularly used within the field of reproductive medicine. This manuscript explains the basics of mixed models, when they could be used, and how they could be applied.

Flexible Bayesian semiparametric mixed-effects model for skewed longitudinal data.

BACKGROUND: In clinical trials and epidemiological research, mixed-effects models are commonly used to examine population-level and subject-specific trajectories of biomarkers over time. Despite their increasing popularity and application, the specification of these models necessitates a great deal of care when analysing longitudinal data with non-linear patterns and asymmetry. Parametric (linear) mixed-effect models may not capture these complexities flexibly and adequately. Additionally, assuming a Gaussian distribution for random effects and/or model errors may be overly restrictive, as it lacks robustness against deviations from symmetry. METHODS: This paper presents a semiparametric mixed-effects model with flexible distributions for complex longitudinal data in the Bayesian paradigm. The non-linear time effect on the longitudinal response was modelled using a spline approach. The multivariate skew-t distribution, which is a more flexible distribution, is utilized to relax the normality assumptions associated with both random-effects and model errors. RESULTS: To assess the effectiveness of the proposed methods in various model settings, simulation studies were conducted. We then applied these models on chronic kidney disease (CKD) data and assessed the relationship between covariates and estimated glomerular filtration rate (eGFR). First, we compared the proposed semiparametric partially linear mixed-effect (SPPLM) model with the fully parametric one (FPLM), and the results indicated that the SPPLM model outperformed the FPLM model. We then further compared four different SPPLM models, each assuming different distributions for the random effects and model errors. The model with a skew-t distribution exhibited a superior fit to the CKD data compared to the Gaussian model. The findings from the application revealed that hypertension, diabetes, and follow-up time had a substantial association with kidney function, specifically leading to a decrease in GFR estimates. CONCLUSIONS: The application and simulation studies have demonstrated that our work has made a significant contribution towards a more robust and adaptable methodology for modeling intricate longitudinal data. We achieved this by proposing a semiparametric Bayesian modeling approach with a spline smoothing function and a skew-t distribution.

Multivariate probit linear mixed models for multivariate longitudinal binary data.

When analyzing multivariate longitudinal binary data, we estimate the effects on the responses of the covariates while accounting for three types of complex correlations present in the data. These include the correlations within separate responses over time, cross-correlations between different responses at different times, and correlations between different responses at each time point. The number of parameters thus increases quadratically with the dimension of the correlation matrix, making parameter estimation difficult; the estimated correlation matrix must also meet the positive definiteness constraint. The correlation matrix may additionally be heteroscedastic; however, the matrix structure is commonly considered to be homoscedastic and constrained, such as exchangeable or autoregressive with order one. These assumptions are overly strong, resulting in skewed estimates of the covariate effects on the responses. Hence, we propose probit linear mixed models for multivariate longitudinal binary data, where the correlation matrix is estimated using hypersphere decomposition instead of the strong assumptions noted above. Simulations and real examples are used to demonstrate the proposed methods. An open source R package, BayesMGLM, is made available on GitHub at https://github.com/kuojunglee/BayesMGLM/ with full documentation to produce the results.