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Multilevel modeling is a term alternately used to describe hierarchical linear models, nested models, mixedeffects models, randomeffects models, and splitplot designs. They are statistical models for estimating parameters that vary at more than one level and which may contain both observed and latent variables at any level. They are generalizations of linear models, particularly linear regression, although they may be extended to nonlinear models.
xxM is an R package which can estimate multilevel SEM models characterized by complex leveldependent data structures containing both observed and latent variables. The package was developed at the University of Houston by a collaborative team headed by Dr. Paras Mehta. xxM implements a modeling framework called nLevel Structural Equation Modeling (NLSEM) which allows the specification of models with any number of levels. Because observed and latent variables are allowed at all levels, a conventional SEM model may be specified for each level and across any levels. Also, the randomeffects of observed variables are allowed both within and across levels. Mehta claims that xxM is the only software tool in the world that is capable of estimating the effects of both observed and latent variables in a SEM nomological network across an unlimited number of levels.
Some of the complex dependent data structures that can be effectively modeled and estimated with xxM include:
⦁ Hierarchically nested data (e.g. students, classrooms, schools)
⦁ Longitudinal data (long or wide)
⦁ Longitudinal data with switching classification (e.g. students changing classrooms)
⦁ Crossclassified data (e.g. students nested within primary and secondary schools)
⦁ Partial nesting (e.g. underperforming students in a classroom receive tutoring)
Model specification with xxM uses a “LEGOlike building block” approach for model construction. With an understanding of these basic building blocks, very complex multilevel models may be constructed by repeating the same key building steps.
This sixsession Multilevel SEM Modeling with xxM course is an overview and tutorial of how to perform these key basic building block steps using xxM. To convey a practical understanding of implementing the core model specification and construction concepts of xxM, seven complete illustrative examples are detailed over the six class sessions. One who completes this course will then be able to construct more complex multilevel models tied to their own research projects. The seven complete examples detailed in the course begin with: (1) a streamlined twolevel bivariate randomintercepts model; and (2) a twolevel randomslopes model. Then a (3) multilevel confirmatory factor analysis (CFA) and a (4) randomslopes multilevel CFA are detailed, followed by randomslopes (5) 'wide' and (6) 'long' latent growth curve model examples. Finally, a (7) threelevel hierarchical model containing both observed and latent variables is fully demonstrated. All of the necessary software, data, manuals, slides and course materials to productively specify and estimate all seven of the course model examples are provided and included in 'resources' folders associated with the video lessons.
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Section 1: Introduction to xxM and Multilevel Modeling  

Lecture 1 
Introduction to Course

01:32  
Lecture 2  09:39  
Multilevel models (also hierarchical linear models, nested models, mixed models, random coefficient, randomeffects models, random parameter models, or splitplot designs) are statistical models of parameters that vary at more than one level.^{[1]} These models can be seen as generalizations of linear models (in particular, linear regression), although they can also extend to nonlinear models. These models became much more popular after sufficient computing power and software became available. 

Lecture 3  10:42  
xxM is a package for multilevel structural equation modeling (MLSEM) with complex dependent data structures. xxM implements a modeling framework called nLevel Structural Equation Modeling (NLSEM) and can estimate models with any number of levels. Observed and latent variables are allowed at all levels. 

Lecture 4 
More xxM Description and Explanation (slides)

07:44  
Lecture 5  09:47  
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. 

Lecture 6 
MixedEffects Models: Important Concepts (slides, part 2)

12:06  
Lecture 7  09:52  
LISREL (which stands for “linear structural relations”) involves eight matrices that organize the causal paths, loadings, correlations, and error terms in any model. Although this makes a cumbersome syntax, it is used in the mathematical description of SEM in the vast majority of statistical articles. A shortened, simpler fourmatrix version can be used instead for specifying models in LISREL and is presented in some articles. 

Lecture 8  13:51  
The lavaan package is developed to provide useRs, researchers and teachers a free opensource, but commercialquality package for latent variable modeling. You can use lavaan to estimate a large variety of multivariate statistical models, including path analysis, confirmatory factor analysis, structural equation modeling and growth curve models. 

Section 2: Bivariate Random Intercepts Model (BRIM) Example  
Lecture 9  11:02  
This tutorial introduces core concepts of xxM as a modeling framework and as a software package. Key elements of model specification in xxM are introduced in the context of fitting a bivariate randomintercepts model (Mehta, Neale, & Flay, 2005). Although the example is relatively trivial, once you understand the building blocks presented in this tutorial, you should be able to construct complex models easily. The presentation is in three sections:


Lecture 10  11:48  
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. 

Lecture 11 
BRIM (slides, part 3)

11:38  
Lecture 12 
BRIM Preliminaries with xxM Scripts
Preview

06:31  
Lecture 13 
Fit and Estimate BRIM with xxM Scripts (part 1)

10:17  
Lecture 14 
Fit and Estimate BRIM with xxM Scripts (part 2)

08:57  
Section 3: Random Intercept and Slope (RANSLP) Model Example  
Lecture 15 
Errata (in advance) to RANSLP Description that Follows

06:47  
Lecture 16 
RANSLP Model Description (slides, part 1)

08:18  
Lecture 17  09:48  
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. 

Lecture 18 
RANSLP Model Fit and Estimation (slides and script, part3)
Preview

08:04  
Lecture 19 
RANSLP Model Fit and Estimation (slides and scripts, part 4)

08:22  
Lecture 20 
RANSLP Model Fit and Estimation (scripts, part 5)

10:29  
Lecture 21 
Conclude RANSLP Model Fit and Estimation (scripts, part 6)

10:09  
Section 4: Multilevel Confirmatory Factor Analysis (CFA) Examples  
Lecture 22  10:00  
In statistics, confirmatory factor analysis (CFA) is a special form of factor analysis, most commonly used in social research. It is used to test whether measures of a construct are consistent with a researcher's understanding of the nature of that construct (or factor). As such, the objective of confirmatory factor analysis is to test whether the data fit a hypothesized measurement model. This hypothesized model is based on theory and/or previous analytic research. 

Lecture 23 
Multilevel CFA (slides, part 2)

07:10  
Lecture 24 
Multilevel CFA (slides, part 3)

07:09  
Lecture 25 
Multilevel CFA (slides, part 4)

08:28  
Lecture 26 
Multilevel CFA (slides, part 5)

05:56  
Lecture 27 
Multilevel CFA Fit and Estimation (scripts, part 1)
Preview

07:09  
Lecture 28 
Multilevel CFA Fit and Estimation (scripts, part 2)

07:51  
Lecture 29 
Random Slope Multilevel CFA Example (slides, part 1)

06:03  
Lecture 30 
Random Slope Multilevel CFA Example (slides, part 2)

07:45  
Lecture 31 
Random Slope Multilevel CFA Fit and Estimation (scripts)

04:50  
Section 5: Random Slopes, Wide and Long Latent Growth Curve Models Examples  
Lecture 32 
Review RANSLP (part 1)

10:17  
Lecture 33 
Review RANSLP (part 2)

07:50  
Lecture 34  10:21  
Latent growth modeling is a statistical technique used in the structural equation modeling (SEM) framework to estimate growth trajectory. It is a longitudinal analysis technique to estimate growth over a period of time. It is widely used in the field of behavioral science, education and social science. It is also called latent growth curve analysis. The latent growth model was derived from theories of SEM. General purpose SEM software, such as OpenMx, lavaan (both open source packages based in R), AMOS, Mplus, LISREL, or EQS among others may be used to estimate the trajectory of growth. The R xxM package can estimate the trajectory of growth using multilevel models comprised of both latent (SEMlike) and observed (directlymeasured) variables. 

Lecture 35 
Long Format LGC Example (script, part 1)

08:52  
Lecture 36 
Long Format LGC Example (script, part 2)

09:52  
Lecture 37 
Wide Format LGC Example Slides and Script (part 1)
Preview

09:08  
Lecture 38 
Wide Format LGC Example Script (part 2)

10:07  
Section 6: ThreeLevel Hierarchical Model Example  
Lecture 39  10:28  
Multilevel models (also hierarchical linear models, nested models, mixed models, random coefficient, randomeffects models, random parameter models, or splitplot designs) are statistical models of parameters that vary at more than one level.^{[1]} These models can be seen as generalizations of linear models (in particular, linear regression), although they can also extend to nonlinear models. These models became much more popular after sufficient computing power and software became available. 

Lecture 40 
3Level Hierarchical Model Specification (slides, part 2)

07:51  
Lecture 41 
3Level Hierarchical Model Specification (slides, part 3)

10:07  
Lecture 42 
3Level Hierarchical Model Specification (slides, part 4)

09:39  
Lecture 43 
3Level Hierarchical Model Specification (slides, part 5)

07:35  
Lecture 44 
3Level Hierarchical Model Specification (slides, part 6)

06:12  
Lecture 45 
Estimate 3Level Hierarchical Model in xxM (part 1)
Preview

07:59  
Lecture 46 
Estimate 3Level Hierarchical Model in xxM (part 2)

07:18 
Dr. Geoffrey Hubona held fulltime tenuretrack, and tenured, assistant and associate professor faculty positions at 3 major state universities in the Eastern United States from 19932010. In these positions, he taught dozens of various statistics, business information systems, and computer science courses to undergraduate, master's and Ph.D. students. He earned a Ph.D. in Business Administration (Information Systems and Computer Science) from the University of South Florida (USF) in Tampa, FL (1993); an MA in Economics (1990), also from USF; an MBA in Finance (1979) from George Mason University in Fairfax, VA; and a BA in Psychology (1972) from the University of Virginia in Charlottesville, VA. He was a fulltime assistant professor at the University of Maryland Baltimore County (19931996) in Catonsville, MD; a tenured associate professor in the department of Information Systems in the Business College at Virginia Commonwealth University (19962001) in Richmond, VA; and an associate professor in the CIS department of the Robinson College of Business at Georgia State University (20012010). He is the founder of the Georgia R School (20102014) and of RCourseware (2014Present), online educational organizations that teach research methods and quantitative analysis techniques. These research methods techniques include linear and nonlinear modeling, multivariate methods, data mining, programming and simulation, and structural equation modeling and partial least squares (PLS) path modeling. Dr. Hubona is an expert of the analytical, opensource R software suite and of various PLS path modeling software packages, including SmartPLS. He has published dozens of research articles that explain and use these techniques for the analysis of data, and, with software codevelopment partner Dean Lim, has created a popular cloudbased PLS software application, PLSGUI.