# Basic and Advanced Multilevel Modeling with MPlus

**Course content**

This course will begin with basic multilevel modeling (MLM), including key concepts, equation conventions, and univariate models with random slopes. Several advanced MLM topics will be discussed, including: estimating, plotting, and probing interaction effects; modeling cross-classified data; modeling discrete (e.g., binary, count) dependent variables; and power analysis for MLM using a general Monte Carlo technique. Multilevel structural equation modeling (MSEM) will be introduced as a general approach for more complex modeling tasks. We will cover some important advantages of MSEM over MLM (e.g. inclusion of latent variables, complex causal pathways, upper-level outcomes, and model fit assessment). We will cover a variety of MSEM topics, including: multilevel exploratory and confirmatory factor analysis, multilevel path analysis, multilevel structural models with latent variables, multilevel mediation analysis, and multilevel reliability estimation. Throughout the course, models will be presented in several formats—path diagrams, equations, and software syntax. Data and Mplus syntax for all of the examples will be included in the provided materials.

**Structure**

Day 1:

- Introduction to multilevel modeling
- Orientation to Mplus for MLM
- Univariate MLM
- Power analysis for MLM using a general Monte Carlo technique
- Cross-classified random effects models

Day 2:

- Overview of single-level SEM
- Orientation to Mplus for SEM
- Introduction to multilevel SEM
- MSEM equations and path diagrams
- Orientation to Mplus for MSEM
- SEM and MLM as special cases of MSEM

Day 3:

- Mutilevel path analysis
- Multilevel confirmatory factor analysis
- Model fit in MSEM
- Multilevel exploratory factor analysis

Day 4:

- General MSEM with latent variables
- 3-level models in MLM and MSEM
- Multilevel reliability estimation
- Mediation in MLM and MSEM

Day 5:

- Review: Estimating, plotting, and probing interaction effects
- Moderation in MLM and MSEM
- Modeling discrete dependent variables

**Prerequisites (knowledge of topic)**

Students should have a working knowledge of multiple regression. Some knowledge of structural equation modeling also would be beneficial, but is not necessary.

**Hardware**

If students want to follow along with Mplus and run the example models in class, they will need a laptop computer capable of running Mplus. The demo version of Mplus is sufficient to run most, but not all, of the example models. Details at http://www.statmodel.com

**Software**

Mplus will be used to run all example models, but it is not essential to be familiar with Mplus. Much of the workshop is devoted to instruction on how to use Mplus to fit models. If students bring Mplus, it must have either the multilevel add-on or the combination add-on installed.

**Literature**

**Mandatory**

None.

**Supplementary / voluntary:**

Snijders, T. A. B., & Bosker, R. (2012). *Multilevel analysis: An introduction to basic and advanced multilevel modeling* (2nd ed.). London: Sage.

Muthen, L. K., & Muthen, B. O. (1998 – 2016). *Mplus user’s guide: Statistical analysis with latent variables* (7th ed.). Los Angeles, CA: Author.

http://www.statmodel.com/download/usersguide/MplusUserGuideVer_7.pdf

**Mandatory readings before course start:**

None.

**Examination part**

Students will be evaluated on the basis of performance on a set of exercises (a problem set) to be completed and submitted within 2 weeks after the course.

**Supplementary aids**

It will be necessary to have a working copy of Mplus and access to the (free) *Mplus User Guide*. It will be helpful to use the course slides and to refer to examples of Mplus syntax used during the course.

**Examination content**

The problem set will potentially cover the following topics: basic multilevel models with fixed and random slopes; power analysis for MLM; cross-classified random effets; basic SEM; Mplus syntax; interpretation of Mplus output; multilevel versions of path analysis, factor analysis, and SEM; 3-level models; multilevel reliability; multilevel mediation and moderation; and MLM with discrete outcomes. All relevant material is contained in the course slides and example Mplus syntax.

**Exam Literature**

It will be necessary to have a working copy of Mplus and access to the (free) *Mplus User Guide*.

**Work load**

At least 24 units 45 minutes each on 5 consecutive days