## Thursday, July 15, 2010

### Quantoids corner: Intro to hierarchical linear modeling (HLM)

I LOVE it when more applied journals publish articles where complex statistical methods are presented to a less statistically oriented audience, as I often find these "quanatoid explanations for dummies" an excellent introduction to complex statistical methods.  Today I discovered that Gifted Child Quarterly has published a brief two-part series of articles that provide a nice introduction to HLM.  I've never run HLM models, so I found the introduction very helpful.  So much so that I might run some HLM on some appropriate datasets I have just to see it work.

Below are the two articles.  Enjoy.  Kudos to GCQ and Dr. McCoach.

McCoach, D. B. & Adelson, J. L.  Dealing with dependence (Part 1):  Understanding the effects of clustered data.  Gifted Child Quarterly, 54(2), 152-155.
This article provides a conceptual introduction to the issues surrounding the analysis of clustered (nested) data. We define the intraclass correlation coefficient (ICC) and the design effect, and we explain their effect on the standard error. When the ICC is greater than 0, then the design effect is greater than 1. In such a scenario, the standard error produced under the assumption of independence is underestimated. This increases the Type I error rate. We provide a short illustration of the effect of non-independence on the standard error. We show that after accounting for the design effect, our decision about the statistical significance of the test statistic changes. When we fail to account for the clustered nature of the data, we conclude that the difference between the two groups is statistically significant. However, once we adjust the standard error for the design effect, the difference is no longer statistically significant.

McCoach, D. B. (2010). Dealing With Dependence (Part II): A Gentle Introduction to Hierarchical Linear
Modeling. Gifted Child Quarterly, 54(3), 252-256.
In education, most naturally occurring data are clustered within contexts. Students are clustered within classrooms, classrooms are clustered within schools, and schools are clustered within districts. When people are clustered within naturally occurring organizational units such as schools, classrooms, or districts, the responses of people from the same cluster are likely to exhibit some degree of relatedness with each other. The use of hierarchical linear modeling allows researchers to adjust for and model this non-independence. Furthermore, it may be of great substantive interest to try to understand the degree to which people from the same cluster are similar to each other and then to try to identify variables that help us to understand differences both within and across clusters. In HLM, we endeavor to understand and explain between- and within-cluster variability of an outcome variable of interest. We can also use predictors at both the individual level (level 1), and the contextual level (level 2) to explain the variance in the dependent variable. This article presents a simple example using a real data set and walk through the interpretation of a simple hierarchical linear model to illustrate the utility of the technique.

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