## Course "Structural equation modeling with lavaan" |

28.-30.04.2015 in Tartu

Structural equation modeling (SEM) is a general statistical modeling technique to study the relationships among a set of observed variables. It spans a wide range of multivariate methods including path analysis, mediation analysis, confirmatory factor analysis, growth curve modeling, and many more. Many applications of SEM can be found in the social, economic, behavioral and health sciences, but the technology is increasingly used in disciplines like biology, neuroscience and operation research. SEM is often used to test theories or hypotheses that can be represented by a path diagram. In a path diagram, observed variables are depicted by boxes, while latent variables (hypothetical constructs measured by multiple indicators) are depicted by circles. Hypothesized (possibly causal) effects among these variables are represented by single-headed arrows. If you have ever found yourself drawing a path diagram in order to get a better overview of the complex interrelations among some key variables in your data, this course is for you. The first day of the course provides an introduction to the theory and application of structural equation modeling. The second and third day of the course are more advanced and discuss the use of SEM with categorical and longitudinal data respectively.

The aim of this workshop is twofold. First, we will present a concise overview of the theory of structural equation modeling (SEM), including many special topics (e.g. handling missing data, nonnormal data, categorical data, longitudinal data, etc.). Second, hands-on sessions are included in order to ensure that all participants are able to perform the analyses using SEM software. The software used in this course is the open-source R package lavaan' (see http://lavaan.org).

This three-day course will be based on lecture-style presentations interchanged with practical sessions.

Prior knowledge:

Participants should have a solid understanding of regression analysis and basic statistics (hypothesis testing, p-values, etc.). Some knowledge of exploratory factor analysis (or PCA) is recommended, but not required. Because lavaan is an R package, some experience with R (reading in a dataset, fitting a regression model) is recommended, but not required.

Please install the latest version of R (3.2.0), and the latest version of lavaan (0.5-18). See http://lavaan.ugent.be/start.html for further instructions.

Optionally, you may want to install Rstudio (see http://www.rstudio.com/products/RStudio/) as it provides a convenient working environment to work with R.

• SEM basics

• model estimation, model evaluation, and model respecification

• introduction to lavaan

• meanstructures, multiple groups, and measurement invariance

• missing data

• non-normal continuous data and alternative estimators

• refresher of probit and logit regression

• history of SEM with categorical data

• when should we use categorical techniques?

• tetrachoric, polychoric and polyserial correlations

• the limited-information (three-stage) approach (ULS, WLS and robust variants)

• the full-information approach (ML)

• new approaches to handle categorical data

• the relationship with item response theory (IRT)

• overview of longitudinal data

• repeated measures ANOVA in a SEM framework

• the longitudinal CFA model, establishing time invariance

• autoregressive models, cross-lagged effects

• growth curve models, and the relationship with linear mixed effects models

• autoregressive latent trajectory models

• latent change score models

- Rosseel, Y. (2012). lavaan: An R Package for Structural Equation Modeling. Journal of Statistical Software, 48(2), 1-36.
- MacCallum, R. C., & Austin, J. T. (2000). Applications of structural equation modeling in psychological research. Annual review of psychology, 51(1), 201-226.
- Tomarken, A. J., & Waller, N. G. (2005). Structural equation modeling: Strengths, limitations, and misconceptions. Annu. Rev. Clin. Psychol., 1, 31-65

- Schreiber, J. B., Nora, A., Stage, F. K., Barlow, E. A., & King, J. (2006). Reporting structural equation modeling and confirmatory factor analysis results: A review. The Journal of Educational Research, 99(6), 323-338.
- McArdle, J. J. (2009). Latent variable modeling of differences and changes with longitudinal data. Annual review of psychology, 60, 577-605.

- Muthén, B. (1984). A general structural equation model with dichotomous, ordered categorical, and continuous latent variable indicators. Psychometrika, 49(1), 115-132.
- Takane, Y. & DeLeeuw, J. (1987). On the relationship between item response theory and factor analysis of discretized variables. Psychometrika, 52, 393-408.
- Rabe-Hesketh, S., Skrondal, A., & Pickles, A. (2004). Generalized multilevel structural equation modeling. Psychometrika, 69(2), 167-190.

After the course, all participants are encouraged to analyze their own data using SEM, and write up the results as a short project paper. The paper should contain a brief description of the context and the research questions, and a full description of the SEM analysis. The appendix should include the full R script that has been used to produce the results as they are reported in the paper. Projects papers are corrected, and participants receive feedback.