Multilevel Modeling Using R

Instructor. David Rogosa (usually)Sequoia 224, rag{AT}stanford{DOT}edu

For recreation of in-classroom experience, linked below are youtube versions of the music I play

before starting lecture and after lecture concludes. Some may wish to reverse that ordering.

To see full course materials from Spring 2020 go here

From explorecourses

STATS 196A (EDUC 401D): Multilevel Modeling Using R Multilevel data analysis examples using R. Topics include: two-level nested data, growth curve modeling, generalized linear models for counts and categorical data, nonlinear models, three-level analyses. For more information, see course website: http://rogosateaching.com/stat196/ Terms: Spr | Units: 1 | Grading: Satisfactory/Unsatisfactory Remote: Asyncrhonous Instructors: Rogosa, D. (PI) STATS 196A | 1 units | Class # 21356 | Section 01 | Grading: Satisfactory/No Credit | WKS |

For the 1-unit enrollment in this short course, students are expected to engage in (i.e. consume) the four presentation class sessions.Course Schedule, Remote AsynchronousFour (2hr) classes (formerly located in Sequoia 200) Weeks 1 - 4. a. Introduction: Basic analyses for two-level nested data, normal models (UK Exam data) b. Additional two-level (normal) models: experimental designs (Dyestuff), longitudinal data (growth curves, sleepstudy), observational data (High School and Beyond) c. Generalized linear mixed models for counts and categorical outcomes d. Three-level analyses (nested data and longitudinal data) e. Specialized applications (as time permits): regression diagnostics, power calculations and design, ecological inference, survival analysis, nonlinear functional forms, mediation analysis, propensity scores and matching, imputation, item response theory Week 5. Substitute for live "Student presentations of multilevel data analyses" by online submission of materials

For the fifth session, formerly each student made a short (~10 min) presentation of a relevant data analysis they have conducted.

In Spring 2021, as it was in Spring 2020, students instead submit the small project online (such as using rpubs or google drive). Refer to Week0 audio.

Many of the example presented in this short course are described in Examples from Multilevel Software Comparative Reviews Douglas Bates.

Code version of MlmSoftRev R-package containing mlmRev data examples. Bates talk on mlmRev U Bristol documentation

Additional examples in core package lme4

Another set of examples: lmer for SAS PROC MIXED Users Douglas Bates Department of Statistics University of Wisconsin Madison

Data sets from SAS System for Mixed Models

Overviews and additional examples from Doug Bates:

lme4: Mixed-effects modeling with R February 17, 2010 Springer (book chapters).

A merged updated version of Bates book lme4: Mixed-effects modeling with R May 2020

R Journal intro Fitting linear mixed models in R Using the lme4 package Douglas Bates (pp.27-30)

Collection of all Doug Bates lme4 talks

lme4 vignette: Douglas Bates Martin Machler Ben Bolker. Fitting linear mixed-effects models using lme4,

Technical topics: Mixed models in R using the lme4 package Part 4: Theory of linear mixed models

HSB and growth curve examples in John Fox lme tutorial

Another nice lmer exposition with life sciences examples: Mixed-effects models, Remko Duursma, Jeff Powell Hawkesbury Institute for the Environment, Western Sydney University. September 2016. HIE Datasets

Current version of R is R version 4.0.4 released on 2021-02-15. For references and software: The R Project for Statistical Computing

Berkeley mirror is no longer, choose a mirror from the main R page (first link, I use TN).

A recent text (potentially) provides more infrastructure for this short course, but sadly it has many shortcomings.

This text has free access at Stanford via crcnetbase.com

Multilevel Modeling Using R http://www.crcpress.com/product/isbn/9781466515857 Chapman & Hall/CRC Statistics in the Social and Behavioral Sciences Published:June 23, 2014 by CRC Press Journal of Statistical Software Book Review Book website, including data

Updated from 2020 content each instructional week, starting Second Week of Spring Quarter

1. Introductory Example. Nested data, two-levels. Goldstein Exam Data.

a. Introductory descriptive approaches for gender gap analysis (Smart First Year Student analyses using lmList, additional plots).

b. Various lmer analyses for gender gap.

Gender gap data analysis: scanned class handout Rogosa R-session basic plots models used 2020 isSingular fix

c. Residual plots, add-on regression diagnostics: packages

Rogosa session with Exam data (week 1) (ascii) resulting plots

d. more P-values, tests add-ons to lmer.

afex package with Exam data ggaplmer2

Faraway text addendums: Inferential Methods for Linear Mixed Models

e. Plus Plots for random, fixed effects.

2. Matrix Formulation for Mixed Effects Models (growth curves and nested data).

1. Recap Introductory Example. Nested data, two-levels. Goldstein Exam Data.

Add-on package

prediction with lmer :

Rogosa session. plots

2. Common/canonical two-level examples (measured outcome)

A. Growth Curve models and analysis. Bates Sleepstudy example (week2 Stat222).

Chap. 4 Bates book [more Doug Bates Slides (pdf pages 8-28) ]

Sleepstudy class handout, pdf scan Sleepstudy, 2018 clean ascii Individual plots (frame-by-frame) Plot of straight-line fits

Reduced/constrained models: growth curve example

B. Two-level nested (normal) data recap. Brief overview of HSB (High School and Beyond) analysis (from Stat209): plots and model.

a full single Bryk dataset (longform) (abbreviated) Rogosa R-session Bryk data plots, Rogosa R-session

Caution froma prior year: side-by-side boxplot creation and lmList subset issue

A nice teaching document from Indiana that does HSB data with every known statistical package (including

3. Growth Curve Modeling exercise, Brain Volume Data Analysis. analyses from "Variation in longitudinal trajectories of regional brain volumes of healthy men and women (ages 10 to 85 years) measured with atlas-based parcellation of MRI" cartoon plot of Lateral Ventricles data; actual data plot of Lateral Ventricles data; development of lmer (mixed effect) growth models

4. Data from designed experiments.(basics).

a. Dyestuff data, Bates book, Chapter 1 (sec 1.2, 1.3) Rogosa Dyestuff session

b. Penicillin data (also Pastes, ratbrain), Bates book, Chapter 2.

From Doug Bates presentation Rogosa R-session

Random effects anova recap (see Bates book Chap1, Chap2).

Main topic: Generalized Linear Mixed Models: counts and proportions.

nice overview: Generalized Linear Mixed Models from

Github GLMM Faq (Ben Bolker)

1. Dichotomous outcomes,

a. Respiratory clinical trial from HSAUR. lmList does logistic, introducing glmer lmList, glmer for respiration data (placebo group)

b. Contraception (Bangladesh) use from Bates review Rogosa R-session glmer model slide

c. Test scores (pass/fail outcome) from Ch 8, Multilevel Modeling Using R. Rogosa R-session

2. Count outcome, GLMM poisson models.

a. Count data: Contagious bovine pleuropneumonia, data(cbpp) in lme4.

Rogosa R-session herd plots

b. Factorial design, Count outcome. From HIE Sydney. EucFACE ground cover data Rogosa glmer session.

c. Another count data example from mlmRev package,

data(Mmmec): Malignant Melanoma Mortality in the European Community associated with the impact of UV radiation exposure.

Rogosa glmer session more Rogosa Mmmec session

3. hglm -- a different package for fitting hierarchical generalized linear models.

R Journal December 2010. manual vignette

pdf slides companion audio Rogosa R-session

Resources: Basic Overdispersion Overview: Overdispersion, and how to deal with it in R

Overdispersion in Github GLMM Faq (Ben Bolker)

R-package

Measured outcomes

a. Achieve data from

b. example from mlmRev package, data(Chem97): Scores on A-level Chemistry in 1997. Rogosa R-session

Count outcome.

c. data(Mmmec): Malignant Melanoma Mortality in the European Community associated with the impact of UV radiation exposure. Rogosa 3-level session

Vignette: Analyzing Imputed Data with Multilevel Models and merTools

Rogosa R-session for vignette

Missing data wide-form imputation:

Missing data background. Multiple Imputation. Nhanes data example (mice primer) in van Buuren S and Groothuis-Oudshoorn K (2011). mice: Multivariate Imputation by Chained Equations in R. Journal of Statistical Software, 45(3), 1-67.

See also Flexible Imputation of Missing Data. Stef van Buuren Chapman and Hall/CRC 2012. Chapter 9, Longitudinal Data Sec 3.8 Multilevel data. He is the originator of

R resources. Multivariate Analysis Task View,

New package:

Most activity and resources are for longitudinal designs (c.f Week2, topic 2A): How often and How many subjects?

In my Stat222 course longitudinal experimental design is taken up in Week 5, Lecture topic 4.

Audio for the topic starts at partc that week, with the lecture content for design starting at pdf page 93.

Resources for that Stat222, Week5 content Power Calculations for Longitudinal Group Comparsions.

R-package

R-package: powerlmm

Background pubs: Power for linear models of longitudinal data with applications to Alzheimer's Disease Phase II study design Michael C. Donohue, Steven D. Edland, Anthony C. Gamst

Sample Size Planning for Longitudinal Models: Accuracy in Parameter Estimation for Polynomial Change Parameters Ken Kelley Notre Dame Joseph R. Rausch

Additional Resources: basic R analogues,

Power calculations and Design packages;

Package pamm Title Power Analysis for Random Effects in Mixed Models

Package simr Title Power Analysis for Generalised Linear Mixed Models by Simulation.

Package MultiRR Title Bias, Precision, and Power for Multi-Level Random Regression

more

intro: Introducing 'powerlmm' an R package for power calculations for longitudinal multilevel models

vignette: Power Analysis for Two-level Longitudinal Models with Missing Data

more simulation approaches to mixed-model power calculations:

Power for Multilevel Analysis Power Analysis in R for Multilevel Models Simulation approaches for mixed-model power calculations