# Advanced Multilevel Analysis

This three-day course will teach you advanced topics in multilevel modelling. It builds upon the contents of the other summer course ‘Introduction to multilevel analysis’. It consists of three days with lectures in the morning and computer labs in the afternoon. During the computer labs, the R and R studio programmes will be used. After taking this course, you should be able to analyse more complex multilevel models and interpret and report the results.

This three-day course builds upon the contents of the course ‘Introduction to multilevel analysis’. It consists of three days with lectures in the morning and computer labs in the afternoon.

The focus of the first day is on categorical outcome data, in particular binary, ordinal and event history outcomes. It will be shown why linear multilevel models are not appropriate for such data and how multilevel generalized linear models can be used to fit this type of outcome data. Attention will be paid to estimation procedures that are available and how the intraclass correlation coefficients and proportions explained variance are calculated. Special attention is paid to the interpretation of the estimated regression weights in terms of the logits and odds ratios. Analyses will be done in HLM, Mplus and R.

The focus of the second day is on multilevel factor analysis and multilevel structural equation modelling. The interest of such models is generally on theoretical constructs, which are presented by latent factors. It will be shown how to specify factor models at the between- and within-level and how to use fit indices to evaluate model fit. Path models consist of complex paths between latent and/or observed variables, possibly including direct and indirect effects. With multilevel path models, we often have the complication that there are different variables at the individual and group level. Mplus and R will be used to specify and fit such models.

The focus of day three is on random cross-classifications and statistical power analysis. An example of a random cross-classification is pupils nested within schools and neighbourhoods. In this example a random effect should be included for schools and another one for neighborhoods, and the two may even covary. Such models can be fitted in HLM and R and special attention to the interpretation of results will be given. The aim of an a priori statistical power analysis is a calculation of sample size such that an effect can be detected with a sufficient probability. With a two-level model there are two sample sizes: the number of groups and the group size. For some simple experimental designs these sample sizes can be calculated on the basis of mathematical formulae and a demonstration of software will be given. For more complex designs, a simulation study has to be conducted to calculate sample size. It will be shown how to design such a simulation study and how to execute it in Mplus.

Participants are expected to have taken the course Introduction to Multilevel Analysis or a similar course with the same contents (i.e. chapters 1-5 from Hox, Moerbeek and Van de Schoot (2018). Participants are also expected to have experience with analyzing multilevel data in common software such as Mplus, SPSS, R, HLM, or MLwiN. During the computer labs the R and R studio programmes will be used.

Hox, J., Moerbeek, M., & Van de Schoot, R. (2018). Multilevel analysis. Techniques and Applications. 3rd edition. New York: Routledge.

The book is not included in fee (about € 45).

Participants are requested to bring their own laptop computer. Software will be available online.

## Target audience

PhD students and researchers in the fields of social and behavioural sciences, medicine, health sciences, social geography, A maximum of 40 participants will be admitted to this course. The selection for this course will be done on a first-come-first-served basis. Please note that there are no graded activities included in this course. So we will not be providing students with a transcript of grades. You will obtain a certificate of participation upon completion of this course.

## Aim of the course

Participants will learn to analyze advanced multilevel models and interpret the output and to perform a power analysis.