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Inga BEck posted on Monday, August 18, 2008  10:11 am



Hello I am wondering whether there is any explanation why the size of stdyxstandardised b's (regression coefficients, thus also factor loadings of continous variables)for the betweenpart in type = twolevel seem to be typically larger than stdyxstandardised b's on the within level. Hence here are two questions: Q#1: Could it be that the betweenlevel b's appear larger as they (ultimately, at least)reflect aggregatelevel relations, whereby measurement error among aggregated constructs is often lower as compared to withinlevel relations? Q#2: Could it also be that the betweenlevel b's are relatively larger because the 'explainable' variance on the betweenlevel is often (perhaps not always) smaller as compared to the 'explainable' variance on the withinlevel  and hence effects of betweenlevel covariates 'explain a lot' from a relative small amount of explainable variance? I would also be grateful for literature references! Thanks 


Q1 Yes, this is the reason. See also the literature on "ecological correlations" (Robinson and others). Q2 I don't think that's it. See also my 1994 Soc Meths & Res article  on my UCLA web site (reached via this web site). 


I have a related question regarding MLM. First, I have standardized my main predictor (achievement) and my outcome variable, then I averaged achievement across classes to obtain a measure of classaverage achievement (this measure was not restandardized). I also have a dummy variable (sex) coded 1 or 0. When I look at the between part of the output of my "twolevel" analysis I see that the stdyx option shows larger coefficients for classaverage achievement than the std or estimate (unstandardized) option (as mentioned in the previous post), BUT these stdyx values seem out of proportion with previous studies on this matter). So, my question then is: which coefficients do I report and which coefficients should I use to be able to compare with the (individual) achievement coefficient at the withinlevel? 


The withinlevel coefficient is standardized using the withinlevel variance. The betweenlevel coefficient is standardized using the betweenlevel variance. You may want to standardize using the total variance which you can obtain using the RESIDUAL option by adding the within variance and the between variance. 


Thank you, Linda, for your quick response! I used the RESIDUAL option and used the standardized coefficients based on within + between variance, which now seem more realistic values indeed! Do you have any references for this standardization based on total variance that I might use when publishing these analyses or is this quite common to do? 


No, I don't. You would need to look at the multilevel literature perhaps Raudenbush and Bryk discuss this. 


OK, thank you, Linda! After doing further analyses yesterday, I have an additional question regarding this matter. How do you calculate the total variance when working with a latent dependent variable? Because in the residual output you then only see the covariances of the indicators but not of the latent factor. Maybe you have to take the average of the indicators' covariances? 


See TECH4 of the OUTPUT command. 

Utkun Ozdil posted on Tuesday, March 22, 2011  8:16 am



Hi,, In a twolevel model is it appropriate to interpret the STDYX values for the relationship between two "latent variables"? Since STDYX is used for continuous covariates is it sufficient to just report the values in the "Model Results" part for the relationship between two "latent variables"? Thanks... 


Yes, STDYX can be used for reporting a slope between two latent variables. Here, being observed or latent doesn't matter. Nor, does singlelevel versus twolevel, as long as you understand which variance the standardization refers to (within specific or between specific). 

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