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Linear Mixed Models: A Practical Guide Using Statistical Software
22 Nov 2006-
TL;DR: The Implied Marginal Variance-Covariance Matrix for the Final Model Diagnostics for theFinal Model Software Notes and Recommendations Other Analytic Approaches Recommendations.
Abstract: INTRODUCTION What Are Linear Mixed Models (LMMs)? A Brief History of Linear Mixed Models LINEAR MIXED MODELS: AN OVERVIEW Introduction Specification of LMMs The Marginal Linear Model Estimation in LMMs Computational Issues Tools for Model Selection Model-Building Strategies Checking Model Assumptions (Diagnostics) Other Aspects of LMMs Power Analysis for Linear Mixed Models Chapter Summary TWO-LEVEL MODELS FOR CLUSTERED DATA: THE RAT PUP EXAMPLE Introduction The Rat Pup Study Overview of the Rat Pup Data Analysis Analysis Steps in the Software Procedures Results of Hypothesis Tests Comparing Results across the Software Procedures Interpreting Parameter Estimates in the Final Model Estimating the Intraclass Correlation Coefficients (ICCs) Calculating Predicted Values Diagnostics for the Final Model Software Notes and Recommendations THREE-LEVEL MODELS FOR CLUSTERED DATA THE CLASSROOM EXAMPLE Introduction The Classroom Study Overview of the Classroom Data Analysis Analysis Steps in the Software Procedures Results of Hypothesis Tests Comparing Results across the Software Procedures Interpreting Parameter Estimates in the Final Model Estimating the Intraclass Correlation Coefficients (ICCs) Calculating Predicted Values Diagnostics for the Final Model Software Notes Recommendations MODELS FOR REPEATED-MEASURES DATA: THE RAT BRAIN EXAMPLE Introduction The Rat Brain Study Overview of the Rat Brain Data Analysis Analysis Steps in the Software Procedures Results of Hypothesis Tests Comparing Results across the Software Procedures Interpreting Parameter Estimates in the Final Model The Implied Marginal Variance-Covariance Matrix for the Final Model Diagnostics for the Final Model Software Notes Other Analytic Approaches Recommendations RANDOM COEFFICIENT MODELS FOR LONGITUDINAL DATA: THE AUTISM EXAMPLE Introduction The Autism Study Overview of the Autism Data Analysis Analysis Steps in the Software Procedures Results of Hypothesis Tests Comparing Results across the Software Procedures Interpreting Parameter Estimates in the Final Model Calculating Predicted Values Diagnostics for the Final Model Software Note: Computational Problems with the D Matrix An Alternative Approach: Fitting the Marginal Model with an Unstructured Covariance Matrix MODELS FOR CLUSTERED LONGITUDINAL DATA: THE DENTAL VENEER EXAMPLE Introduction The Dental Veneer Study Overview of the Dental Veneer Data Analysis Analysis Steps in the Software Procedures Results of Hypothesis Tests Comparing Results across the Software Procedures Interpreting Parameter Estimates in the Final Model The Implied Marginal Variance-Covariance Matrix for the Final Model Diagnostics for the Final Model Software Notes and Recommendations Other Analytic Approaches MODELS FOR DATA WITH CROSSED RANDOM FACTORS: THE SAT SCORE EXAMPLE Introduction The SAT Score Study Overview of the SAT Score Data Analysis Analysis Steps in the Software Procedures Results of Hypothesis Tests Comparing Results across the Software Procedures Interpreting Parameter Estimates in the Final Model The Implied Marginal Variance-Covariance Matrix for the Final Model Recommended Diagnostics for the Final Model Software Notes and Additional Recommendations APPENDIX A: STATISTICAL SOFTWARE RESOURCES APPENDIX B: CALCULATION OF THE MARGINAL VARIANCE-COVARIANCE MATRIX APPENDIX C: ACRONYMS/ABBREVIATIONS BIBLIOGRAPHY INDEX
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TL;DR: In this article, the authors provide an introduction to mixed-effects models for the analysis of repeated measurement data with subjects and items as crossed random effects, and a worked-out example of how to use recent software for mixed effects modeling is provided.
6,853 citations
Cites background or methods from "Linear Mixed Models: A Practical Gu..."
...West et al. (2007) provide a comprehensive software review for nested mixed-effects models....
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...The lme4 package (Bates, 2005; Bates & Sarkar, 2007) offers fast and reliable algorithms for parameter estimation (see also West et al., 2007:14) as well as tools for evaluating the model (using Markov chain Monte Carlo sampling, as explained below)....
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...West, Welch, and Gałlechki (2007) provide a guide to mixed models for five different software packages....
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...The recent textbook by West et al. (2007), for instance, does not discuss models with crossed random effects, although it clearly distinguishes between nested and crossed random effects, and advises the reader to make use of the lmer() function in R, the software (developed by the third author)…...
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TL;DR: This paper introduced the concept of moderation and described how moderator effects are tested and interpreted for a series of model types, beginning with straightforward two-way interactions with Normal outcomes, moving to three-way and curvilinear interactions, and then to models with non-Normal outcomes including binary logistic regression and Poisson regression.
Abstract: Many theories in management, psychology, and other disciplines rely on moderating variables: those which affect the strength or nature of the relationship between two other variables. Despite the near-ubiquitous nature of such effects, the methods for testing and interpreting them are not always well understood. This article introduces the concept of moderation and describes how moderator effects are tested and interpreted for a series of model types, beginning with straightforward two-way interactions with Normal outcomes, moving to three-way and curvilinear interactions, and then to models with non-Normal outcomes including binary logistic regression and Poisson regression. In particular, methods of interpreting and probing these latter model types, such as simple slope analysis and slope difference tests, are described. It then gives answers to twelve frequently asked questions about testing and interpreting moderator effects.
2,032 citations
TL;DR: The authors found that adolescents are concerned about the COVID-19 crisis and are particularly worried about schooling and peer relationships, while more time connecting to friends virtually during the pandemic was associated with greater depression, but family time and schoolwork was related to less depression.
Abstract: We are facing an unprecedented time during the COVID-19 pandemic. Measures have been taken to reduce the spread of the virus, including school closures and widespread lockdowns. Physical isolation combined with economic instability, fear of infection, and uncertainty for the future has had a profound impact on global mental health. For adolescents, the effects of this stress may be heightened due to important developmental characteristics. Canadian adolescents (n = 1,054; M age= 16.68, SD = 0.78) completed online surveys and responded to questions on stress surrounding the COVID-19 crisis, feelings of loneliness and depression, as well as time spent with family, virtually with friends, doing schoolwork, using social media, and engaging in physical activity. Results showed that adolescents are very concerned about the COVID-19 crisis and are particularly worried about schooling and peer relationships. COVID-19 stress was related to more loneliness and more depression, especially for adolescents who spend more time on social media. Beyond COVID-19 stress, more time connecting to friends virtually during the pandemic was related to greater depression, but family time and schoolwork was related to less depression. For adolescents with depressive symptoms, it may be important to monitor the supportiveness of online relationships. Results show promising avenues to stave off loneliness, as time with family, time connecting to friends, as well as physical activity were related to lower loneliness, beyond COVID-19 stress. These results shed light on the implications of the COVID-19 pandemic for adolescents and document possible pathways to ameliorate negative effects.
481 citations
TL;DR: Mexican American and African American individuals meeting 12-month major depression criteria consistently and significantly had lower odds for any depression therapy and guideline-concordant therapies despite depression severity ratings not significantly differing between ethnic/racial groups.
Abstract: Objective To determine the prevalence and adequacy of depression care among different ethnic and racial groups in the United States. Design Collaborative Psychiatric Epidemiology Surveys (CPES) data were analyzed to calculate nationally representative estimates of depression care. Setting The 48 coterminous United States. Participants Household residents 18 years and older (N = 15 762) participated in the study. Main Outcome Measures Past-year depression pharmacotherapy and psychotherapy using American Psychiatric Association guideline-concordant therapies. Depression severity was assessed with the Quick Inventory of Depressive Symptomatology Self-Report. Primary predictors were major ethnic/racial groups (Mexican American, Puerto Rican, Caribbean black, African American, and non-Latino white) and World Mental Health Composite International Diagnostic Interview criteria for 12-month major depressive episode. Results Mexican American and African American individuals meeting 12-month major depression criteria consistently and significantly had lower odds for any depression therapy and guideline-concordant therapies despite depression severity ratings not significantly differing between ethnic/racial groups. All groups reported higher use of any past-year psychotherapy and guideline-concordant psychotherapy compared with pharmacotherapy; however, Caribbean black and African American individuals reported the highest proportions of this use. Conclusions Few Americans with recent major depression have used depression therapies and guideline-concordant therapies; however, the lowest rates of use were found among Mexican American and African American individuals. Ethnic/racial differences were found despite comparable depression care need. More Americans with recent major depression used psychotherapy over pharmacotherapy, and these differences were most pronounced among Mexican American and African American individuals. This report underscores the importance of disaggregating ethnic/racial groups and depression therapies in understanding and directing efforts to improve depression care in the United States.
404 citations
References
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TL;DR: This book provides a comprehensive treatment of linear mixed models for continuous longitudinal data and attempts to target applied statisticians and biomedical researchers in industry, public health organizations, contract research organizations, and academia.
Abstract: (2001). Linear Mixed Models for Longitudinal Data. Technometrics: Vol. 43, No. 3, pp. 375-375.
1,970 citations
1,020 citations
"Linear Mixed Models: A Practical Gu..." refers background in this paper
...Although this overview in Chapter 2 is, as already said, quite thorough, owing to the brevity of the exposition, the reader not only needs to be previously familiar with some of the terminology commonly used in modeling (we refer to terms like “covariate,” “factor,” “level,” “subject,” “unit of measurement,” “cluster,” “repeated measure,” “longitudinal data”) but also may find useful some previous knowledge on issues related to general linear models, variance components, or even some further details on LMMs, which may be acquired from books like the ones by Searle (1971), Searle, Casella, and McCulloch (1992), McCulloch and Searle (2001), McCulloch, Searle, and Neuhaus (2008), or Verbeke and Molenberghs (2000)....
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...Although this overview in Chapter 2 is, as already said, quite thorough, owing to the brevity of the exposition, the reader not only needs to be previously familiar with some of the terminology commonly used in modeling (we refer to terms like “covariate,” “factor,” “level,” “subject,” “unit of measurement,” “cluster,” “repeated measure,” “longitudinal data”) but also may find useful some previous knowledge on issues related to general linear models, variance components, or even some further details on LMMs, which may be acquired from books like the ones by Searle (1971), Searle, Casella, and McCulloch (1992), McCulloch and Searle (2001), McCulloch, Searle, and Neuhaus (2008), or Verbeke and Molenberghs (2000). Some further attention should, however, have been given to some details like the issues raised around the treatment of model matrices, which are not indeed full rank....
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TL;DR: In this article, a hierarchical generalised linear model (GLM) is developed as a synthesis of generalized linear models, mixed linear models and structured dispersions, and a restricted maximum likelihood method for the estimation of dispersion is extended to a wider class of models.
Abstract: SUMMARY Hierarchical generalised linear models are developed as a synthesis of generalised linear models, mixed linear models and structured dispersions. We generalise the restricted maximum likelihood method for the estimation of dispersion to the wider class and show how the joint fitting of models for mean and dispersion can be expressed by two interconnected generalised linear models. The method allows models with (i) any combination of a generalised linear model distribution for the response with any conjugate distribution for the random effects, (ii) structured dispersion components, (iii) different link and variance functions for the fixed and random effects, and (iv) the use of quasilikelihoods in place of likelihoods for either or both of the mean and dispersion models. Inferences can be made by applying standard procedures, in particular those for model checking, to components of either generalised linear model. We also show by numerical studies that the new method gives an efficient estimation procedure for substantial class of models of practical importance. Likelihood-type inference is extended to this wide class of models in a unified way.
325 citations
"Linear Mixed Models: A Practical Gu..." refers methods in this paper
...Download Linear Mixed Models: A Practical Guide Using Stati ...pdf Read Online Linear Mixed Models: A Practical Guide Using Sta ...pdf...
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TL;DR: In this paper, a score test for autocorrelation in the within-individual errors for the conditional independence random effects model was developed and an explicit maximum likelihood estimation procedure using the scoring method for the model with random effects and AR(1) errors was derived.
Abstract: For longitudinal data on several individuals, linear models that contain both random effects across individuals and autocorrelation in the within-individual errors are studied. A score test for autocorrelation in the within-individual errors for the “conditional independence” random effects model is first developed. An explicit maximum likelihood estimation procedure using the scoring method for the model with random effects and (autoregressive) AR(1) errors is then derived. Empirical Bayes estimation of the random effects and prediction of future responses of an individual based on this random effects with AR(1) errors model are also considered. A numerical example is presented to illustrate these methods.
250 citations