Inga BEck posted on Monday, August 18, 2008 - 10:11 am
I am wondering whether there is any explanation why the size of stdyx-standardised b's (regression coefficients, thus also factor loadings of continous variables)for the between-part in type = twolevel seem to be typically larger than stdyx-standardised b's on the within level. Hence here are two questions:
Q#1: Could it be that the between-level b's appear larger as they (ultimately, at least)reflect aggregate-level relations, whereby measurement error among aggregated constructs is often lower as compared to within-level relations?
Q#2: Could it also be that the between-level b's are relatively larger because the 'explainable' variance on the between-level is often (perhaps not always) smaller as compared to the 'explainable' variance on the within-level - and hence effects of between-level covariates 'explain a lot' from a relative small amount of explainable variance?
I would also be grateful for literature references!
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 class-average 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 class-average 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 within-level?
The within-level coefficient is standardized using the within-level variance. The between-level coefficient is standardized using the between-level 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?
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?
Utkun Ozdil posted on Tuesday, March 22, 2011 - 8:16 am
In a two-level 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"?
Yes, STDYX can be used for reporting a slope between two latent variables. Here, being observed or latent doesn't matter. Nor, does single-level versus two-level, as long as you understand which variance the standardization refers to (within specific or between specific).