references.bib

@article{brown_introduction_2021,
	title = {An {Introduction} to {Linear} {Mixed}-{Effects} {Modeling} in {R}},
	volume = {4},
	issn = {2515-2459},
	url = {https://doi.org/10.1177/2515245920960351},
	doi = {10.1177/2515245920960351},
	abstract = {This Tutorial serves as both an approachable theoretical introduction to mixed-effects modeling and a practical introduction to how to implement mixed-effects models in R. The intended audience is researchers who have some basic statistical knowledge, but little or no experience implementing mixed-effects models in R using their own data. In an attempt to increase the accessibility of this Tutorial, I deliberately avoid using mathematical terminology beyond what a student would learn in a standard graduate-level statistics course, but I reference articles and textbooks that provide more detail for interested readers. This Tutorial includes snippets of R code throughout; the data and R script used to build the models described in the text are available via OSF at https://osf.io/v6qag/, so readers can follow along if they wish. The goal of this practical introduction is to provide researchers with the tools they need to begin implementing mixed-effects models in their own research.},
	language = {en},
	number = {1},
	urldate = {2024-02-12},
	journal = {Advances in Methods and Practices in Psychological Science},
	author = {Brown, Violet A.},
	month = jan,
	year = {2021},
	note = {Publisher: SAGE Publications Inc},
	pages = {2515245920960351},
	file = {SAGE PDF Full Text:/Users/jcook0312/Zotero/storage/R4PPPSNN/Brown - 2021 - An Introduction to Linear Mixed-Effects Modeling i.pdf:application/pdf},
}

@article{harrison_brief_2018,
	title = {A brief introduction to mixed effects modelling and multi-model inference in ecology},
	volume = {6},
	issn = {2167-8359},
	url = {https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5970551/},
	doi = {10.7717/peerj.4794},
	abstract = {The use of linear mixed effects models (LMMs) is increasingly common in the analysis of biological data. Whilst LMMs offer a flexible approach to modelling a broad range of data types, ecological data are often complex and require complex model structures, and the fitting and interpretation of such models is not always straightforward. The ability to achieve robust biological inference requires that practitioners know how and when to apply these tools. Here, we provide a general overview of current methods for the application of LMMs to biological data, and highlight the typical pitfalls that can be encountered in the statistical modelling process. We tackle several issues regarding methods of model selection, with particular reference to the use of information theory and multi-model inference in ecology. We offer practical solutions and direct the reader to key references that provide further technical detail for those seeking a deeper understanding. This overview should serve as a widely accessible code of best practice for applying LMMs to complex biological problems and model structures, and in doing so improve the robustness of conclusions drawn from studies investigating ecological and evolutionary questions.},
	urldate = {2024-02-12},
	journal = {PeerJ},
	author = {Harrison, Xavier A. and Donaldson, Lynda and Correa-Cano, Maria Eugenia and Evans, Julian and Fisher, David N. and Goodwin, Cecily E.D. and Robinson, Beth S. and Hodgson, David J. and Inger, Richard},
	month = may,
	year = {2018},
	pmid = {29844961},
	pmcid = {PMC5970551},
	pages = {e4794},
	file = {PubMed Central Full Text PDF:/Users/jcook0312/Zotero/storage/H8A9YQLG/Harrison et al. - 2018 - A brief introduction to mixed effects modelling an.pdf:application/pdf},
}

@article{bolker_generalized_2009,
	title = {Generalized linear mixed models: a practical guide for ecology and evolution},
	volume = {24},
	issn = {0169-5347},
	shorttitle = {Generalized linear mixed models},
	url = {https://www.sciencedirect.com/science/article/pii/S0169534709000196},
	doi = {10.1016/j.tree.2008.10.008},
	abstract = {How should ecologists and evolutionary biologists analyze nonnormal data that involve random effects? Nonnormal data such as counts or proportions often defy classical statistical procedures. Generalized linear mixed models (GLMMs) provide a more flexible approach for analyzing nonnormal data when random effects are present. The explosion of research on GLMMs in the last decade has generated considerable uncertainty for practitioners in ecology and evolution. Despite the availability of accurate techniques for estimating GLMM parameters in simple cases, complex GLMMs are challenging to fit and statistical inference such as hypothesis testing remains difficult. We review the use (and misuse) of GLMMs in ecology and evolution, discuss estimation and inference and summarize ‘best-practice’ data analysis procedures for scientists facing this challenge.},
	number = {3},
	urldate = {2024-02-12},
	journal = {Trends in Ecology \& Evolution},
	author = {Bolker, Benjamin M. and Brooks, Mollie E. and Clark, Connie J. and Geange, Shane W. and Poulsen, John R. and Stevens, M. Henry H. and White, Jada-Simone S.},
	month = mar,
	year = {2009},
	pages = {127--135},
}

@article{magezi_linear_2015,
	title = {Linear mixed-effects models for within-participant psychology experiments: an introductory tutorial and free, graphical user interface ({LMMgui})},
	volume = {6},
	issn = {1664-1078},
	shorttitle = {Linear mixed-effects models for within-participant psychology experiments},
	doi = {10.3389/fpsyg.2015.00002},
	abstract = {Linear mixed-effects models (LMMs) are increasingly being used for data analysis in cognitive neuroscience and experimental psychology, where within-participant designs are common. The current article provides an introductory review of the use of LMMs for within-participant data analysis and describes a free, simple, graphical user interface (LMMgui). LMMgui uses the package lme4 (Bates et al., 2014a,b) in the statistical environment R (R Core Team).},
	language = {eng},
	journal = {Frontiers in Psychology},
	author = {Magezi, David A.},
	year = {2015},
	pmid = {25657634},
	pmcid = {PMC4302710},
	keywords = {experimental psychology, graphical user interface, linear mixed-effects models, R, within-participant design},
	pages = {2},
	file = {Full Text:/Users/jcook0312/Zotero/storage/CQQGHLAR/Magezi - 2015 - Linear mixed-effects models for within-participant.pdf:application/pdf},
}

@article{verbeeck_linear_2023,
	title = {A linear mixed model to estimate {COVID}-19-induced excess mortality},
	volume = {79},
	issn = {1541-0420},
	doi = {10.1111/biom.13578},
	abstract = {The Corona Virus Disease (COVID-19) pandemic has increased mortality in countries worldwide. To evaluate the impact of the pandemic on mortality, the use of excess mortality rather than reported COVID-19 deaths has been suggested. Excess mortality, however, requires estimation of mortality under nonpandemic conditions. Although many methods exist to forecast mortality, they are either complex to apply, require many sources of information, ignore serial correlation, and/or are influenced by historical excess mortality. We propose a linear mixed model that is easy to apply, requires only historical mortality data, allows for serial correlation, and down-weighs the influence of historical excess mortality. Appropriateness of the linear mixed model is evaluated with fit statistics and forecasting accuracy measures for Belgium and the Netherlands. Unlike the commonly used 5-year weekly average, the linear mixed model is forecasting the year-specific mortality, and as a result improves the estimation of excess mortality for Belgium and the Netherlands.},
	language = {eng},
	number = {1},
	journal = {Biometrics},
	author = {Verbeeck, Johan and Faes, Christel and Neyens, Thomas and Hens, Niel and Verbeke, Geert and Deboosere, Patrick and Molenberghs, Geert},
	month = mar,
	year = {2023},
	pmid = {34694627},
	pmcid = {PMC8652760},
	keywords = {5-year weekly average, COVID-19, excess mortality, Humans, linear mixed model, Linear Models, Pandemics},
	pages = {417--425},
	file = {Full Text:/Users/jcook0312/Zotero/storage/KWJ697W6/Verbeeck et al. - 2023 - A linear mixed model to estimate COVID-19-induced .pdf:application/pdf},
}

@article{touraine_when_2023,
	title = {When a joint model should be preferred over a linear mixed model for analysis of longitudinal health-related quality of life data in cancer clinical trials},
	volume = {23},
	issn = {1471-2288},
	doi = {10.1186/s12874-023-01846-3},
	abstract = {BACKGROUND: Patient-reported outcomes such as health-related quality of life (HRQoL) are increasingly used as endpoints in randomized cancer clinical trials. However, the patients often drop out so that observation of the HRQoL longitudinal outcome ends prematurely, leading to monotone missing data. The patients may drop out for various reasons including occurrence of toxicities, disease progression, or may die. In case of informative dropout, the usual linear mixed model analysis will produce biased estimates. Unbiased estimates cannot be obtained unless the dropout is jointly modeled with the longitudinal outcome, for instance by using a joint model composed of a linear mixed (sub)model linked to a survival (sub)model. Our objective was to investigate in a clinical trial context the consequences of using the most frequently used linear mixed model, the random intercept and slope model, rather than its corresponding joint model.
METHODS: We first illustrate and compare the models on data of patients with metastatic pancreatic cancer. We then perform a more formal comparison through a simulation study.
RESULTS: From the application, we derived hypotheses on the situations in which biases arise and on their nature. Through the simulation study, we confirmed and complemented these hypotheses and provided general explanations of the bias mechanisms.
CONCLUSIONS: In particular, this article reveals how the linear mixed model fails in the typical situation where poor HRQoL is associated with an increased risk of dropout and the experimental treatment improves survival. Unlike the joint model, in this situation the linear mixed model will overestimate the HRQoL in both arms, but not equally, misestimating the difference between the HRQoL trajectories of the two arms to the disadvantage of the experimental arm.},
	language = {eng},
	number = {1},
	journal = {BMC medical research methodology},
	author = {Touraine, Célia and Cuer, Benjamin and Conroy, Thierry and Juzyna, Beata and Gourgou, Sophie and Mollevi, Caroline},
	month = feb,
	year = {2023},
	pmid = {36765307},
	pmcid = {PMC9912607},
	keywords = {Clinical trials, Humans, Linear Models, Cancer, Clinical Trials as Topic, Computer Simulation, Health-related quality of life, Informative dropout, Joint model, Linear mixed model, Longitudinal outcome, Longitudinal Studies, Neoplasms, Quality of Life, Random intercept and slope model},
	pages = {36},
	file = {Full Text:/Users/jcook0312/Zotero/storage/RLE454A7/Touraine et al. - 2023 - When a joint model should be preferred over a line.pdf:application/pdf},
}

@article{pusponegoro_linear_2017,
	series = {Discovery and innovation of computer science technology in artificial intelligence era: {The} 2nd {International} {Conference} on {Computer} {Science} and {Computational} {Intelligence} ({ICCSCI} 2017)},
	title = {Linear {Mixed} {Model} for {Analyzing} {Longitudinal} {Data}: {A} {Simulation} {Study} of {Children} {Growth} {Differences}},
	volume = {116},
	issn = {1877-0509},
	shorttitle = {Linear {Mixed} {Model} for {Analyzing} {Longitudinal} {Data}},
	url = {https://www.sciencedirect.com/science/article/pii/S187705091732121X},
	doi = {10.1016/j.procs.2017.10.071},
	abstract = {Growth developmental research is one example of the application of longitudinal data that have correlated value over time. Linear Mixed Model (LMM) is an extension of classic statistical procedures that provides flexibility analysis in correlated longitudinal data and allows researcher to model the covariance structures that represent its random effects. This paper briefly describes growth curves model as a single LMM that represent two levels of observation, which focused on modeling its covariance structure to capture correlated information over time of individual performance. We apply LMM and model different types of its covariance structure in the simulation study of children’s growth differences based on the feeding methods. We perform simulation scenario using MIXED procedure in SAS system, based on three fit indices (-2RLL, AIC and SBC) and p-value significance level, we obtain Unstructured (UN) covariance is always be the best fit in presenting the characteristic of data but not the best choice considering inefficient numbers of parameters while Heterogeneous First-order Autoregressive (ARH(1)) is a proper alternative covariance structure with ease of data interpretation from fewer numbers of estimated parameters.},
	urldate = {2024-02-12},
	journal = {Procedia Computer Science},
	author = {Pusponegoro, Novi Hidayat and Rachmawati, Ro’fah Nur and Notodiputro, Khairil Anwar and Sartono, Bagus},
	month = jan,
	year = {2017},
	keywords = {covariance structure, growth curves, marjinal model, reapated measurement},
	pages = {284--291},
}

@article{monsalves_level_2020,
	title = {{LEVEL} ({Logical} {Explanations} \& {Visualizations} of {Estimates} in {Linear} mixed models): recommendations for reporting multilevel data and analyses},
	volume = {20},
	issn = {1471-2288},
	shorttitle = {{LEVEL} ({Logical} {Explanations} \& {Visualizations} of {Estimates} in {Linear} mixed models)},
	url = {https://doi.org/10.1186/s12874-019-0876-8},
	doi = {10.1186/s12874-019-0876-8},
	number = {1},
	urldate = {2024-02-12},
	journal = {BMC Medical Research Methodology},
	author = {Monsalves, Maria Jose and Bangdiwala, Ananta Shrikant and Thabane, Alex and Bangdiwala, Shrikant Ishver},
	month = jan,
	year = {2020},
	keywords = {Multilevel diagram, Multilevel models, Reporting guidelines, Variance partition coefficients},
	pages = {3},
	file = {Full Text PDF:/Users/jcook0312/Zotero/storage/3LBRIEF6/Monsalves et al. - 2020 - LEVEL (Logical Explanations & Visualizations of Es.pdf:application/pdf},
}

@article{lee_estimation_nodate,
	title = {Estimation and selection in linear mixed models with missing data under compound symmetric structure},
	volume = {49},
	issn = {0266-4763},
	url = {https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9621253/},
	doi = {10.1080/02664763.2021.1969342},
	abstract = {It is quite appealing to extend existing theories in classical linear models to correlated responses where linear mixed-effects models are utilized and the dependency in the data is modeled by random effects. In the mixed modeling framework, missing values occur naturally due to dropouts or non-responses, which is frequently encountered when dealing with real data. Motivated by such problems, we aim to investigate the estimation and model selection performance in linear mixed models when missing data are present. Inspired by the property of the indicator function for missingness and its relation to missing rates, we propose an approach that records missingness in an indicator-based matrix and derive the likelihood-based estimators for all parameters involved in the linear mixed-effects models. Based on the proposed method for estimation, we explore the relationship between estimation and selection behavior over missing rates. Simulations and a real data application are conducted for illustrating the effectiveness of the proposed method in selecting the most appropriate model and in estimating parameters.},
	number = {15},
	urldate = {2024-02-12},
	journal = {Journal of Applied Statistics},
	author = {Lee, Yi-Ching and Shang, Junfeng},
	pmid = {36324480},
	pmcid = {PMC9621253},
	pages = {4003--4027},
	file = {PubMed Central Full Text PDF:/Users/jcook0312/Zotero/storage/V5JSS27G/Lee and Shang - Estimation and selection in linear mixed models wi.pdf:application/pdf},
	year = {n.d.}  % Placeholder for the missing year; consider using a more appropriate value
}

@article{schielzeth_robustness_2020,
	title = {Robustness of linear mixed-effects models to violations of distributional assumptions},
	volume = {11},
	url = {https://besjournals.onlinelibrary.wiley.com/doi/abs/10.1111/2041-210X.13434},
	doi = {https://doi.org/10.1111/2041-210X.13434},
	abstract = {Abstract Linear mixed-effects models are powerful tools for analysing complex datasets with repeated or clustered observations, a common data structure in ecology and evolution. Mixed-effects models involve complex fitting procedures and make several assumptions, in particular about the distribution of residual and random effects. Violations of these assumptions are common in real datasets, yet it is not always clear how much these violations matter to accurate and unbiased estimation. Here we address the consequences of violations in distributional assumptions and the impact of missing random effect components on model estimates. In particular, we evaluate the effects of skewed, bimodal and heteroscedastic random effect and residual variances, of missing random effect terms and of correlated fixed effect predictors. We focus on bias and prediction error on estimates of fixed and random effects. Model estimates were usually robust to violations of assumptions, with the exception of slight upward biases in estimates of random effect variance if the generating distribution was bimodal but was modelled by Gaussian error distributions. Further, estimates for (random effect) components that violated distributional assumptions became less precise but remained unbiased. However, this particular problem did not affect other parameters of the model. The same pattern was found for strongly correlated fixed effects, which led to imprecise, but unbiased estimates, with uncertainty estimates reflecting imprecision. Unmodelled sources of random effect variance had predictable effects on variance component estimates. The pattern is best viewed as a cascade of hierarchical grouping factors. Variances trickle down the hierarchy such that missing higher-level random effect variances pool at lower levels and missing lower-level and crossed random effect variances manifest as residual variance. Overall, our results show remarkable robustness of mixed-effects models that should allow researchers to use mixed-effects models even if the distributional assumptions are objectively violated. However, this does not free researchers from careful evaluation of the model. Estimates that are based on data that show clear violations of key assumptions should be treated with caution because individual datasets might give highly imprecise estimates, even if they will be unbiased on average across datasets.},
	number = {9},
	journal = {Methods in Ecology and Evolution},
	author = {Schielzeth, Holger and Dingemanse, Niels J. and Nakagawa, Shinichi and Westneat, David F. and Allegue, Hassen and Teplitsky, Céline and Réale, Denis and Dochtermann, Ned A. and Garamszegi, László Zsolt and Araya-Ajoy, Yimen G.},
	year = {2020},
	note = {\_eprint: https://besjournals.onlinelibrary.wiley.com/doi/pdf/10.1111/2041-210X.13434},
	keywords = {linear mixed-effects models, biostatistics, correlated predictors, distributional assumptions, missing random effects, statistical quantification of individual differences (SQuID)},
	pages = {1141--1152},
}

@article{peng_model_2012,
	title = {Model selection in linear mixed effect models},
	volume = {109},
	issn = {0047-259X},
	url = {https://www.sciencedirect.com/science/article/pii/S0047259X12000395},
	doi = {10.1016/j.jmva.2012.02.005},
	abstract = {Mixed effect models are fundamental tools for the analysis of longitudinal data, panel data and cross-sectional data. They are widely used by various fields of social sciences, medical and biological sciences. However, the complex nature of these models has made variable selection and parameter estimation a challenging problem. In this paper, we propose a simple iterative procedure that estimates and selects fixed and random effects for linear mixed models. In particular, we propose to utilize the partial consistency property of the random effect coefficients and select groups of random effects simultaneously via a data-oriented penalty function (the smoothly clipped absolute deviation penalty function). We show that the proposed method is a consistent variable selection procedure and possesses some oracle properties. Simulation studies and a real data analysis are also conducted to empirically examine the performance of this procedure.},
	urldate = {2024-02-13},
	journal = {Journal of Multivariate Analysis},
	author = {Peng, Heng and Lu, Ying},
	month = aug,
	year = {2012},
	keywords = {Group selection, Model selection, Oracle property, Penalized least squares, SCAD function},
	pages = {109--129},
}

@article{barr_random_2013,
	title = {Random effects structure for testing interactions in linear mixed-effects models},
	volume = {4},
	issn = {1664-1078},
	url = {https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3672519/},
	doi = {10.3389/fpsyg.2013.00328},
	urldate = {2024-02-13},
	journal = {Frontiers in Psychology},
	author = {Barr, Dale J.},
	month = jun,
	year = {2013},
	pmid = {23761778},
	pmcid = {PMC3672519},
	pages = {328},
	file = {PubMed Central Full Text PDF:/Users/jcook0312/Zotero/storage/IR27RYM5/Barr - 2013 - Random effects structure for testing interactions .pdf:application/pdf},
}

@article{steibel_powerful_2009,
	title = {A powerful and flexible linear mixed model framework for the analysis of relative quantification {RT}-{PCR} data},
	volume = {94},
	issn = {1089-8646},
	doi = {10.1016/j.ygeno.2009.04.008},
	abstract = {Quantitative reverse transcription polymerase chain reaction (qRT-PCR) is currently viewed as the most precise technique to quantify levels of messenger RNA. Relative quantification compares the expression of a target gene under two or more experimental conditions normalized to the measured expression of a control gene. The statistical methods and software currently available for the analysis of relative quantification of RT-PCR data lack the flexibility and statistical properties to produce valid inferences in a wide range of experimental situations. In this paper we present a novel method for the analysis of relative quantification of qRT-PCR data, which consists of the analysis of cycles to threshold values (C(T)) for a target and a control gene using a general linear mixed model methodology. Our method allows testing of a broader class of hypotheses than traditional analyses such as the classical comparative C(T). Moreover, a simulation study using plasmode datasets indicated that the estimated fold-change in pairwise comparisons was the same using either linear mixed models or a comparative C(T) method, but the linear mixed model approach was more powerful. In summary, the method presented in this paper is more accurate, powerful and flexible than the traditional methods for analysis of qRT-PCR data. This new method is especially useful for studies involving multiple experimental factors and complex designs.},
	language = {eng},
	number = {2},
	journal = {Genomics},
	author = {Steibel, Juan Pedro and Poletto, Rosangela and Coussens, Paul M. and Rosa, Guilherme J. M.},
	month = aug,
	year = {2009},
	pmid = {19422910},
	keywords = {Linear Models, Computer Simulation, Gene Expression, Reverse Transcriptase Polymerase Chain Reaction},
	pages = {146--152},
}

@article{jolly_pymer4_2018,
	title = {Pymer4: {Connecting} {R} and {Python} for {Linear} {Mixed} {Modeling}},
	volume = {3},
	issn = {2475-9066},
	shorttitle = {Pymer4},
	url = {https://joss.theoj.org/papers/10.21105/joss.00862},
	doi = {10.21105/joss.00862},
	abstract = {Jolly, (2018). Pymer4: Connecting R and Python for Linear Mixed Modeling. Journal of Open Source Software, 3(31), 862, https://doi.org/10.21105/joss.00862},
	language = {en},
	number = {31},
	urldate = {2024-02-13},
	journal = {Journal of Open Source Software},
	author = {Jolly, Eshin},
	month = nov,
	year = {2018},
	pages = {862},
	file = {Full Text PDF:/Users/jcook0312/Zotero/storage/5SST3UZS/Jolly - 2018 - Pymer4 Connecting R and Python for Linear Mixed M.pdf:application/pdf},
}

@article{bates_fitting_2015,
	title = {Fitting {Linear} {Mixed}-{Effects} {Models} {Using} lme4},
	volume = {67},
	copyright = {Copyright (c) 2015 Douglas Bates, Martin Mächler, Ben Bolker, Steve Walker},
	issn = {1548-7660},
	url = {https://doi.org/10.18637/jss.v067.i01},
	doi = {10.18637/jss.v067.i01},
	abstract = {Maximum likelihood or restricted maximum likelihood (REML) estimates of the parameters in linear mixed-effects models can be determined using the lmer function in the lme4 package for R. As for most model-fitting functions in R, the model is described in an lmer call by a formula, in this case including both fixed- and random-effects terms. The formula and data together determine a numerical representation of the model from which the profiled deviance or the profiled REML criterion can be evaluated as a function of some of the model parameters. The appropriate criterion is optimized, using one of the constrained optimization functions in R, to provide the parameter estimates. We describe the structure of the model, the steps in evaluating the profiled deviance or REML criterion, and the structure of classes or types that represents such a model. Sufficient detail is included to allow specialization of these structures by users who wish to write functions to fit specialized linear mixed models, such as models incorporating pedigrees or smoothing splines, that are not easily expressible in the formula language used by lmer.},
	language = {en},
	urldate = {2024-02-17},
	journal = {Journal of Statistical Software},
	author = {Bates, Douglas and Mächler, Martin and Bolker, Ben and Walker, Steve},
	month = oct,
	year = {2015},
	keywords = {Cholesky decomposition, linear mixed models, penalized least squares, sparse matrix methods},
	pages = {1--48},
	file = {Full Text:/Users/jcook0312/Zotero/storage/CFJ9DZQ4/Bates et al. - 2015 - Fitting Linear Mixed-Effects Models Using lme4.pdf:application/pdf},
}

@article{wang_statistical_2022,
	title = {Statistical primer: an introduction to the application of linear mixed-effects models in cardiothoracic surgery outcomes research-a case study using homograft pulmonary valve replacement data},
	volume = {62},
	issn = {1873-734X},
	shorttitle = {Statistical primer},
	doi = {10.1093/ejcts/ezac429},
	abstract = {OBJECTIVES: The emergence of big cardio-thoracic surgery datasets that include not only short-term and long-term discrete outcomes but also repeated measurements over time offers the opportunity to apply more advanced modelling of outcomes. This article presents a detailed introduction to developing and interpreting linear mixed-effects models for repeated measurements in the setting of cardiothoracic surgery outcomes research.
METHODS: A retrospective dataset containing serial echocardiographic measurements in patients undergoing surgical pulmonary valve replacement from 1986 to 2017 in Erasmus MC was used to illustrate the steps of developing a linear mixed-effects model for clinician researchers.
RESULTS: Essential aspects of constructing the model are illustrated with the dataset including theories of linear mixed-effects models, missing values, collinearity, interaction, nonlinearity, model specification, results interpretation and assumptions evaluation. A comparison between linear regression models and linear mixed-effects models is done to elaborate on the strengths of linear mixed-effects models. An R script is provided for the implementation of the linear mixed-effects model.
CONCLUSIONS: Linear mixed-effects models can provide evolutional details of repeated measurements and give more valid estimates compared to linear regression models in the setting of cardio-thoracic surgery outcomes research.},
	language = {eng},
	number = {4},
	journal = {European Journal of Cardio-Thoracic Surgery: Official Journal of the European Association for Cardio-Thoracic Surgery},
	author = {Wang, Xu and Andrinopoulou, Eleni-Rosalina and Veen, Kevin M. and Bogers, Ad J. J. C. and Takkenberg, Johanna J. M.},
	month = sep,
	year = {2022},
	pmid = {36005884},
	pmcid = {PMC9496250},
	keywords = {Allografts, Homograft, Humans, Linear Models, Mixed-effects model, Outcome Assessment, Health Care, Pulmonary Valve, Pulmonary valve replacement, Retrospective Studies},
	pages = {ezac429},
	file = {Full Text:/Users/jcook0312/Zotero/storage/JLRSVHE2/Wang et al. - 2022 - Statistical primer an introduction to the applica.pdf:application/pdf},
}

@article{lo_transform_2015,
	title = {To transform or not to transform: using generalized linear mixed models to analyse reaction time data},
	volume = {6},
	issn = {1664-1078},
	shorttitle = {To transform or not to transform},
	url = {https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2015.01171},
	abstract = {Linear mixed-effect models (LMMs) are being increasingly widely used in psychology to analyse multi-level research designs. This feature allows LMMs to address some of the problems identified by Speelman and McGann (2013) about the use of mean data, because they do not average across individual responses. However, recent guidelines for using LMM to analyse skewed reaction time (RT) data collected in many cognitive psychological studies recommend the application of non-linear transformations to satisfy assumptions of normality. Uncritical adoption of this recommendation has important theoretical implications which can yield misleading conclusions. For example, Balota et al. (2013) showed that analyses of raw RT produced additive effects of word frequency and stimulus quality on word identification, which conflicted with the interactive effects observed in analyses of transformed RT. Generalized linear mixed-effect models (GLMM) provide a solution to this problem by satisfying normality assumptions without the need for transformation. This allows differences between individuals to be properly assessed, using the metric most appropriate to the researcher's theoretical context. We outline the major theoretical decisions involved in specifying a GLMM, and illustrate them by reanalysing Balota et al.'s datasets. We then consider the broader benefits of using GLMM to investigate individual differences.},
	urldate = {2024-02-17},
	journal = {Frontiers in Psychology},
	author = {Lo, Steson and Andrews, Sally},
	year = {2015},
	file = {Full Text PDF:/Users/jcook0312/Zotero/storage/J44VWFW5/Lo and Andrews - 2015 - To transform or not to transform using generalize.pdf:application/pdf},
}

@article{piepho_analysing_1999,
	title = {Analysing disease incidence data from designed experiments by generalized linear mixed models},
	volume = {48},
	url = {https://bsppjournals.onlinelibrary.wiley.com/doi/abs/10.1046/j.1365-3059.1999.00383.x},
	doi = {https://doi.org/10.1046/j.1365-3059.1999.00383.x},
	abstract = {As a result of aggregation or clustering of sampling units, disease incidence data from designed experiments frequently show overdispersion relative to the binomial distribution. This paper discusses generalized linear mixed models (GLMM) suitable for analysing overdispersed disease incidence data. The methods are exemplified using data from a randomized complete block experiment on the incidence of downy mildew (Plasmopara viticola) of grape (Vitis lambrusca). Hints are given regarding implementation of the methods using the \%GLIMMIX macro for the SAS system.},
	number = {5},
	journal = {Plant Pathology},
	author = {{Piepho}},
	year = {1999},
	note = {\_eprint: https://bsppjournals.onlinelibrary.wiley.com/doi/pdf/10.1046/j.1365-3059.1999.00383.x},
	keywords = {clustering, disease incidence, downy mildew of grape, epidemiology, linear models, overdispersion},
	pages = {668--674},
}

@article{tu_using_2015,
title = {Using Generalized Linear Mixed Models to Evaluate Inconsistency within a Network Meta-Analysis},
journal = {Value in Health},
volume = {18},
number = {8},
pages = {1120-1125},
year = {2015},
issn = {1098-3015},
doi = {https://doi.org/10.1016/j.jval.2015.10.002},
url = {https://www.sciencedirect.com/science/article/pii/S1098301515050706},
author = {Yu-Kang Tu},
keywords = {generalized linear mixed models, design-by-treatment interaction, network meta-analysis, randomized controlled trials},
abstract = {Background
Network meta-analysis compares multiple treatments by incorporating direct and indirect evidence into a general statistical framework. One issue with the validity of network meta-analysis is inconsistency between direct and indirect evidence within a loop formed by three treatments. Recently, the inconsistency issue has been explored further and a complex design-by-treatment interaction model proposed.
Objective
The aim of this article was to show how to evaluate the design-by-treatment interaction model using the generalized linear mixed model.
Methods
We proposed an arm-based approach to evaluating the design-by-treatment inconsistency, which is flexible in modeling different types of outcome variables. We used the smoking cessation data to compare results from our arm-based approach with those from the standard contrast-based approach.
Results
Because the contrast-based approach requires transformation of data, our example showed that such a transformation may yield biases in the treatment effect and inconsistency evaluation, when event rates were low in some treatments. We also compared contrast-based and arm-based models in the evaluation of design inconsistency when different heterogeneity variances were estimated, and the arm-based model yielded more accurate results.
Conclusions
Because some statistical software commands can detect the collinearity among variables and automatically remove the redundant ones, we can use this advantage to help with placing the inconsistency parameters. This could be very useful for a network meta-analysis involving many designs and treatments.}
}


@article{fokkema_generalized_2021,
author = {Marjolein Fokkema, Julian Edbrooke-Childs and Miranda Wolpert},
title = {Generalized linear mixed-model (GLMM) trees: A flexible decision-tree method for multilevel and longitudinal data},
journal = {Psychotherapy Research},
volume = {31},
number = {3},
pages = {329-341},
year = {2021},
publisher = {Routledge},
doi = {10.1080/10503307.2020.1785037},

    note ={PMID: 32602811},


URL = { 
    
        https://doi.org/10.1080/10503307.2020.1785037
    
    

},
eprint = { 
    
        https://doi.org/10.1080/10503307.2020.1785037
    
    

}
}

@article{grueber_2011,
	title = {Multimodel inference in ecology and evolution: challenges and solutions},
	volume = {24},
	url = {https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1420-9101.2010.02210.x},
	doi = {https://doi.org/10.1111/j.1420-9101.2010.02210.x},
	abstract = {Abstract Information theoretic approaches and model averaging are increasing in popularity, but this approach can be difficult to apply to the realistic, complex models that typify many ecological and evolutionary analyses. This is especially true for those researchers without a formal background in information theory. Here, we highlight a number of practical obstacles to model averaging complex models. Although not meant to be an exhaustive review, we identify several important issues with tentative solutions where they exist (e.g. dealing with collinearity amongst predictors; how to compute model-averaged parameters) and highlight areas for future research where solutions are not clear (e.g. when to use random intercepts or slopes; which information criteria to use when random factors are involved). We also provide a worked example of a mixed model analysis of inbreeding depression in a wild population. By providing an overview of these issues, we hope that this approach will become more accessible to those investigating any process where multiple variables impact an evolutionary or ecological response.},
	number = {4},
	journal = {Journal of Evolutionary Biology},
	author = {GRUEBER, C. E. and NAKAGAWA, S. and LAWS, R. J. and JAMIESON, I. G.},
	keywords = {Akaike Information Criterion, generalized linear mixed models, inbreeding, information theory, lethal equivalents, model averaging, random factors, standardized predictors},
	eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1420-9101.2010.02210.x},
	year = {2011},
	pages = {699-711},
}

@article{zuur_2016,
	author = {Zuur, Alain F. and Ieno, Elena N.},
	title = {A protocol for conducting and presenting results of regression-type analyses},
	journal = {Methods in Ecology and Evolution},
	volume = {7},
	number = {6},
	pages = {636-645},
	keywords = {effective communication, protocol, statistical analysis, visualization},
	doi = {https://doi.org/10.1111/2041-210X.12577},
	url = {https://besjournals.onlinelibrary.wiley.com/doi/abs/10.1111/2041-210X.12577},
	eprint = {https://besjournals.onlinelibrary.wiley.com/doi/pdf/10.1111/2041-210X.12577},
	abstract = {Summary Scientific investigation is of value only insofar as relevant results are obtained and communicated, a task that requires organizing, evaluating, analysing and unambiguously communicating the significance of data. In this context, working with ecological data, reflecting the complexities and interactions of the natural world, can be a challenge. Recent innovations for statistical analysis of multifaceted interrelated data make obtaining more accurate and meaningful results possible, but key decisions of the analyses to use, and which components to present in a scientific paper or report, may be overwhelming. We offer a 10-step protocol to streamline analysis of data that will enhance understanding of the data, the statistical models and the results, and optimize communication with the reader with respect to both the procedure and the outcomes. The protocol takes the investigator from study design and organization of data (formulating relevant questions, visualizing data collection, data exploration, identifying dependency), through conducting analysis (presenting, fitting and validating the model) and presenting output (numerically and visually), to extending the model via simulation. Each step includes procedures to clarify aspects of the data that affect statistical analysis, as well as guidelines for written presentation. Steps are illustrated with examples using data from the literature. Following this protocol will reduce the organization, analysis and presentation of what may be an overwhelming information avalanche into sequential and, more to the point, manageable, steps. It provides guidelines for selecting optimal statistical tools to assess data relevance and significance, for choosing aspects of the analysis to include in a published report and for clearly communicating information.},
	year = {2016}
}

@article{aarts_2015,
	author={Aarts, Emmeke
	and Dolan, Conor V.
	and Verhage, Matthijs
	and van der Sluis, Sophie},
	title={Multilevel analysis quantifies variation in the experimental effect while optimizing power and preventing false positives},
	journal={BMC Neuroscience},
	year={2015},
	month={Dec},
	day={19},
	volume={16},
	number={1},
	pages={94},
	abstract={In neuroscience, experimental designs in which multiple measurements are collected in the same research object or treatment facility are common. Such designs result in clustered or nested data. When clusters include measurements from different experimental conditions, both the mean of the dependent variable and the effect of the experimental manipulation may vary over clusters. In practice, this type of cluster-related variation is often overlooked. Not accommodating cluster-related variation can result in inferential errors concerning the overall experimental effect.},
	issn={1471-2202},
	doi={10.1186/s12868-015-0228-5},
	url={https://doi.org/10.1186/s12868-015-0228-5}
}

@article{casals_methodological_2014,
	title = {Methodological quality and reporting of generalized linear mixed models in clinical medicine (2000-2012): a systematic review},
	volume = {9},
	issn = {1932-6203},
	shorttitle = {Methodological quality and reporting of generalized linear mixed models in clinical medicine (2000-2012)},
	doi = {10.1371/journal.pone.0112653},
	abstract = {BACKGROUND: Modeling count and binary data collected in hierarchical designs have increased the use of Generalized Linear Mixed Models (GLMMs) in medicine. This article presents a systematic review of the application and quality of results and information reported from GLMMs in the field of clinical medicine.
METHODS: A search using the Web of Science database was performed for published original articles in medical journals from 2000 to 2012. The search strategy included the topic "generalized linear mixed models","hierarchical generalized linear models", "multilevel generalized linear model" and as a research domain we refined by science technology. Papers reporting methodological considerations without application, and those that were not involved in clinical medicine or written in English were excluded.
RESULTS: A total of 443 articles were detected, with an increase over time in the number of articles. In total, 108 articles fit the inclusion criteria. Of these, 54.6\% were declared to be longitudinal studies, whereas 58.3\% and 26.9\% were defined as repeated measurements and multilevel design, respectively. Twenty-two articles belonged to environmental and occupational public health, 10 articles to clinical neurology, 8 to oncology, and 7 to infectious diseases and pediatrics. The distribution of the response variable was reported in 88\% of the articles, predominantly Binomial (n = 64) or Poisson (n = 22). Most of the useful information about GLMMs was not reported in most cases. Variance estimates of random effects were described in only 8 articles (9.2\%). The model validation, the method of covariate selection and the method of goodness of fit were only reported in 8.0\%, 36.8\% and 14.9\% of the articles, respectively.
CONCLUSIONS: During recent years, the use of GLMMs in medical literature has increased to take into account the correlation of data when modeling qualitative data or counts. According to the current recommendations, the quality of reporting has room for improvement regarding the characteristics of the analysis, estimation method, validation, and selection of the model.},
	language = {eng},
	number = {11},
	journal = {PloS One},
	author = {Casals, Martí and Girabent-Farrés, Montserrat and Carrasco, Josep L.},
	year = {2014},
	pmid = {25405342},
	pmcid = {PMC4236119},
	keywords = {Clinical Medicine, Linear Models},
	pages = {e112653},
	file = {Full Text:/Users/jcook0312/Zotero/storage/A76SK4QZ/Casals et al. - 2014 - Methodological quality and reporting of generalize.pdf:application/pdf},
}

@book{galecki_linear_2014,
	address = {New York},
	edition = {2},
	title = {Linear {Mixed} {Models}: {A} {Practical} {Guide} {Using} {Statistical} {Software}, {Second} {Edition}},
	isbn = {978-0-429-18656-1},
	shorttitle = {Linear {Mixed} {Models}},
	abstract = {Highly recommended by JASA, Technometrics, and other journals, the first edition of this bestseller showed how to easily perform complex linear mixed model (LMM) analyses via a variety of software programs. Linear Mixed Models: A Practical Guide Using Statistical Software, Second Edition continues to lead readers step by step through the process of},
	publisher = {Chapman and Hall/CRC},
	author = {Galecki, Kathleen B. Welch, Andrzej T., Brady T. West},
	month = jul,
	year = {2014},
	doi = {10.1201/b17198},
	file = {Accepted Version:/Users/jcook0312/Zotero/storage/KURST9L4/Galecki - 2014 - Linear Mixed Models A Practical Guide Using Stati.pdf:application/pdf},
}