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Multilevel SEM Modeling with xxM
Rating: 3.7 out of 5(41 ratings)
1,355 students

Multilevel SEM Modeling with xxM

How to estimate a multilevel SEM model containing both observed and latent variables and any number of dependent levels.
Last updated 9/2020
English

What you'll learn

  • Specify, model, and estimate either: (1) multilevel SEM models using latent variables; and/or (2) multilevel regression models using only observed data: and/or (3) mixed (both observed and latent variables) multilevel path-based models.
  • Effectively use the only software that exists in the world (which is freely provided with the course materials) capable of N-Level (any number of levels) multilevel SEM modeling.
  • Incorporate both observed and latent variables in a data-dependent structural network both within and across levels.
  • Incorporate any number of data-dependent levels in the SEM model.
  • Be able to include both fixed and random effects for the observed data across any number of dependent levels.
  • Be able to specify both random-intercept and random-slopes multilevel SEM models.

Course content

6 sections46 lectures6h 43m total length
  • Introduction to Course1:32
  • Introduction to xxM Materials and RStudio Configuration9:39

    Multilevel models (also hierarchical linear models, nested models, mixed models, random coefficient, random-effects models, random parameter models, or split-plot 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 non-linear models. These models became much more popular after sufficient computing power and software became available.

  • Continue RStudio Configuration and xxM Description (slides)10:42

    xxM is a package for multilevel structural equation modeling (ML-SEM) with complex dependent data structures. xxM implements a modeling framework called n-Level Structural Equation Modeling (NL-SEM) and can estimate models with any number of levels. Observed and latent variables are allowed at all levels.

  • More xxM Description and Explanation (slides)7:44
  • Mixed-Effects Models: Important Concepts (slides, part 1)9:47

    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.

  • Mixed-Effects Models: Important Concepts (slides, part 2)12:06
  • LISREL-Style Matrix Model Specification9:52

    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 four-matrix version can be used instead for specifying models in LISREL and is presented in some articles.

  • A lavaan Example of Relevance13:51

    The lavaan package is developed to provide useRs, researchers and teachers a free open-source, but commercial-quality 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.

Requirements

  • Students will need to install no-cost R software and the provided xxM package. Both are freely-provided with the course materials and come with both written and video instructions.

Description

Multilevel modeling is a term alternately used to describe hierarchical linear models, nested models, mixed-effects models, random-effects models, and split-plot 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 non-linear models.

xxM is an R package which can estimate multilevel SEM models characterized by complex level-dependent 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 n-Level Structural Equation Modeling (NL-SEM) 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 random-effects 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)

⦁ Cross-classified 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 “LEGO-like 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 six-session 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 two-level bivariate random-intercepts model; and (2) a two-level random-slopes model. Then a (3) multilevel confirmatory factor analysis (CFA) and a (4) random-slopes multilevel CFA are detailed, followed by random-slopes (5) 'wide' and (6) 'long' latent growth curve model examples. Finally, a (7) three-level 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.

Who this course is for:

  • Anyone interested or involved with covariance-based structural equation modeling (SEM) or variance-based path modeling (for example, PLS path modeling) would benefit from taking this course.
  • Anyone interested in acquiring with the course materials, and learning to use the only software in the world capable of N-Level multilevel modeling with both observed and latent variables would benefit from this course.
  • The course is useful for anyone involved with multilevel modeling using either observed variables and/or latent variables.
  • The course is relevant and helpful for undergraduate and graduate students involved with linear regression or linear mixed-effects modeling or SEM.
  • Quantitatively-oriented working professionals (research scientists, data analytics professionals) who utilize regression, path modeling, and/or SEM would benefit from the course.
  • It is helpful to have some knowledge about and understanding of linear regression before taking this course.
  • It is helpful (but not essential) to have some knowledge of either path modeling and/or SEM using latent variables.