Inequality Constrained Multilevel Models
In many areas of research, datasets have a multilevel or hierarchical structure. By hierarchy we mean that units at a certain level are grouped or clustered into, or nested within, higher-level units. The “level” signifies the position of a unit or observation within the hierarchy. This implies that the data are collected in groups or clusters. Examples of clusters are families, schools, and firms. In each of these examples a cluster is a collection of units on which observations can be made. In the case of schools, we can have three levels in the hierarchy with pupils (level 1) within classes (level 2) within schools (level 3). The key thing that defines a variable as being a level is that its units can be regarded as a random sample from a wider population of units.
KeywordsPosterior Distribution Prior Distribution Mathematics Achievement Markov Chain Monte Carlo Method Catholic School
Unable to display preview. Download preview PDF.
- Berg, W. van den, Eerde, H.A.A. van, Klein, A.S.: Proef op de som: Praktijk en resultaten van reken/wiskundeonderwijs aan allochtone leerlingen op de basisschool [Practice and Results of Education Arithmatics and Mathematics for Immigrant Children in Elementary School]. Rotterdam, RISBO (1993)Google Scholar
- Browne, W.J.: MCMC Estimation in MLwiN (Version 2.0). London, Institute of Education University of London (2003)Google Scholar
- Bryk, A.S., Raudenbush, S.W.: Hierarchical Linear Models: Applications and Data Analysis Methods. London, Sage (1999)Google Scholar
- Gelman, A.: Scaling regression inputs by dividing by two standard deviations. Statistics in Medicine (in press)Google Scholar
- Gelman, A., Hill, J.: Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge, Cambridge University Press (2007)Google Scholar
- Goldstein, H.: Multilevel Statistical Models (2nd edition). London, Edward Arnold (1995)Google Scholar
- Hox, J.: Multilevel Analysis: Techniques and Applications. London, Lawrence Erlbaum Associates (2002)Google Scholar
- Singer, J.D.: Using SAS PROC MIXED to fit multilevel models, hierarchical models, and individual growth models. Journal of Educational and behavioral Statistics, 24, 323–355 (1998)Google Scholar
- Singer, J.D., Willett, J.B.: Applied Longitudinal Data Analysis: Modeling Change and Event Occurrence. New York, Oxford University Press (2003)Google Scholar