Multi-level Analysis using Mplus

This course is designed as an introduction to the concepts and techniques required to analyse data that is multi-level in nature. (That is data that is derived from subjects who are nested within groups or data that involves repeated measures that are nested within subjects)

Level 4 - runs over 5 days

Mr Philip Holmes-Smith is the principal consultant with School Research, Evaluation and Measurements Services (SREAMS), an independent educational research consultancy business. His research, evaluation and measurement interests lie in the areas of teacher effectiveness and school improvement, accountability models and benchmarking, improving the quality of teaching, using student performance data to inform teaching, and large-scale achievement testing programs. He is an experienced teacher of social science research methods and is a regular instructor at the ACSPRI programs. He also regularly teaches Structural Equation Modeling (SEM) and Multi-Level Analysis (MLA) at various universities around Australia.

Course dates: Monday 8 February 2016 - 5 12 February 2016
Course status: Course completed (no new applicants)
Week 3
About this course: 

In conventional regression analysis it is assumed that subjects are randomly selected and, therefore, all the variance in your dependent variables is due solely to variation amongst individuals. However, when subjects are clustered within a group and multiple groups are sampled (e.g. students clustered within multiple classes), although some of the variance in your dependent variables will be due to variation amongst individuals, some the variance in your dependent variables will also be due to variation amongst the groups themselves. In such cases, multilevel analysis (MLA) should be employed to account for the different levels of variation.

Repeated measure designs should also be analysed using multilevel analysis because the repeated observations are nested within subjects. (For example, in marketing we may have repeated measures of consumers’ attitudes to a brand over the life of a marketing campaign; in epidemiology we may have repeated measures of a health outcome over the life of a drug treatment regime.)

This course is designed take participants from an introductory level up to an intermediate level of multilevel analysis. That is, the course assumes that participants have had no prior experience with multilevel modeling (or have only a basic understanding) and takes participants through the basics up to an intermediate level. Although there are several programs that can be used to conduct multilevel analysis, in this course we will use the Mplus program.


Detailed notes with worked examples and references will be provided as a basis for both the lecture and hands-on computing aspect of the course.


The target audience for this course is researchers needing to learn how to analyse data that has been collected through a hierachical sampling approach using Mplus software.

Course syllabus: 

Day 1  
Introduction to multilevel data, revision of basic analytical techniques and an introduction to multilevel modeling. This part of the course describes the nature of multilevel data, introduces the Mplus programming language by revising basic single-level regression models and basic single-level confirmatory factor analysis and introduces to principals and nomenclature of multilevel modeling. We will note the difference between the conventional (single-level) regression approach and the multilevel regression approach, we will highlight the dangers of not treating nested data as multilevel data and we will discuss the advantages of multilevel analysis.


Day 2
Two-level regression models. These models investigate two-level research questions where subjects are nested within groups and explanatory (independent) variables have been measured at the subject level (Level 1) and/or the group level (Level 2). For example, in education, our outcome variable may be “reading comprehension” and we could regress this outcome on both Level 1 independent variables (e.g. the student’s verbal reasoning skills, their motivation to learn, etc.) and Level 2 independent variables (e.g. the teachers experience, the average ability of all students within the class, etc.). In each example we will build models from the simplest variance component model to investigating random intercepts and finally, random slopes.


Day 3
Two-level latent growth-curve models (repeated measure designs): These models investigate change over time and enable the researcher to describe how an outcome (dependent) variable is improving or declining across a number of repeated measures. For example, in marketing we may be interested in analysing consumers’ attitudes to a brand over the life of a marketing campaign. The repeated measure (attitudes) may improve as a function of time but different marketing techniques (a time varying independent variable) may also influence the rate of improvement. Both linear and non-linear growth will be investigated.


Day 4
Two-level confirmatory factor analysis (CFA) and structural equation modeling (SEM): These models introduce latent variables into the multilevel modeling framework. In multilevel CFA models, the dependent variable is a factor (rather than an observed variable). Such models may or may not contain observed explanatory variables. In multilevel SEM the independent variable(s) is/are a factor (rather than an observed variable). Such models may contain observed and/or latent dependent variables.
Three-level Models. These models investigate three-level research questions where subjects are either nested within sub-groups and sub-groups are nested within higher level groups or repeated measures are nested within subjects who, in turn, are nested within groups. Now, not only are the explanatory (independent) variables measured at the subject level (Level 1) and/or the sub-group level (Level 2) but they may also be measure at a third level (e.g. students nested within classes, classes nested in schools).
Mixture Modeling (including Latent Class Analysis). Mixture models are similar to Multilevel models in that patterns in the data vary across different groups. The difference, however, is that group membership is determined by the data, not some a priori allocation to groups. Cross-sectional models include Mixture regression analysis; Latent Class Analysis (LCA); CFA mixture modeling; and Structural equation mixture modeling. Longitudinal models include Growth Mixture Modeling (GMM) for a continuous outcome; and Latent Class Growth Analysis (LCGA) for a binary, ordinal or count outcome.


Day 5
Personal Research. Finally, on the last day, participants have an opportunity to work on their own research problems with the instructor’s assistance. Therefore participants are encouraged to bring a multilevel data set and/or research problem with them.

Course format: 

This course will take place in a computer lab. All equipment will be supplied. You are encouraged to bring a data set and/or research problem with you.

Recommended Background: 

No prior knowledge of multilevel analysis is required nor is it assumed that participants have had experience with Mplus – the Mplus programming language will be taught as part of the course. However, it is assumed that all participants will have a thorough understanding of regression analysis and factor analysis. Furthermore, it is assumed that all participants have completed a course in Structural Equation Modeling (SEM) or have had equivalent SEM experience.

Recommended Texts: 

Other references include:

  • Muthén, L.K. and Muthén, B.O. (1998-2012). Mplus User’s Guide. Seventh Edition. Los Angeles, CA: Muthén & Muthén.
  • Snijders, Tom A.B. and Bosker, Roel J. (2012). Multilevel Analysis: An Introduction to Basic and Advanced Multilevel Modeling. (2nd Ed.). London: Sage Publications
  • Kline, Rex B. (2015). Principles and Practice of Structural Equation Modeling (4th Ed.). New York: Guilford Press.
Course fees
Non Member: 
Full time student Member: 

Q: Do I have to have to know anything about Multilevel Analysis before attempting the course?

A: No prior knowledge of multilevel analysis is required nor is it assumed that participants have had experience with Mplus.

Participant feedback: 

Great notes, clear explanation & a focus on our own research with one on one time was excellent (Winter 2014)


The instructor is very patient and he responds to every question very well. (Winter 2014)


It was not only helpful so far as the specific course content was concerned but also so far as all the additional material & background revision was concerned (eg. reviewing regression analysis & explanatory & confirmatory factor analysis dealing with mis (Summer 2015)


More advanced knowledge on the topic - and particularly a different perspective. Understood some new concepts that I’d had trouble grasping when taught previously. (Summer 2015)


Course was found to be good pace & quality. (Summer 2015)

Summer Program 2016

The instructor's bound, book length course notes will serve as the course texts.

Supported by: 

Mplus Logo