

"Negative Nonindependence"/"Frog Pond... 

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Hi, does anyone have any experience with modeling multilevel data where there is a negative ICC? I have run across such a problem and believe that, whenever there is a type of "zero sum" effect (e.g., amount of time talking for each person within a group in a 5 minute period) or an effect where ingroup members want maximal differentiation within group, this will be very common. I can also imagine other instances (e.g., outcomes of tennis matches, where 1 = win and 0 = lose, and players are nested within matches) where this type of effect is common. I know that HLM, because it calculates nonindependence using variance terms, cannot handle such a model. Can Mplus (I am assuming not)? If not, in singlelevel analyses, should correction to parameters based on ICCs be done by hand (computing ICC with a method which allows it to be negative... this would be simple because when ICC = .5 or .5, this is the same degree of nonindependence)? How 'bout multilevel analyses, any possibilities? Thanks for any reply. 

bmuthen posted on Monday, July 18, 2005  5:14 pm



I don't have experience with this. I know there is some writing on it, say in the Gary Koch's encyclopedia entrance on icc. Perhaps you can attempt to capture this if you can model the interaction between group members using a "multivariate approach", that is having all members explicitly in the model. 


Klein, Dansereau and Hall in their AMR paper "Levels issues in theory development, data collection, and analysis" refer to the Frog Pond effect, when individuals' scores on Y depend not only on their scores on X, but also on the size of the X relative to those of others in the social group. Thus, relative, not absolute, value is predictive. What would be the strategy to perform such analysis using Mplus? 


See the following paper which is available on the website: Lüdtke, O., Marsh, H.W., Robitzsch, A., Trautwein, U., Asparouhov, T., & Muthén, B. (2008). The multilevel latent covariate model: A new, more reliable approach to grouplevel effects in contextual studies. Psychological Methods, 13, 203229. Google Marsh et al. for big fish small pond papers. 

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