Linear Mixed-Effects Models with R

Name: Linear Mixed-Effects Models with R
Rating: 4.0 (276 reviews)

Learn how to specify, fit, interpret, evaluate and compare estimated parameters with linear mixed-effects models in R.

Created byGeoffrey Hubona, Ph.D.

Last updated 8/2020

English

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What you'll learn

Specify an appropriate linear mixed-effects model structure with their own data.
Compare alternative modeling structures and choose the best specification.
Represent, fit, and choose among different, competing correlational structures appropriate to both temporal and spatial pseudo-replicated models.
Validate the "goodness" of the model and the model assumptions.
Represent, estimate, interpret and report on linear mixed-effects model parameters using R software.

Course content

7 sections • 77 lectures • 10h 14m total length

Introduction to the Course1:32
Learn to fit, estimate, interpret, and evaluate linear mixed effects models using R. Explore multiple variance sources and correlation structures to understand model fit.
Introduction to R Scripting and RStudio10:00
RStudio Integrated Development Environment (IDE) is a powerful and productive user interface for R. It’s free and open source, and works great on Windows, Mac, and Linux.
Basic Quantitative Operations in R (part 1)5:53
Create a temperature vector tamps in R and use vectorized operations, such as subtracting 32 to convert Fahrenheit to Celsius, and compare with Connecticut temps.
Basic Quantitative Operations in R (part 2)6:59
Explore creating and manipulating numeric vectors in R, generate year sequences with seq, index and assign elements, and work with multi-dimensional structures like matrices and data frames.
More R Scripting and Plotting (part 1)9:45
More R Scripting and Plotting (part 2)4:52
Compute sample mean and variance from death counts. Fit a Poisson model with lambda approximately 0.61, then compare observed and expected counts using manual and built-in Poisson probabilities.
Functions in R (part 1)6:18
One of the great strengths of R is the user's ability to add functions. In fact, many of the functions in Rare actually functions of functions. The structure of a function is given below.

myfunction <- function(arg1, arg2, ... ){statement}
Functions in R (part 2)7:39
Create and evaluate user defined functions in R, with default arguments and nested function calls. Compare custom integration with the built in beta and integrate functions and plot the results.
Vectors and Matrices9:54
R has a wide variety of data types including scalars, vectors (numerical, character, logical).

All columns in a matrix must have the same mode(numeric, character, etc.) and the same length.
Dataframes and Histograms11:12
A data frame is more general than a matrix, in that different columns can have different modes (numeric, character, factor, etc.). This is similar to SAS and SPSS datasets.
Exercises: Getting Started with R as a Statistical Environment5:39

Solution to Getting Started with R as a Statistical Environment Exercise13:32
Practice essential R functions for probability and plotting, including qnorm for percentiles, chi-squared and gamma densities, binomial probabilities via choose and d, and curve plotting with add=TRUE, plus saving plots.
Some LME Background from MVA Package (scripts, part 1)6:05
Install and load the MBA multi-variate analysis package in R, explore datasets timber and plasma, and compare wide versus long forms through a clinical trial example with repeated measures.
Some LME Background (scripts, part 2)9:27
Explore transforming data from wide to long for linear models, using the reshape function, and examine timber and plasma datasets with repeated measures to illustrate longitudinal and pseudo replication concepts.
Some LME Background (scripts, part 3)7:27
Explore linear mixed-effects modeling in R by specifying fixed and random effects, and compare random intercept and random intercept with slope models under the local independence assumption.
Some LME Background (scripts, part 4)8:40
Explore a random intercept LME with fixed effects and variance components, conditioning on specimen, compare to linear model with likelihood ratio test, and plan to test random intercept with slope.
Temporal Pseudoreplication Fertilizer Exercise3:00
Solution to Temporal Pseudoreplication Fertilizer Exercise4:26
Set the working directory, verify file existence, and read the fertilizer dataset into results to examine a replicated, repeated-measures root length study with two fertilizer treatments.
Basic LME Concepts (slides, part 1)7:27
A mixed model is a statistical model containing both fixed effects and random effects. These models are useful in a wide variety of disciplines in the physical, biological and social sciences. They are particularly useful in settings where repeated measurements are made on the same statistical units (longitudinal study), or where measurements are made on clusters of related statistical units. Because of their advantage in dealing with missing values, mixed effects models are often preferred over more traditional approaches such as repeated measures ANOVA.
Basic LME Concepts (slides, part 2)8:19
Identify fixed and random effects, estimate variance components from nested levels, and account for multiple error sources in longitudinal mixed-effects models using nlme and lme4.
Basic LME Concepts (slides, part 3)7:32
Explore how random effects differ from fixed effects and compare the random intercept model with the random intercept and slope model to see how intercepts and slopes vary across groups.
Mixed-Effects Fertilized Plants Example using nlme Package (part 1)8:04
Examine fertilizer's effect on root growth using an nlme mixed-effects model with random intercept and slope, and visualize group data with lattice panels to compare with a linear model.
Finish Fertilized Plants Example and Begin Zuur Material6:58
Compare linear models with linear mixed-effects models, highlighting random intercepts, slopes, and random effects in a nested data set across nine beaches of species richness.
Two-Stage Beaches Example (part 1)7:39
Explore linear mixed-effects modeling with a two-stage regression: estimate height effects on species richness within each beach, then relate those per-beach coefficients to exposure levels to interpret overall patterns.
Two-Stage Beaches Example (part 2)9:25
Explore estimating a second stage linear mixed effects model with random intercepts for nine beaches, converting exposure to a factor, and interpreting fixed betas and random effects.
Random Intercepts Model Example7:33
Compare AIC, BIC, and log-likelihood to assess random intercepts linear mixed-effects models in R. Examine population and beach-specific intercepts, fixed effects, and plot fitted lines from the LME object.
Random Intercepts and Slopes Model Example8:36
Explore random intercept and slope models in linear mixed-effects, modeling richness as a function of station height with beach-specific intercepts and slopes.

Split-Plot Exercise Solution (part 1)9:23
Split-plot designs result when a particular type of restricted randomization has occurred during the experiment. A simple factorial experiment can result in a split-plot type of design because of the way the experiment was actually executed.
Split-Plot Exercise Solution (part 2)8:25
Explore how to interpret linear mixed-effects models in R for a split-plot design, focusing on fixed effects, two-way and three-way interactions, and model simplification via summary and log-likelihood ratio tests.
Split-Plot Exercise Solution (part 3)9:46
Compare linear mixed-effects models in R by updating a fitted model to exclude the three-way interaction, use LRT and anova to favor the simpler model, and assess residuals for assumptions.
Timber Data Random Intercept and Slope (part 1)7:44
A random intercepts model is a model in which intercepts are allowed to vary, and therefore, the scores on the dependent variable for each individual observation are predicted by the intercept that varies across groups. This model assumes that slopes are fixed (the same across different contexts). In addition, this model provides information about intraclass correlations, which are helpful in determining whether multilevel models are required in the first place.
Timber Data Random Intercept and Slope (part 2)6:25
A random slopes model is a model in which slopes are allowed to vary, and therefore, the slopes are different across groups. This model assumes that intercepts are fixed (the same across different contexts).
Timber Data Random Intercept and Slope (part 3)6:08
A model that includes both random intercepts and random slopes is likely the most realistic type of model, although it is also the most complex. In this model, both intercepts and slopes are allowed to vary across groups, meaning that they are different in different contexts.
Plasma Data Example (part 1)7:49
Explore plasma glucose data from obese and control groups in a repeated-measures design, reshaping long form to wide, and assess potential quadratic time effects and group-by-time interactions for mixed-effects models.
Plasma Data Example (part 2)6:50
Fit a linear mixed-effects model with random intercept and slope, including time and time squared, and compare to a linear fit to reveal significant effects and a time-by-group interaction.
Vatiance Components Analysis Exercise3:14
Explore variance components in a nested linear mixed-effects model with random intercepts using R, comparing models to quantify how random factors explain disease count variation.

Variance Components Analysis Exercise Solution (part 1)10:23
In statistics, a random effect(s) model, also called a variance components model, is a kind of hierarchical linear model. It assumes that the dataset being analysed consists of a hierarchy of different populations whose differences relate to that hierarchy. In econometrics, random effects models are used in the analysis of hierarchical or panel data when one assumes no fixed effects (it allows for individual effects). The random effects model is a special case of the fixed effects model.
Variance Components Analysis Exercise Solution (part 2)10:14
Analyze variance components in a linear mixed effects model, compute relative contributions of random effects (including gender), and compare nested models using log-likelihood ratio, AIC, and REML versus ML.
Variance Components Analysis Exercise Solution (part 3)8:50
compare fixed and random models in mixed-effects analysis, showing gender as a fixed effect yields better fit on measures accounting for complexity, with residual and qq plots validating assumptions.
LME Model Structure Selection (part 1)13:04
Explore how to specify and compare linear mixed-effects models, including random intercept, random intercept and slope, and marginal structures with induced covariance and compound symmetry.
LME Model Structure Selection (part 2)13:07
Learn to structure linear mixed-effects models in R, with random intercepts and slopes and fixed effects. Compare ML and REML, and use AIC/BIC and LRT for fixed-vs-random selection.
LME Model Structure Selection (part 3)7:04
Select the best random structure for linear mixed-effects models in R, comparing random intercept and random intercept with slope, using maximum likelihood and REML, and nested likelihood ratio tests.
LME Model Structure Selection (part 4)6:55
Choose the random intercept and slope structure using AIC and log-likelihood ratio tests, then refine fixed effects with exposure and interaction terms, testing via ANOVA and ML, ensuring convergence.
LME Model Structure Selection (part 5)5:10
Select the optimal lme structure by comparing fixed effects, including exposure and interaction, with random intercepts and slopes, using reml and log-likelihood tests to avoid overfitting.
Regression versus Fixed Effects Bias Exercise1:44

Regression versus Fixed Effects Exercise Solution (part 1)9:55
In econometrics and statistics, a fixed effects model is a statistical model that represents the observed quantities in terms of explanatory variables that are treated as if the quantities were non-random. This is in contrast to random effects models and mixed models in which either all or some of the explanatory variables are treated as if they arise from random causes.
Regression versus Fixed Effects Exercise Solution (part 2)9:29
Apply linear mixed-effects modeling with R to account for farm-level variability by using a random intercept and slope, compare lme and the mixed-effects outputs, and interpret intercept-slope relationships in regression.
Regression versus Fixed Effects Exercise Solution (part 3)7:16
Compare full mixed-effects models with fixed effects and random effects, examining nitrogen and farm effects and their interaction, then progressively simplify from M2 to M5 using nested likelihood ratio tests.
Regression versus Fixed Effects Exercise Solution (part 4)6:02
Compare fixed and random effects in linear mixed-effects modeling with R, using log-likelihood ratio tests and anova to identify that the common-slope model M3 best fits nitrogen and farm data.
Nestling Barn Owls (part 1)5:55
We analyze calls of nestling barn owls from 2007 to illustrate linear and mixed effects modeling, considering parent sex, arrival time, and food treatment with nest as a random effect.
Nestling Barn Owls (part 2)7:08
Nestling Barn Owls: Find Optimal Structure (part 1)6:42
Transform the response with log10 plus 1, refit, and assess residuals by nest to justify a random intercept model with fixed effects for sex, treatment, arrival time, and their interactions.
Nestling Barn Owls: Find Optimal Structure (part 2)6:47
Fit linear mixed-effects models with R, compare random intercept and no-random-intercept structures using nest as a random effect, assess with log-likelihood ratio and anova; examine residuals and variable significance.
Nestling Barn Owls: Find Optimal Structure (part 3)6:35
Apply likelihood ratio tests and anova-style comparisons in R to update linear mixed-effects models, assess interaction terms, and decide which covariates like food treatment and gender matter.
Exercise: Beat the Blues I2:30
Explore the beat the blues longitudinal study, comparing old couch therapy to computer-based therapy for depression, using a basic mixed-effects model and model comparison to estimate treatment effects.

Beat the Blues I Exercise Solution (part 1)9:00
Analyze the beat the blues longitudinal study comparing CBT and computer-based therapy for depression, using linear mixed effects models (LME4) on 100 participants with dropout handling and two covariates.
Beat the Blues I Exercise Solution (part 2)9:36
Learn to convert wide to long data in R for linear mixed-effects analyses, compare beat the blues and treatment as usual across pre and post time points.
Beat the Blues I Exercise Solution (part 3)10:15
Fit linear mixed-effects models in R to beat the blues data, compare random intercept and slope, and select the simpler model; Preece score and time are significant, treatment is not.
10-Step Protocol for Optimal Structure (part 1)10:13
Apply a 10-step protocol to build a mixed-effects model of nestling barn owl begging counts, with nest as random and gender, arrival time, and food treatment as fixed effects.
10-Step Protocol for Optimal Structure (part 2)10:07
Learn to build and simplify a linear mixed-effects model in R by using log-likelihood ratio tests to retain food treatment and arrival time as fixed effects, with a random intercept.
10-Step Protocol for Optimal Structure (part 3)9:47
10-Step Protocol for Optimal Structure (part 4)8:36
Explore fitting a generalized additive mixed model using Wood's package, highlighting additive model components, smooth terms, and how to inspect a fitted object.
The Problem of Dropouts in Longitudinal Studies (part 1)12:13
One application of multilevel modeling (MLM) is the analysis of repeated measures data. Multilevel modeling for repeated measures data is most often discussed in the context of modeling change over time (i.e. growth curve modeling for longitudinal designs); however, it may also be used for repeated measures data in which time is not a factor. The issue of subjects leaving the study ("dropouts") midway through the periodic intervals of data collection is a perennial problem with these types of studies.
The Problem of Dropouts in Longitudinal Studies (part 2)9:23
Explore dropout patterns in longitudinal data using plots to compare dropouts and non-dropouts, assess normality of random effects and residuals in linear mixed-effects models.
Beat the Blues II Exercises1:45
Compare linear regression and the optimal mixed model on the beat the blues longitudinal data to assess parameter significance, beta changes, and potential treatment-by-time interaction.

Beat the Blues II Exercise Solutions7:23
Fit a linear regression vs a random intercept mixed-effects model to beat the blues data, showing inflated significance from ignoring correlation, and test for a treatment by time interaction.
Time-Based Violation of Independence Assumption (part 1)12:28
Just as with ordinary least-squared linear regression, the observed distribution of error terms (residuals) is assumed to be normally distributed and characterized by statistical independence from other error terms in the practice of linear mixed-effects modeling.
Time-Based Residual Patterns (part 1)6:32
Explore how linear regression is used with time-based residuals. Examine the assumption that residuals are normally distributed with zero mean and constant variance, and model the covariance across years.
Time-Based Residual Patterns (part 2)7:15
Independence and Compound Symmetry10:55
Examine residual independence with year-to-year correlations via the auto correlation function and apply a GLS model with fixed compound symmetry to adjust standard errors.
AR-1 and ARMA Residual Dependence (part 1)7:39
In the statistical analysis of time series, autoregressive–moving-average (ARMA) models provide a parsimonious description of a (weakly) stationary stochastic process in terms of two polynomials, one for the auto-regression and the second for the moving average.
AR-1 and ARMA Residual Dependence (part 2)6:37
Examine AR-1 and ARMA residual dependence, detailing P and Q shaping correlation and covariance, convergence algorithms relying on starting values, and AIC and SC differences for non-nested models.
Introduction to Spatial Dependence7:59
Explore spatial dependence in mixed models by detecting spatial correlation in residuals and adding appropriate correlation structures, using a boreal forest dataset with wetness, latitude, and longitude.
Prepare Data and Run Bubble Plot11:22
Load the boreal data, transform the response, fit a linear model with wetness, and use bubble plots and a variogram to assess residuals and spatial dependence.
Candidate Spatial Correlative Structures11:26
Investigate spatial dependence in linear mixed-effects models by using variograms, nugget, and isotropy tests, then compare exponential, gaussian, linear, rational quadratic, and spherical correlation structures in R.
Irish Rivers Acid Sensitivity9:07
Learn to analyze acid sensitivity in 205 Irish rivers using the sodium dominance index and visualize forested versus non-forested sites with lattice plots.
Using Spatial Correlational Structures10:53

Requirements

Students will need to install the no-cost R console and the no-cost RStudio application (instructions and provided).

Description

Linear Mixed-Effects Models with R is a 7-session course that teaches the requisite knowledge and skills necessary to fit, interpret and evaluate the estimated parameters of linear mixed-effects models using R software. Alternatively referred to as nested, hierarchical, longitudinal, repeated measures, or temporal and spatial pseudo-replications, linear mixed-effects models are a form of least-squares model-fitting procedures. They are typically characterized by two (or more) sources of variance, and thus have multiple correlational structures among the predictor independent variables, which affect their estimated effects, or relationships, with the predicted dependent variables. These multiple sources of variance and correlational structures must be taken into account in estimating the "fit" and parameters for linear mixed-effects models.

The structure of mixed-effects models may be additive, or non-linear, or exponential or binomial, or assume various other ‘families’ of modeling relationships with the predicted variables. However, in this "hands-on" course, coverage is restricted to linear mixed-effects models, and especially, how to: (1) choose an appropriate linear model; (2) represent that model in R; (3) estimate the model; (4) compare (if needed), interpret and report the results; and (5) validate the model and the model assumptions. Additionally, the course explains the fitting of different correlational structures to both temporal, and spatial, pseudo-replicated models to appropriately adjust for the lack of independence among the error terms. The course does address the relevant statistical concepts, but mainly focuses on implementing mixed-effects models in R with ample R scripts, ‘real’ data sets, and live demonstrations. No prior experience with R is necessary to successfully complete the course as the first entire course section consists of a "hands-on" primer for executing statistical commands and scripts using R.

Who this course is for:

Students do NOT need to be knowledgeable and/or experienced with R software to successfully complete this course.
This course is useful for graduate students in business, the social sciences, education fields, statistics, mathematics and other disciplines who would like to learn about and become proficient estimating and interpreting linear mixed-effects model parameters and values.
This course is useful to practicing quantitative analysis professionals, such as research scientists and other data analytic professionals who use linear modeling techniques on the job.

Linear Mixed-Effects Models with R

What you'll learn

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Course content

Introduction to R as a Statistical Environment11 lectures • 1hr 20min

Basic Linear Mixed-Effects Concepts16 lectures • 2hr 4min

Timber and Plasma Data Examples9 lectures • 1hr 6min

Selecting LME Model Structures9 lectures • 1hr 17min

Compare LM and LME Parameters10 lectures • 1hr 8min

10-Step Protocol for Optimal Structure10 lectures • 1hr 31min

Violation of Independence Errors12 lectures • 1hr 50min

Requirements

Description

Who this course is for: