# Statistics: Hierarchical linear models

## When should we use hierarchical models?

• Osborne, Jason W. (2000). "Advantages of hierarchical linear modeling." Practical Assessment, Research & Evaluation, 7(1). Retrieved November 12, 2005 from http://PAREonline.net/getvn.asp?v=7&n=1.
Hierarchical, or nested, data structures are common throughout many areas of research. However, until recently there has not been any appropriate technique for analyzing these types of data. Now, with several user-friendly software programs available, and some more readable texts and treatments on the topic, researchers need to be aware of the issue, and how it should be dealt with. The goal of this paper is to introduce the problem, how it is dealt with appropriately, and to provide examples of the pitfalls of not doing appropriate analyses.

• Greenland, S. (2000) "When Should Epidemiologic Regressions Use Random Coefficients?", Biometrics, 56, 915-921 [1] (http://80-resolver.scholarsportal.info.ezproxy.library.yorku.ca/resolve/0006341x/v56i0003/915_wserurc&form=pdf&file=file.pdf)
Abstract: Regression models with random coefficients arise naturally in both frequentist and Bayesian approaches to estimation problems. They are becoming widely available in standard computer packages under the headings of generalized linear mixed models, hierarchical models, and multilevel models. I here argue that such models offer a more scientifically defensible framework for epidemiologic analysis than the fixed-effects models now prevalent in epidemiology. The argument invokes an antiparsimony principle attributed to L. J. Savage, which is that models should be rich enough to reflect the complexity of the relations under study. It also invokes the countervailing principle that you cannot estimate anything if you try to estimate everything (often used to justify parsimony). Regression with random coefficients offers a rational compromise between these principles as well as an alternative to analyses based on standard variable-selection algorithms and their attendant distortion of uncertainty assessments. These points are illustrated with an analysis of data on diet, nutrition, and breast cancer. [cf. Make everything as simple as possible, but not simpler. -- Albert Einstein]
• Singer, Judith D. and John B. Willett, (2003) Applied Longitudinal Analysis, Oxford.