Hierarchical linear modeling
Encyclopedia
In statistics
, hierarchical linear modeling (HLM), a form of multi-level analysis
, is a more advanced form of simple linear regression
and multiple linear regression. Multilevel analysis allows variance in outcome variables
to be analysed at multiple hierarchical levels, whereas in simple linear and multiple linear regression all effects are modeled to occur at a single level. Thus, HLM is appropriate for use with nested data.
For example, in educational research, data are often considered with pupils nested in classrooms nested within schools. In organizational psychology
research, data from individuals must often be nested within teams or other functional units. For repeated measures
data, time can be considered as another level which occurs within participants.
Multilevel analysis has been extended to include multilevel structural equation modeling
, multilevel latent class model
ing, and other more general models.
Software
Other resources
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, hierarchical linear modeling (HLM), a form of multi-level analysis
Multilevel model
Multilevel models are statistical models of parameters that vary at more than one level...
, is a more advanced form of simple linear regression
Simple linear regression
In statistics, simple linear regression is the least squares estimator of a linear regression model with a single explanatory variable. In other words, simple linear regression fits a straight line through the set of n points in such a way that makes the sum of squared residuals of the model as...
and multiple linear regression. Multilevel analysis allows variance in outcome variables
Variable (mathematics)
In mathematics, a variable is a value that may change within the scope of a given problem or set of operations. In contrast, a constant is a value that remains unchanged, though often unknown or undetermined. The concepts of constants and variables are fundamental to many areas of mathematics and...
to be analysed at multiple hierarchical levels, whereas in simple linear and multiple linear regression all effects are modeled to occur at a single level. Thus, HLM is appropriate for use with nested data.
For example, in educational research, data are often considered with pupils nested in classrooms nested within schools. In organizational psychology
Industrial and organizational psychology
Industrial and organizational psychology is the scientific study of employees, workplaces, and organizations. Industrial and organizational psychologists contribute to an organization's success by improving the performance and well-being of its people...
research, data from individuals must often be nested within teams or other functional units. For repeated measures
Repeated measures design
The repeated measures design uses the same subjects with every condition of the research, including the control. For instance, repeated measures are collected in a longitudinal study in which change over time is assessed. Other studies compare the same measure under two or more different conditions...
data, time can be considered as another level which occurs within participants.
Multilevel analysis has been extended to include multilevel structural equation modeling
Structural equation modeling
Structural equation modeling is a statistical technique for testing and estimating causal relations using a combination of statistical data and qualitative causal assumptions...
, multilevel latent class model
Latent class model
In statistics, a latent class model relates a set of observed discrete multivariate variables to a set of latent variables. It is a type of latent variable model. It is called a latent class model because the latent variable is discrete...
ing, and other more general models.
External links
Books- Hierarchical Linear Models (Second Edition). Thousand Oaks: Sage Publications, 2002. Stephen RaudenbushStephen RaudenbushStephen Raudenbush is the Lewis-Sebring Professor of Sociology and Chairman of the Committee on Education at the University of Chicago. He is best known for his development and application of hierarchical linear models in the field of education but he has also published on other subjects such as...
and Anthony Bryk. - Applied Longitudinal Data Analysis (Singer & Willett, 2003)
Software
- Mplus
- “HLM” — Proprietary software - http://www.ssicentral.com/hlm/
- MLwiN software
- Don Hedeker: Free Multilevel Software
Other resources