# Learning Multilevel Analysis

**By Professor Kristen Ringdal**

## Introduction

### Multilevel analysis

Multilevel analysis, or modelling, has become popular in many fields of social research that have hierarchically organized data in units of analysis at two or more levels. Multilevel analysis can be regarded as a generalization of OLS regression analysis that accommodates the additional complexities involved in estimating regression models with two or more levels. The concepts of *multilevel models* or *hierarchical linear models* are frequently used in sociology, but the same models are known in other fields as *mixed-effects models*, *random effects models* or *random coefficient models*, and *variance component models*. Multilevel models for categorical dependent variables will not be covered in this module. Examples will be restricted to models with two levels, although extending them to three levels is straightforward. All models can be estimated in SPSS and Stata, and syntaxes for both programs will be included. For SPSS, a definition of models from the menus will also be presented.

### Symbolic notation

The notation also differs between subject fields and between authors. The three most frequently used notation systems stem from the research groups responsible for developing the best known software for multilevel analysis, HLM [Rad02], Mlwin [Gol95], and Stata [Rab12]. This text builds on the Mlwin notation, which is closest to the notation used in OLS regression.

### Outline of the module

The module is divided into chapters. Since a working knowledge of multiple regression analysis is essential to understanding multilevel models, the first chapter reviews the basics of OLS regression based on a wage data set. The second chapter reviews basic concepts and the principle of estimation of multilevel models. Software for multilevel analysis is used to estimate one-level regression models. The basic two-level regression models are presented in Chapter 3. In Chapter 4, the analytic strategy outlined at the end of Chapter 3 is applied to the wage formation example. In Chapters 5 and 6, we will practise multilevel analysis using data from the European Social Survey. The dependent variable in Chapter 5 is happiness and, in Chapter 6, political trust.

#### References

- [Gol95] Goldstein, H. (1995), Multilevel Statistical Models, 2nd edition. London: Edward Arnold.
- [Rab12] Rabe-Hesketh, Sophia and Anders Skrondal (2012), Multilevel and Longitudinal Modeling Using Stata. 3nd edition. Volume I: Continuous Responses. College Station, Texas: Stata Press.
- [Rad02] Raudenbush, S.W. and Bryk, A.S. (2002), Hierarchical Linear Models. Applications and Data Analysis Methods, 2nd edition. Sage: Thousand Oaks.