A three-level mixed-effects location scale model with an application to ecological momentary assessment data

A Mixed-Effects Model in Which the Parameters of the Autocorrelated Error Structure Can Differ between Individuals

Research in psychology has seen a rapid increase in the usage of experience sampling methods and daily diary methods. The data that result from using these methods are typically analyzed with a mixed-effects or a multilevel model because it allows testing hypotheses about the time course of the longitudinally assessed variable or the influence of time-varying predictors in a simple way. Here, we describe an extension of this model that does not only allow to include random effects for the mean structure but also for the residual variance, for the parameter of an autoregressive process of order 1 and/or the parameter of a moving average process of order 1. After we have introduced this extension, we show how to estimate the parameters with maximum likelihood. Because the likelihood function contains complex integrals, we suggest using adaptive Gauss-Hermite quadrature and Quasi-Monte Carlo integration to approximate it. We illustrate the models using a real data example and also report the results of a small simulation study in which the two integral approximation methods are compared.

Detecting influential subjects in intensive longitudinal data using mixed-effects location scale models

BACKGROUND

Collection of intensive longitudinal health outcomes allows joint modeling of their mean (location) and variability (scale). Focusing on the location of the outcome, measures to detect influential subjects in longitudinal data using standard mixed-effects regression models (MRMs) have been widely discussed. However, no existing approach enables the detection of subjects that heavily influence the scale of the outcome.

METHODS

We propose applying mixed-effects location scale (MELS) modeling combined with commonly used influence measures such as Cook's distance and DFBETAS to fill this gap. In this paper, we provide a framework for researchers to follow when trying to detect influential subjects for both the scale and location of the outcome. The framework allows detailed examination of each subject's influence on model fit as well as point estimates and precision of coefficients in different components of a MELS model.

RESULTS

We simulated two common scenarios in longitudinal healthcare studies and found that influence measures in our framework successfully capture influential subjects over 99% of the time. We also re-analyzed data from a health behavior study and found 4 particularly influential subjects, among which two cannot be detected by influence analyses via regular MRMs.

CONCLUSION

The proposed framework can help researchers detect influential subject(s) that will be otherwise overlooked by influential analysis using regular MRMs and analyze all data in one model despite influential subjects.

The Reliability Factor: Modeling Individual Reliability with Multiple Items from a Single Assessment

Reliability is a crucial concept in psychometrics. Although it is typically estimated as a single fixed quantity, previous work suggests that reliability can vary across persons, groups, and covariates. We propose a novel method for estimating and modeling case-specific reliability without repeated measurements or parallel tests. The proposed method employs a "Reliability Factor" that models the error variance of each case across multiple indicators, thereby producing case-specific reliability estimates. Additionally, we use Gaussian process modeling to estimate a nonlinear, non-monotonic function between the latent factor itself and the reliability of the measure, providing an analogue to test information functions in item response theory. The reliability factor model is a new tool for examining latent regions with poor conditional reliability, and correlates thereof, in a classical test theory framework.

Zero-augmented beta-prime model for multilevel semi-continuous data: a Bayesian inference

Semi-continuous data characterized by an excessive proportion of zeros and right-skewed continuous positive values appear frequently in medical research. One example would be the pharmaceutical expenditure (PE) data for which a substantial proportion of subjects investigated may report zero. Two-part mixed-effects models have been developed to analyse clustered measures of semi-continuous data from multilevel studies. In this study, we propose a new flexible two-part mixed-effects model with skew distributions for nested semi-continuous cost data under the framework of a Bayesian approach. The proposed model specification consists of two mixed-effects models linked by the correlated random effects: Part I) a model on the occurrence of positive values using a generalized logistic mixed model; and Part II) a model on the magnitude of positive values using a linear mixed model where the model errors follow skew distributions including beta-prime (BP). The proposed method is illustrated with pharmaceutical expenditure data from a multilevel observational study and the analytic results are reported by comparing potential models under different skew distributions. Simulation studies are conducted to assess the performance of the proposed model. The DIC₃, LPML, WAIC, and LOO as the Bayesian model selection criteria and measures of divergence used to compare the models.

Location-scale models for meta-analysis

Heterogeneity is commonplace in meta-analysis. When heterogeneity is found, researchers often aim to identify predictors that account for at least part of such heterogeneity by using mixed-effects meta-regression models. Another potentially relevant goal is to focus on the amount of heterogeneity as a function of one or more predictors, but this cannot be examined with standard random- and mixed-effects models, which assume a constant (i.e., homoscedastic) value for the heterogeneity variance component across studies. In this paper, we describe a location-scale model for meta-analysis as an extension of the standard random- and mixed-effects models that not only allows an examination of whether predictors are related to the size of the outcomes (i.e., their location), but also the amount of heterogeneity (i.e., their scale). We present estimation methods for such a location-scale model through maximum and restricted maximum likelihood approaches, as well as methods for inference and suggestions for visualization. We also provide an implementation via the metafor package for R that makes this model readily available to researchers. Location-scale models can provide a useful tool to researchers interested in heterogeneity in meta-analysis, with the potential to enhance the scope of research questions in the field of evidence synthesis.

Catching Up on Multilevel Modeling

This review focuses on the use of multilevel models in psychology and other social sciences. We target readers who are catching up on current best practices and sources of controversy in the specification of multilevel models. We first describe common use cases for clustered, longitudinal, and cross-classified designs, as well as their combinations. Using examples from both clustered and longitudinal designs, we then address issues of centering for observed predictor variables: its use in creating interpretable fixed and random effects of predictors, its relationship to endogeneity problems (correlations between predictors and model error terms), and its translation into multivariate multilevel models (using latent-centering within multilevel structural equation models). Finally, we describe novel extensions—mixed-effects location–scale models—designed for predicting differential amounts of variability.

An extension of the mixed-effects growth model that considers between-person differences in the within-subject variance and the autocorrelation

Experience sampling methods have led to a significant increase in the availability of intensive longitudinal data. Typically, this type of data is analyzed with a mixed-effects model that allows to examine hypotheses concerning between-person differences in the mean structure by including multiple random effects per individual (eg, random intercept and random slopes). Here, we describe an extension of this model that-in addition to the random effects for the mean structure-also includes a random effect for the within-subject variance and a random effect for the autocorrelation. After the description of the model, we show how its parameters can be efficiently estimated using a marginal maximum likelihood (ML) approach. We then illustrate the model using a real data example. We also present the results of a small simulation study in which we compare the ML approach with a Bayesian estimation approach.

Diet, Nutrition, Obesity, and Their Implications for COVID-19 Mortality: Development of a Marginalized Two-Part Model for Semicontinuous Data

Background

Nutrition is not a treatment for COVID-19, but it is a modifiable contributor to the development of chronic disease, which is highly associated with COVID-19 severe illness and deaths. A well-balanced diet and healthy patterns of eating strengthen the immune system, improve immunometabolism, and reduce the risk of chronic disease and infectious diseases.

Objective

This study aims to assess the effect of diet, nutrition, obesity, and their implications for COVID-19 mortality among 188 countries by using new statistical marginalized two-part models.

Methods

We globally evaluated the distribution of diet and nutrition at the national level while considering the variations between different World Health Organization regions. The effects of food supply categories and obesity on (as well as associations with) the number of deaths and the number of recoveries were reported globally by estimating coefficients and conducting color maps.

Results

The findings show that a 1% increase in supplementation of pulses reduced the odds of having a zero death by 4-fold (OR 4.12, 95% CI 11.97-1.42). In addition, a 1% increase in supplementation of animal products and meat increased the odds of having a zero death by 1.076-fold (OR 1.076, 95% CI 1.01-1.15) and 1.13-fold (OR 1.13, 95% CI 1.0-1.28), respectively. Tree nuts reduced the odds of having a zero death, and vegetables increased the number of deaths. Globally, the results also showed that populations (countries) who consume more eggs, cereals excluding beer, spices, and stimulants had the greatest impact on the recovery of patients with COVID-19. In addition, populations that consume more meat, vegetal products, sugar and sweeteners, sugar crops, animal fats, and animal products were associated with more death and less recoveries in patients. The effect of consuming sugar products on mortality was considerable, and obesity has affected increased death rates and reduced recovery rates.

Conclusions

Although there are differences in dietary patterns, overall, unbalanced diets are a health threat across the world and not only affect death rates but also the quality of life. To achieve the best results in preventing nutrition-related pandemic diseases, strategies and policies should fully recognize the essential role of both diet and obesity in determining good nutrition and optimal health. Policies and programs must address the need for change at the individual level and make modifications in society and the environment to make healthier choices accessible and preferable.

Modelling inter-individual differences in latent within-person variation: The confirmatory factor level variability model

Psychological theories often produce hypotheses that pertain to individual differences in within-person variability. To empirically test the predictions entailed by such hypotheses with longitudinal data, researchers often use multilevel approaches that allow them to model between-person differences in the mean level of a certain variable and the residual within-person variance. Currently, these approaches can be applied only when the data stem from a single variable. However, it is common practice in psychology to assess not just a single measure but rather several measures of a construct. In this paper we describe a model in which we combine the single-indicator model with confirmatory factor analysis. The new model allows individual differences in latent mean-level factors and latent within-person variability factors to be estimated. Furthermore, we show how the model's parameters can be estimated with a maximum likelihood estimator, and we illustrate the approach using an example that involves intensive longitudinal data.

Bayesian Multivariate Mixed-Effects Location Scale Modeling of Longitudinal Relations Among Affective Traits, States, and Physical Activity

Intensive longitudinal studies and experience sampling methods are becoming more common in psychology. While they provide a unique opportunity to ask novel questions about within-person processes relating to personality, there is a lack of methods specifically built to characterize the interplay between traits and states. We thus introduce a Bayesian multivariate mixed-effects location scale model (M-MELSM). The formulation can simultaneously model both personality traits (the location) and states (the scale) for multivariate data common to personality research. Variables can be included to predict either (or both) the traits and states, in addition to estimating random effects therein. This provides correlations between location and scale random effects, both across and within each outcome, which allows for characterizing relations between any number of personality traits and the corresponding states. We take a fully Bayesian approach, not only to make estimation possible, but also because it provides the necessary information for use in psychological applications such as hypothesis testing. To illustrate the model we use data from 194 individuals that provided daily ratings of negative and positive affect, as well as their physical activity in the form of step counts over 100 consecutive days. We describe the fitted model, where we emphasize, with visualization, the richness of information provided by the M-MELSM. We demonstrate Bayesian hypothesis testing for the correlations between the random effects. We conclude by discussing limitations of the MELSM in general and extensions to the M-MELSM specifically for personality research.

Extending the mixed‐effects model to consider within‐subject variance for Ecological Momentary Assessment data

Ecological Momentary Assessment data present some new modeling opportunities. Typically, there are sufficient data to explicitly model the within-subject (WS) variance, and in many applications, it is of interest to allow the WS variance to depend on covariates as well as random subject effects. We describe a model that allows multiple random effects per subject in the mean model (eg, random location intercept and slopes), as well as random scale in the error variance model. We present an example of the use of this model on a real dataset and a simulation study that shows the benefit of this model, relative to simpler approaches.

Detecting Consensus Emergence in Organizational Multilevel Data: Power Simulations

Theories suggest that groups within organizations often develop shared values, beliefs, affect, behaviors, or agreed-on routines; however, researchers rarely study predictors of consensus emergence over time. Recently, a multilevel-methods approach for detecting and studying emergence in organizational field data has been described. This approach—the consensus emergence model—builds on an extended three-level multilevel model. Researchers planning future studies based on the consensus emergence model need to consider (a) sample size characteristics required to detect emergence effects with satisfactory statistical power and (b) how the distribution of the overall sample size across the levels of the multilevel model influences power. We systematically address both issues by conducting a power simulation for detecting main and moderating effects involving consensus emergence under a variety of typical research scenarios and provide an R-based tool that readers can use to estimate power. Our discussion focuses on the future use and development of multilevel methods for studying emergence in organizational research.

Using Bi-Weekly Surveys to Portray Adolescent Partnership Dynamics: Lessons From a Mobile Diary Study

Partnership formation is an important developmental task for adolescents, but cross-sectional and periodic longitudinal studies have lacked the measurement precision to portray partnership stability and flux and to capture the range of adolescent partnership experiences. This article assesses the promises and challenges of using bi-weekly mobile diaries administered over the course of a year to study adolescent partnership dynamics. Descriptive findings illustrate the potential of bi-weekly diaries for both capturing the longitudinal complexity and fluidity of adolescent partnerships as well as for reducing retrospection biases. Results also underscore several challenges, including those posed by missing data, and highlight several strategies for maximizing participant engagement and reliably tracing adolescent partnerships.

A mixed-effects location scale model for time-to-event data: A smoking behavior application

In general, mixed-effects location scale models (MELS) allow assessment of within-person and between-person variability with time-to-event data for outcomes that follow a normal or ordinal distribution. In this article, we extend the mixed-effects location scale model to time-to-event data in relation to smoking data. Better understanding of the time-graded within-person variability of factors involved in nicotine dependence can be helpful to researchers in their efforts to fine-tune smoking cessation programs. We illustrate the MELS model with data on time to first cigarette measured every day for 7 days in smokers randomized to two groups: a) those asked to keep smoking, or b) those asked to stop. Our results show that some individuals remain very stable in their time to first cigarette over the week, while others show variable patterns. The stable individuals smoked every day, did not smoke immediately upon waking, and were all in the group asked to keep smoking. Conversely, the variable individuals had at least one day during which they did not smoke, other days during which they smoked within the first 5 min of waking, and they were almost all in the group asked to quit smoking. These findings suggested that MELS have the potential to provide insights on how people try to stop smoking. More importantly, this model can be applied to other clinically important outcomes such as time to relapse in a range of cessation programs.

Growth Curves for Headache Research: A Multilevel Modeling Perspective

OBJECTIVE

To introduce growth curve modeling for longitudinal headache research.

BACKGROUND

Longitudinal data play an important role in the study of headache-related outcomes by allowing researchers to test hypotheses about change over time. However, headache researchers are often unfamiliar with the flexibility and power that growth curves can offer in analyzing longitudinal data. The goals of this paper are to introduce growth curve models within the multilevel modeling framework for analyzing longitudinal headache-related data and to show how these models can be applied in practice.

METHODS

Longitudinal data for the empirical example came from publicly available data from Wave I to Wave IV of the National Longitudinal Study of Adolescent to Adult Health. In total, 5608 individuals were included in the study and multilevel models were fit to examine, for individuals with and without adolescent migraine, longitudinal changes in depression from age 13 to 27 years old.

RESULTS

Findings showed that individuals varied in their longitudinal depression trajectories. A cubic time trend best approximated the data with depression increasing through adolescence, decreasing during young adulthood, and then beginning to increase again in adulthood. Further, results also indicated that individuals with adolescent migraine had higher levels of depression throughout the age span compared those without adolescent migraine, but the shape of change did not differ across the groups.

CONCLUSION

Growth curve models offer a flexible alternative to traditional statistical methods and can rigorously evaluate a wide array of headache-related hypotheses.

Multilevel Analysis of Individual, Organizational, and Regional Factors Associated With Patient Safety Culture: A Cross-Sectional Study of Maternal and Child Health Institutions in China

Supplemental digital content is available in the text.

The aim of this study was to assess patient safety culture (PSC) in maternal and child health (MCH) institutions in China and its individual, organizational, and regional variations.

Modeling Intraindividual Variability in Three-Level Multilevel Models

Abstract. The mixed-effects location scale model is an extension of a multilevel model for longitudinal data. It allows covariates to affect both the within-subject variance and the between-subject variance (i.e., the intercept variance) beyond their influence on the means. Typically, the model is applied to two-level data (e.g., the repeated measurements of persons), although researchers are often faced with three-level data (e.g., the repeated measurements of persons within specific situations). Here, we describe an extension of the two-level mixed-effects location scale model to such three-level data. Furthermore, we show how the suggested model can be estimated with Bayesian software, and we present the results of a small simulation study that was conducted to investigate the statistical properties of the suggested approach. Finally, we illustrate the approach by presenting an example from a psychological study that employed ecological momentary assessment.

Leveling up the analysis of the reminiscence bump in autobiographical memory: A new approach based on multilevel multinomial models

In many studies of autobiographical memory, participants are asked to generate more than one autobiographical memory. The resulting data then have a hierarchical or multilevel structure, in the sense that the autobiographical memories (Level 1) generated by the same person (Level 2) tend to be more similar. Transferred to an analysis of the reminiscence bump in autobiographical memory, at Level 1 the prediction of whether an autobiographical memory will fall within the reminiscence bump is based on the characteristics of that memory. At Level 2, the prediction of whether an individual will report more autobiographical memories that fall in the reminiscence bump is based on the characteristics of the individual. We suggest a multilevel multinomial model that allows for analyzing whether an autobiographical memory falls in the reminiscence bump at both levels of analysis simultaneously. The data come from 100 older participants who reported up to 33 autobiographical memories. Our results showed that about 12% of the total variance was between persons (Level 2). Moreover, at Level 1, memories of first-time experiences were more likely to fall in the reminiscence bump than were emotionally more positive memories. At Level 2, persons who reported more emotionally positive memories tended to report fewer memories from the life period after the reminiscence bump. In addition, cross-level interactions showed that the effects at Level 1 partly depended on the Level 2 effects. We discuss possible extensions of the model we present and the meaning of our findings for two prominent explanatory approaches to the reminiscence bump, as well as future directions.

A 3-level Bayesian mixed effects location scale model with an application to ecological momentary assessment data

Ecological momentary assessment studies usually produce intensively measured longitudinal data with large numbers of observations per unit, and research interest is often centered around understanding the changes in variation of people's thoughts, emotions and behaviors. Hedeker et al developed a 2-level mixed effects location scale model that allows observed covariates as well as unobserved variables to influence both the mean and the within-subjects variance, for a 2-level data structure where observations are nested within subjects. In some ecological momentary assessment studies, subjects are measured at multiple waves, and within each wave, subjects are measured over time. Li and Hedeker extended the original 2-level model to a 3-level data structure where observations are nested within days and days are then nested within subjects, by including a random location and scale intercept at the intermediate wave level. However, the 3-level random intercept model assumes constant response change rate for both the mean and variance. To account for changes in variance across waves, as well as clustering attributable to waves, we propose a more comprehensive location scale model that allows subject heterogeneity at baseline as well as across different waves, for a 3-level data structure where observations are nested within waves and waves are then further nested within subjects. The model parameters are estimated using Markov chain Monte Carlo methods. We provide details on the Bayesian estimation approach and demonstrate how the Stan statistical software can be used to sample from the desired distributions and achieve consistent estimates. The proposed model is validated via a series of simulation studies. Data from an adolescent smoking study are analyzed to demonstrate this approach. The analyses clearly favor the proposed model and show significant subject heterogeneity at baseline as well as change over time, for both mood mean and variance. The proposed 3-level location scale model can be widely applied to areas of research where the interest lies in the consistency in addition to the mean level of the responses.

Bayesian inference on mixed-effects location scale models with skew-t distribution and mismeasured covariates for longitudinal data

In AIDS studies, heterogeneous between and within subject variations are often observed on longitudinal endpoints. To accommodate heteroscedasticity in the longitudinal data, statistical methods have been developed to model the mean and variance jointly. Most of these methods assume (conditional) normal distributions for random errors, which is not realistic in practice. In this article, we propose a Bayesian mixed-effects location scale model with skew-t distribution and mismeasured covariates for heterogeneous longitudinal data with skewness. The proposed model captures the between-subject and within-subject (WS) heterogeneity by modeling the between-subject and WS variations with covariates as well as a random effect at subject level in the WS variance. Further, the proposed model also takes into account the covariate measurement errors, and commonly assumed normal distributions for model errors are substituted by skew-t distribution to account for skewness. Parameter estimation is carried out in a Bayesian framework. The proposed method is illustrated with a Multicenter AIDS Cohort Study. Simulation studies are performed to assess the performance of the proposed method. Copyright © 2017 John Wiley & Sons, Ltd.

Mixed-effects location and scale Tobit joint models for heterogeneous longitudinal data with skewness, detection limits, and measurement errors

The joint modeling of mean and variance for longitudinal data is an active research area. This type of model has the advantage of accounting for heteroscedasticity commonly observed in between and within subject variations. Most of researches focus on improving the estimating efficiency but ignore many data features frequently encountered in practice. In this article, we develop a mixed-effects location scale joint model that concurrently accounts for longitudinal data with multiple features. Specifically, our joint model handles heterogeneity, skewness, limit of detection, measurement errors in covariates which are typically observed in the collection of longitudinal data from many studies. We employ a Bayesian approach for making inference on the joint model. The proposed model and method are applied to an AIDS study. Simulation studies are performed to assess the performance of the proposed method. Alternative models under different conditions are compared.

From Heterogeneity to Concentration: Latino Immigrant Neighborhoods and Collective Efficacy Perceptions in Los Angeles and Chicago

Latino immigrant presence in urban neighborhoods has been linked with reduced neighborhood cohesion in social disorganization-based ethnic heterogeneity hypotheses and enhanced cohesion in immigration revitalization approaches. Using the 2000-2002 Los Angeles Family and Neighborhood Survey and the 1994-1995 Project on Human Development in Chicago Neighborhoods Community Survey, we explore the association between Latino immigrant concentration and both levels of, and agreement about, neighborhood collective efficacy. Findings from multilevel models with heteroskedastic variance indicate that Latino immigrant concentration exhibits a nonlinear association with collective efficacy. At low levels, increases in Latino immigrant concentration diminish collective efficacy, consistent with a heterogeneity hypothesis. The negative association between Latino immigrant concentration and collective efficacy declines in magnitude as immigrant concentration increases and, particularly in LA, becomes positive beyond a threshold, consistent with an immigration revitalization effect. We also find an inverse nonlinear pattern of association with the variance of collective efficacy. At low levels, increasing Latino immigrant concentration increases the variance of collective efficacy (reflecting more disagreement), but beyond a threshold, this association becomes negative (reflecting increasing agreement). This pattern is observed in both LA and Chicago. The prevalence of social interaction and reciprocated exchange within neighborhoods explains a modest proportion of the Latino immigrant concentration effect on mean levels of collective efficacy in Chicago, but does little to explain effects on the mean in LA or effects on the variance in either LA or Chicago. These findings offer insight into the complex role Latino immigrant presence plays in shaping neighborhood social climate.

Intra-Individual Variability of Physical Activity in Older Adults With and Without Mild Alzheimer's Disease

Physical activity shows promise for protection against cognitive decline in older adults with and without Alzheimer's disease (AD). To better understand barriers to adoption of physical activity in this population, a clear understanding of daily and weekly activity patterns is needed. Most accelerometry studies report average physical activity over an entire wear period without considering the potential importance of the variability of physical activity. This study evaluated individual differences in the amount and intra-individual variability of physical activity and determined whether these differences could be predicted by AD status, day of wear, age, gender, education, and cardiorespiratory capacity. Physical activity was measured via accelerometry (Actigraph GT3X+) over one week in 86 older adults with and without AD (n = 33 and n = 53, respectively). Mixed-effects location-scale models were estimated to evaluate and predict individual differences in the amount and intra-individual variability of physical activity. Results indicated that compared to controls, participants with AD averaged 21% less activity, but averaged non-significantly greater intra-individual variability. Women and men averaged similar amounts of physical activity, but women were significantly less variable. The amount of physical activity differed significantly across days of wear. Increased cardiorespiratory capacity was associated with greater average amounts of physical activity. Investigation of individual differences in the amount and intra-individual variability of physical activity provided insight into differences by AD status, days of monitor wear, gender, and cardiovascular capacity. All individuals regardless of AD status were equally consistent in their physical activity, which may have been due to a highly sedentary sample and/or the early disease stage of those participants with AD. These results highlight the value of considering individual differences in both the amount and intra-individual variability of physical activity.

Bayesian mixed-effects location and scale models for multivariate longitudinal outcomes: an application to ecological momentary assessment data

In the statistical literature, the methods to understand the relationship of explanatory variables on each individual outcome variable are well developed and widely applied. However, in most health-related studies given the technological advancement and sophisticated methods of obtaining and storing data, a need to perform joint analysis of multivariate outcomes while explaining the impact of predictors simultaneously and accounting for all the correlations is in high demand. In this manuscript, we propose a generalized approach within a Bayesian framework that models the changes in the variation in terms of explanatory variables and captures the correlations between the multivariate continuous outcomes by the inclusion of random effects at both the location and scale levels. We describe the use of a spherical transformation for the correlations between the random location and scale effects in order to apply separation strategy for prior elicitation while ensuring positive semi-definiteness of the covariance matrix. We present the details of our approach using an example from an ecological momentary assessment study on adolescents.

MIXREGLS: A Program for Mixed-Effects Location Scale Analysis

MIXREGLS is a program which provides estimates for a mixed-effects location scale model assuming a (conditionally) normally-distributed dependent variable. This model can be used for analysis of data in which subjects may be measured at many observations and interest is in modeling the mean and variance structure. In terms of the variance structure, covariates can by specified to have effects on both the between-subject and within-subject variances. Another use is for clustered data in which subjects are nested within clusters (e.g., clinics, hospitals, schools, etc.) and interest is in modeling the between-cluster and within-cluster variances in terms of covariates. MIXREGLS was written in Fortran and uses maximum likelihood estimation, utilizing both the EM algorithm and a Newton-Raphson solution. Estimation of the random effects is accomplished using empirical Bayes methods. Examples illustrating stand-alone usage and features of MIXREGLS are provided, as well as use via the SAS and R software packages.