

Withinvariables with betweenvariance 

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student07 posted on Tuesday, July 31, 2007  2:40 pm



I would be glad for advice concerning the following question: when using 'type = twolevel basic', I find considerable betweengroup variance (e.g. ICCs around .10) for a number of variables (e.g. education, age). However, originally I wanted to use these variables as control variables for my substantive construct (a factor measured on both the within and betweenlevel) only. Thus, given that I am not interested in modelling the betweengroup variation of these controls, I thought it be would be fine to declare these controls as withinvariables using the WITHINcommand. However, I am unsure whether this would be correct  does declaring variables with betweengroup variation as WITHINvariables necessarily bias the findings? 


It is ok to keep these variables as WITHIN. This simply says that you are using the whole variable and don't divide it up into within and between components. If on the other hand you had a control variable that only varied across between units you would have to declare it as BETWEEN to get the right SEs. 


Whether or not an independent variable is declared as WITHIN in TYPE=TWOLEVEL does appear to make some differences in my results. Is there a reason for going one way or the other? Do you happen to know what GLLAMM and XTREG and XTMIXED do with this issue in Stata? Thanks 


You are correct that it makes a difference whether you put an indepednent variable on the WITHIN list or not. Conventional multilevel programs estimate the model as thought the independent variable is on the WITHIN list. Mplus has an alternative option which can be advantageous in some cases. This will be discussed in Example 9.1 in the new Mplus user's guide which will be available on the website Monday or Tuesday. See the following paper for more information: Lüdtke, O., Marsh, H.W., Robitzsch, A., Trautwein, U., Asparouhov, T., & Muthén, B. (2007). The multilevel latent covariate model: A new, more reliable approach to grouplevel effects in contextual studies. 


Step 1: I run a twolevel analysis with level1 covariates and no level2 covariates, I have no Rsquare for the BETWEEN portion. Step 2: I run the same model with level2 covariates added, I do have an Rsquare for the BETWEEN. Step 3: I remove some of the level1 covariates (which originally accounted for no BETWEEN variance according to the BETWEEN rsquare in step 1) and the BETWEEN rsquare drops significantly. I understand that levelone variables will account for BETWEEN variance, but I'm not sure how to explain that they don't add to the BETWEEN rsquare in step 1, but they then take away from the BETWEEN rsquare in step 3. (all levelone covariates are declared in the WITHIN = statement, and the level2 covariates are declared in the BETWEEN = statement) Isn't this a problem? Should I use these rsquares in a paper submitted for publication? If so, how do I explain what's happening, i.e., why do these levelone covariates explain no between variance unless there are leveltwo covariates included in the model? 


Clarification on Step 1  there shouldn't be an Rsquare printed for Between if there are not Between covariates. Is that what you are getting?  I don't understand what you mean when you talk about explaining how levelone variables don't add to the Between Rsquare in step 1. 


Correct: there is no Rsquare printed in step 1 where I have no Between covariates. Because of this, in step 2, it looks like my Between Rsquare is the variance being explained specifically by my Between covariates; but in step3, since the Between Rsquare drops so much when I remove some of the Within covariates, it's clear that the step 2 Between Rsquare isn't merely the result of the Between covariates. Should I simply hand calculate the Between Rsquare in step 1, since the Within variables are explaining Between variance, or do I treat the Between Rsquare in step 1 as zero (in other words, am I supposed to interpret the Rsquare as zero since it's not printed in step 1)? Maybe an easier way to ask this is: Why isn't there a Between Rsquare in step 1? I understand it isn't printed unless there are Between covariates, but if it's a twolevel model, and Between variance is being explained by Within variables, why isn't this shown with a Between Rsquare? Thanks 


It sounds like you have individuallevel variables that are not placed on the Within list and therefore have variances estimated on both the Within and Between level. To answer you properly, we probably need to look at your specific setting, so please send the input, output, data, and license number to support@statmodel.com. Note also the multilevel literature on Rsquare behavior in books like Snijders and Bosker. 


Hi, I want to compute how much additional variance is explained at level 2 when adding an interaction between two betweenlevel variables (thus, I am comparing a model with only main effects at level 2 with a model that includes main effects and an interaction). Should I just compare R squares for two models (R2model2 minus R2model1)? Or, should I subtract unstandardized residual variance for model 2 (the one that includes an interaction) from the unstandardized residual variance for model 1 and divide it by the unstandardized residual variance for model 1. The problem is that these two methods do not give me the same estimate (e.g., .10 vs. 12). Which one is correct? And, why don’t I get the same result? 


Go with the Rsquares. 

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