student07 posted on Tuesday, July 31, 2007 - 8:40 am
I would be glad for advice concerning the following question:
when using 'type = twolevel basic', I find considerable between-group 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 between-level) only.
Thus, given that I am not interested in modelling the between-group variation of these controls, I thought it be would be fine to declare these controls as within-variables using the WITHIN-command. However, I am unsure whether this would be correct - does declaring variables with between-group variation as WITHIN-variables 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?
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 group-level effects in contextual studies.
Step 1: I run a two-level analysis with level-1 covariates and no level-2 covariates, I have no R-square for the BETWEEN portion.
Step 2: I run the same model with level-2 covariates added, I do have an R-square for the BETWEEN.
Step 3: I remove some of the level-1 covariates (which originally accounted for no BETWEEN variance according to the BETWEEN r-square in step 1) and the BETWEEN r-square drops significantly.
I understand that level-one variables will account for BETWEEN variance, but I'm not sure how to explain that they don't add to the BETWEEN r-square in step 1, but they then take away from the BETWEEN r-square in step 3. (all level-one covariates are declared in the WITHIN = statement, and the level-2 covariates are declared in the BETWEEN = statement) Isn't this a problem? Should I use these r-squares in a paper submitted for publication? If so, how do I explain what's happening, i.e., why do these level-one covariates explain no between variance unless there are level-two covariates included in the model?
Clarification on Step 1 - there shouldn't be an R-square 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 level-one variables don't add to the Between R-square in step 1.
Correct: there is no R-square printed in step 1 where I have no Between covariates.
Because of this, in step 2, it looks like my Between R-square is the variance being explained specifically by my Between covariates; but in step3, since the Between R-square drops so much when I remove some of the Within covariates, it's clear that the step 2 Between R-square isn't merely the result of the Between covariates. Should I simply hand calculate the Between R-square in step 1, since the Within variables are explaining Between variance, or do I treat the Between R-square in step 1 as zero (in other words, am I supposed to interpret the R-square as zero since it's not printed in step 1)?
Maybe an easier way to ask this is: Why isn't there a Between R-square 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 R-square?
It sounds like you have individual-level 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 firstname.lastname@example.org.
Note also the multilevel literature on R-square behavior in books like Snijders and Bosker.
I want to compute how much additional variance is explained at level 2 when adding an interaction between two between-level 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 (R2-model2 minus R2-model1)? 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?