Multi-level Analysis using Mplus: Online

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 the 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 measured at a third level (e.g. multiple students nested within multiple classes, multiple classes nested in multiple schools).

Day 5

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.

Consultations. During the course, Phil will make appointments with participants who want help with their own research problems. These appointments will be scheduled either before, between or after instruction time on the last two days of the course.