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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Quantoids corner: Rasch psychological measurement (IRT) references

Someone just asked me a question about Rasch (item response theory) measurement. I ran a search of the IAP Reference Database and flagged any reference that had "Rasch" as a keyword (in Procite). I've posted a copy in case anyone is looking for a relatively list of contemporary Rasch psychometric references.

Quantoids corner: Confirmatory factor analysis guidelines

Just read a good article in Psychological Methods on the state-of-the-art of CFA methods, statistical methods used with considerable frequency in intelligence research. Here is a nifty manuscript/research checklist ... double click on image to enlarge. I will follow-up with a more detailed post in the next few days.

Quantoids corner: Psychological Methods - Volume 14, Issue 1

Sent from KMcGrew iPhone (IQMobile). (If message includes an image-double click on it to make larger-if hard to see)

Begin forwarded message

Psychological Methods

Volume 14, Issue 1

Estimating standardized linear contrasts of means with desired precision.

Pages 1-5

Bonett, Douglas G.

Reporting practices in confirmatory factor analysis: An overview and some recommendations.

Pages 6-23

Jackson, Dennis L.; Gillaspy Jr., J. Arthur; Purc-Stephenson, Rebecca

Meta-analysis of correlations revisited: Attempted replication and extension of Field's (2001) simulation studies.

Pages 24-42

Hafdahl, Adam R.; Williams, Michelle A.

Effect sizes for growth-modeling analysis for controlled clinical trials in the same metric as for classical analysis.

Pages 43-53

Feingold, Alan

Evaluating cognitive theory: A joint modeling approach using responses and response times.

Pages 54-75

Klein Entink, Rinke H.; Kuhn, Jörg-Tobias; Hornke, Lutz F.; Fox, Jean-Paul

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Quantoids corner: Dealing with (and planning for) missing data in data gathering

It has been a long time since I've made a post that may tweak the cockles of the quantoids who read this blog. This is one for my fellow quants....and is also intended for those less quantitatively oriented---as the topic is one that will mentioned with greater regularity in research articles, test manuals, etc.

Missing data has been a problem that has plagued researchers and test developers for decades. Over the past 20 years very sophisticated methods of handling missing data and producing "complete" data sets via sophisticated statistical algorithms have become available. And....many individuals who have run data may have used these procedures and have been completely unaware that their analysis used imputed or plausible values! For example, if you use one of the primary structural equation modeling (SEM) software programs (e.g., LISREL; Mplus; AMOS), and you had incomplete data on some subjects, the programs most likely utilized one of these new algorithms to impute plausable values before running the SEM model.

I've been schooling myself on this literature for the past 15 years and have found these contemporary missing data imputation methods very useful. More and more researchers need to become aware of the benefits of these methods, as well as some of the nuances of using it correctly.

This past week I received a copy of the latest issue of the Annual Review of Psychology and found (to my pleasure) probably the most simple, conceputal, understandable summary of this area of statistics. I was not surprsied to see that it was written by John Graham, who has written many other important journal articles on this topic. I would urge the readers of IQs Corner who conduct applied research or test develpoment projects to read this overview article. It is well worth the read. Also, I would suggest that readers take a serious look at the NORM software of Schaefer...the program I use when serious data imputation is necessary. A nicely written description of the program, as well as a short and sweet overview of some of the missing data literature, is available in an article written by Darmawan (2004).

What is really cool is the concept of "planned missing data"-----that is, designing one's data collection project to deliberately have missing data in order to allow for the collection of more variables across a larger number of subjects....which can then be handled (if designed correctly) via these new quantoid toys.

Fellow (and future) quantoids...enjoy

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