I have individual level data from several rounds of surveys. These individual responses are nested within sites. I have other data measured just at the site level. However, there are only 10 sites, and I have a number of factors (more than 5) I would like to turn into a composite score. Is there a way to create a composite score for sites with so few cases (N=10) and use that to predict average individual responses?
Even with as few as 10 cases, a composite score could be obtained. In the composite score, the individual scores have lost their identities, just like in the sample mean, the individual sample scores have lost their identities. Yet just as the sample mean can be a basis of group comparison (which is why it is called a measure of location), the composite score can be a basis of comparing one group with another group. Also, the group mean can be used to represent each individual score as an average or a measure of central tendency. To that extent, I think that the group composite score may be used to predict each individual score.
I think your confidence intervals will be very wide for such few cases.
you can use the group mean as a predictor of individual means, but check the standard error (it will be a poor predictor if the variance is high, and the inter group distributions overlap)
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