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I am using a linear model to predict under-nutrition in children under 5. The common metric discussed is stunting (a binary outcome) which is defined as being more than two standard deviations away from a standard age-for height (I'm predicting the z-score which underlies the stunting status). Below are overlapping histograms of actual (blue) versus predicted (red) height for age scores. What I am really interested in predicting is whether or not an individual falls below a z-score of -2, and my distribution is very restricted. Any tips? Right now, my model looks like this:

Height.Age.Z ~ age + mothers.education + wealth + sanitation + (fixed effect on region)

Any tips, general and specific, are appreciated. Thanks, enter image description here

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    $\begingroup$ These histograms are inconsistent, because one (blue) represents approximately five times as much data as the other. They also don't show much, because they cannot portray the paired comparisons of actual and predicted values: you need a scatterplot (or something similar) for this. $\endgroup$
    – whuber
    Dec 4, 2012 at 7:04

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Stunting is defined by general norms, not by your data. You need to find the standard height for age with its standard deviation for each age. Then you can find which people are more than 2 sd below the mean for their age. Then you can run logistic regression using stunting (yes/no) as the DV.

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  • $\begingroup$ Right -- Stunting is supposed to be measured against a standard (I'm not actually interested in finding -2SD in my data), but the challenge is still generating more dispersion in my predictions. Also, I am choosing not to use logistic regression on stunting because it is a less precise measurement of height for age Z-score (which therefore uses more information). $\endgroup$
    – mike
    Dec 3, 2012 at 23:58
  • $\begingroup$ OK, another alternative is quantile regression. You can model any percentile that you like. If you wanted 2 SD below the mean, you would choose the 2.2 percentile, approximately. $\endgroup$
    – Peter Flom
    Dec 4, 2012 at 0:02
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    $\begingroup$ Mike, all predictions, if they are any good, will exhibit less variation than actual data, because a prediction cannot hope to project random variation. "Generating more dispersion" perhaps can be accomplished with a better model, but beyond a certain point requires making poorer predictions. $\endgroup$
    – whuber
    Dec 4, 2012 at 7:06

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