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

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- 10 hours on-demand video
- 2 Supplemental Resources
- Full lifetime access
- Access on mobile and TV

- Certificate of Completion

What Will I 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.

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

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 is the target audience?

- 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.

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Curriculum For This Course

Expand All 77 Lectures
Collapse All 77 Lectures
10:14:58

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Introduction to R as a Statistical Environment
11 Lectures
01:19:43

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.

Introduction to R Scripting and RStudio

10:00

Basic Quantitative Operations in R (part 2)

06:59

More R Scripting and Plotting (part 1)

09:45

More R Scripting and Plotting (part 2)

04:52

One of the great strengths of **R** is the user's ability to add functions. In fact, many of the functions in **R**are actually functions of functions. The structure of a function is given below.

`myfunction <- function(arg1, arg2, ... ){statement}`

Functions in R (part 1)

06:18

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.

Vectors and Matrices

09:54

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.

Dataframes and Histograms

11:12

Exercises: Getting Started with R as a Statistical Environment

05:39

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Basic Linear Mixed-Effects Concepts
16 Lectures
02:01:10

Solution to Getting Started with R as a Statistical Environment Exercise

13:32

Some LME Background from MVA Package (scripts, part 1)

06:05

Some LME Background (scripts, part 2)

09:27

Some LME Background (scripts, part 3)

07:27

Some LME Background (scripts, part 4)

08:40

Temporal Pseudoreplication Fertilizer Exercise

3 pages

Solution to Temporal Pseudoreplication Fertilizer Exercise

04:26

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 1)

07:27

Basic LME Concepts (slides, part 3)

07:32

Finish Fertilized Plants Example and Begin Zuur Material

06:58

Two-Stage Beaches Example (part 2)

09:25

Random Intercepts Model Example

07:33

Random Intercepts and Slopes Model Example

08:36

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Timber and Plasma Data Examples
9 Lectures
01:05:44

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 1)

09:23

Split-Plot Exercise Solution (part 2)

08:25

Split-Plot Exercise Solution (part 3)

09:46

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.

Preview
07:44

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 2)

06:25

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.

Timber Data Random Intercept and Slope (part 3)

06:08

Plasma Data Example (part 1)

07:49

Plasma Data Example (part 2)

06:50

Vatiance Components Analysis Exercise

03:14

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Selecting LME Model Structures
9 Lectures
01:16:31

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 1)

10:23

Variance Components Analysis Exercise Solution (part 2)

10:14

Variance Components Analysis Exercise Solution (part 3)

08:50

LME Model Structure Selection (part 2)

13:07

LME Model Structure Selection (part 3)

07:04

LME Model Structure Selection (part 4)

06:55

LME Model Structure Selection (part 5)

05:10

Regression versus Fixed Effects Bias Exercise

01:44

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Compare LM and LME Parameters
10 Lectures
01:08:19

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 1)

09:55

Regression versus Fixed Effects Exercise Solution (part 2)

09:29

Regression versus Fixed Effects Exercise Solution (part 3)

07:16

Regression versus Fixed Effects Exercise Solution (part 4)

06:02

Nestling Barn Owls (part 1)

05:55

Nestling Barn Owls (part 2)

07:08

Nestling Barn Owls: Find Optimal Structure (part 2)

06:47

Nestling Barn Owls: Find Optimal Structure (part 3)

06:35

Exercise: Beat the Blues I

02:30

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10-Step Protocol for Optimal Structure
10 Lectures
01:30:55

Beat the Blues I Exercise Solution (part 1)

09:00

Beat the Blues I Exercise Solution (part 2)

09:36

Beat the Blues I Exercise Solution (part 3)

10:15

10-Step Protocol for Optimal Structure (part 1)

10:13

10-Step Protocol for Optimal Structure (part 2)

10:07

10-Step Protocol for Optimal Structure (part 3)

09:47

10-Step Protocol for Optimal Structure (part 4)

08:36

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.

Preview
12:13

The Problem of Dropouts in Longitudinal Studies (part 2)

09:23

Beat the Blues II Exercises

01:45

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Violation of Independence Errors
12 Lectures
01:49:36

Beat the Blues II Exercise Solutions

07:23

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 Violation of Independence Assumption (part 1)

12:28

Time-Based Residual Patterns (part 1)

06:32

Time-Based Residual Patterns (part 2)

07:15

Independence and Compound Symmetry

10:55

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 1)

07:39

AR-1 and ARMA Residual Dependence (part 2)

06:37

Introduction to Spatial Dependence

07:59

Candidate Spatial Correlative Structures

11:26

Irish Rivers Acid Sensitivity

09:07

Using Spatial Correlational Structures

10:53

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