Multilevel analysis

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Multilevel analyzes ( English Multi Level Modeling ), also called Hierarchical linear modeling ( English Hierarchical Linear Modeling known) are a group of multivariate statistical method for analysis of hierarchically structured data ( English nested data ), which especially in the empirical research apply.

In contrast to models with only one level, the data is sampled on several levels. Multi-level analyzes are significantly more flexible than, for example, applications of the general linear model such as analysis of variance and linear regression, but this also makes them much more methodologically demanding. The parameters are estimated using the maximum likelihood method; a computational determination is not possible. There are typically two reasons for using a multilevel model: 

 1. Es liegen gruppierte (geclusterte) Daten vor (siehe Abschnitt Ebenen).
 2. Es liegen Daten im Längsschnitt vor (siehe Abschnitt Messwiederholungen).

Related terms are the panel data model with fixed effects ( English fixed effects model ) and the panel data model with random effects ( English random effects model ), mixed model , variance component model , or latent curve analysis .

In the meantime, all major statistical software packages have implemented multi-level models. B. in IBM SPSS Statistics MIXED, in SAS PROC MIXED.

Levels

Lots of dates, v. a. in the social and natural sciences, are hierarchically structured, i.e. H. they can be assigned to groups or clusters , e.g. B. children to families, pupils to school classes, people to places of residence, patients to clinics, etc. Many experiments in the social sciences also lead to group formation, e.g. B. Participants in study centers (in a multicenter study ).

Examples of hierarchical data are e.g. B. the grouping of students in classes and schools (3-level model: level 1: individual student; level 2: school class; level 3: school) or the assignment of individuals to families (2-level model: level 1: Child; level 2: family).

If an examined individual can be assigned to a group, a mutual influencing process between the individual and the group can be assumed. Therefore, neglecting grouping effects can lead to misinterpretation of empirical results.

Repeated measurements

If the same measurement is carried out repeatedly on the same individual, the levels can be assigned as follows:

  • Level 1: individual measurement in the individual i
  • Level 2: individual i

Process such as B. Analyzes of variance for repeated measurements require a special data structure, e.g. B. the same number of measurement times for all individuals or completeness of the data for an individual over all measurement times. When using multi-level models, the number of measurement times can vary, which makes the method less susceptible to individual missing data.

In addition to the flexible handling of missing data, multilevel models have the advantage that, in contrast to traditional regressions, they correctly associate the subject with its repeated measurements. Furthermore, it is possible to differentiate between temporally stable and unstable predictors and to better estimate the intra- and inter-individual variance components of the test subjects.

application

Multi-level models are used, among other things, in social science modeling and simulation , in particular to model context effects. In psychotherapy research , multi-level models are used, for example, as part of so-called patient profiling in order to obtain information on the expected course of therapy in the respective patient based on context factors at the start of therapy (e.g. characteristics of the patient, type of therapy).

literature

  • Anthony S. Bryk & Stephan W. Raudenbush: Hierarchical Linear Models. Applications And Data Analysis Methods . Sage Publications, 1992.
  • Ditton, Hartmut: multilevel analysis. Basics and applications of the hierarchical linear model . Juventa Verlag Weinheim and Munich, 1998.
  • Engel, Uwe: Introduction to multilevel analysis. Basics, evaluation methods and practical examples . Opladen / Wiesbaden: Westdeutscher Verlag, 1998, ISBN 978-3531221823 .
  • Harvey Goldstein : Multilevel Statistical Models. Chichester: Wiley, 4th ed., 2011, ISBN 978-0-470-74865-7 .
  • Hox, JJ: Multilevel analysis. Techniques and applications. Mahwah: Lawrence Erlbaum, 2002.
  • Langer, Wolfgang: Multi-level analysis. An introduction to research and practice . Wiesbaden: VS-Verlag, 2nd edition, 2009, ISBN 978-3-531-15685-9 .
  • Jan de Leeuw and Erik Meijer: Handbook of Multilevel Analysis . Springer, 2008, ISBN 978-0-387-73183-4 .
  • Long, JD: Longitudinal Data Analysis for the Behavioral Sciences Using R . Thousands Oaks: Sage, 2012.

Individual evidence

  1. ^ Harvey Goldstein: Multilevel Models in Educational and Social Research . London, Griffin, 1987.
  2. ^ A b Anthony S. Bryk, Stephen W. Raudenbush: Application of Hierarchical Linear Models to Assessing Change . Psychological Bulletin , 1987, 101, pp. 147-158.
  3. ^ P. Diggle, K. Liang, S. Zeger: Analysis of Longitudinal Data . New York: Oxford Univ. Press, 1994.
  4. ^ SR Searle, G. Casella, CE McCulloch: Variance components. New York: Wiley, 1992.
  5. ↑ W. Meredith, J. Tisak: Latent curve analysis. Psychometrika 55, 1990, pp. 107-22.
  6. ↑ a b Stephen W. Raudenbush: Comparing Personal Trajectories and Drawing Causal Inferences from Longitudinal Data. Annual Review of Psychology, 2001, 52, pp. 501-525.
  7. ↑ a b Ferdinand Keller: Analysis of longitudinal data: evaluation options with hierarchical linear models. Journal for Clinical Psychology and Psychotherapy, 2003, 32 (1), pp. 51–61.
  8. ↑ a b Harvey Goldstein: Multilevel Statistical Models. First Internet Edition, 1999. http://www.ats.ucla.edu (accessed May 14, 2012)
  9. ↑ Wolfgang Lutz , Zoran Martinovich, Kenneth I. Howard : Patient Profiling: An Application of Random Coefficient Regression Models to Depicting the Response of a Patient to Outpatient Psychotherapy . Journal of Consulting and Clinical Psychology , 1999, 67 (4), pp. 571-77.