mixed - Stata
mixed - Stata
mixed - Stata
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40 <strong>mixed</strong> — Multilevel <strong>mixed</strong>-effects linear regression<br />
magnitudes of these weights need to be normalized so that they are “consistent” from group to group.<br />
This is in stark contrast to a standard analysis, where the scale of sampling weights does not factor<br />
into estimation, instead only affecting the estimate of the total population size.<br />
<strong>mixed</strong> offers three methods for standardizing weights in a two-level model, and you can specify<br />
which method you want via the pwscale() option. If you specify pwscale(size), then the w i|j (or<br />
w ij , it does not matter) are scaled to sum to the cluster size n j . Method pwscale(effective) adds<br />
in a dependence on the sum of the squared weights so that level-one weights sum to the “effective”<br />
sample size. Just like pwscale(size), pwscale(effective) also behaves the same whether you<br />
have w i|j or w ij , and so it can be used with either.<br />
Although both pwscale(size) and pwscale(effective) leave w j untouched, the pwscale(gk)<br />
method is a little different in that 1) it changes the weights at both levels and 2) it does assume<br />
you have w i|j for level-one weights and not w ij (if you have the latter, then first divide by w j ).<br />
Using the method of Graubard and Korn (1996), it sets the weights at the group level (level two) to<br />
the cluster averages of the products of both level weights (this product being w ij ). It then sets the<br />
individual weights to 1 everywhere; see Methods and formulas for the computational details of all<br />
three methods.<br />
Determining which method is “best” is a tough call and depends on cluster size (the smaller<br />
the clusters, the greater the sensitivity to scale), whether the sampling is informative (that is, the<br />
sampling weights are correlated with the residuals), whether you are interested primarily in regression<br />
coefficients or in variance components, whether you have a simple random-intercept model or a<br />
more complex random-coefficients model, and other factors; see Rabe-Hesketh and Skrondal (2006),<br />
Carle (2009), and Pfeffermann et al. (1998) for some detailed advice. At the very least, you want<br />
to compare estimates across all three scaling methods (four, if you add no scaling) and perform a<br />
sensitivity analysis.<br />
If you choose to rescale level-one weights, it does not matter whether you have w i|j or w ij . For<br />
the pwscale(size) and pwscale(effective) methods, you get identical results, and even though<br />
pwscale(gk) assumes w i|j , you can obtain this as w i|j = w ij /w j before proceeding.<br />
If you do not specify pwscale(), then no scaling takes place, and thus at a minimum, you need<br />
to make sure you have w i|j in your data and not w ij .<br />
Example 12<br />
Rabe-Hesketh and Skrondal (2006) analyzed data from the 2000 Programme for International<br />
Student Assessment (PISA) study on reading proficiency among 15-year-old American students, as<br />
performed by the Organisation for Economic Co-operation and Development (OECD). The original<br />
study was a three-stage cluster sample, where geographic areas were sampled at the first stage, schools<br />
at the second, and students at the third. Our version of the data does not contain the geographic-areas<br />
variable, so we treat this as a two-stage sample where schools are sampled at the first stage and<br />
students at the second.