AK14 posted on Thursday, October 01, 2009 - 3:56 pm
a short question relating to the calculation of the mean of between-variables:
I was playing with the centering options and noticed the following: When I used the grandmean centering option for a between-level variable as follows
BETWEEN = z_betw; CENTERING = GRANDMEAN(z_betw);
the estimated mean of the between level variable is not zero but
Means Z_BETW -0.341 0.160 -2.128 0.033
In my dataset, cluster sizes differed considerably and the estimated value corresponds to the unweighted mean of the values of Z_BETW, i.e. weighting every cluster equally without adjusting for the size of the cluster. The weighted mean, accounting for the cluster sizes, would in fact be equal to zero.
- What is your rationale for using the unweighted average?
- Is their a way to obtain the weighted mean that takes different cluster sizes into account?
If you use GROUPMEAN centering, I believe the mean will be zero. I think GRANDMEAN centering is weighted for cluster size given that clusters with more members contribute more values to computation of the grand mean.
thanks for your reply and for confirming my suspicion about the GRANDMEAN centering weighting for cluster size!
I am still wondering why you have chosen to estimate the mean of a cluster-level variable without weighting for cluster size and if and how I would be able to obtain the weighted mean in Mplus as an estimated parameter. Unfortunately using GROUPMEAN centering did not do the trick as I am looking at a between-level variable and Mplus would - predictably - not let me GROUPMEAN center it.
So just to be clear; we are talking about several different methods:
Method 1. Mplus currently grandmean centers a between-level variable by averaging it over all observations (so with 50 clusters and 2000 individuals, 2000 observations are used).
Method 2. Probably a more common approach is to average the variable over the clusters (so an average over the 50 values).
I would call Method 1 a weighted approach in the sense that bigger clusters contribute more to the grandmean.
Method 3. You can estimate the between-level mean also by Type=Basic Twolevel using ML. This mean will be a bit different from the mean of Method 2 (different estimators are esssentially used); ML gives heavier weight to larger clusters.