# Fewer variables have higher R-squared value in logistic regression

I am testing out 3 modeling approaches for malnutrition in children. Theoretically, distal determinants (education,poverty) operate through proximal determinants (water, sanitation) in determining malnutrition rates. The three logistic models, where stunting is a binary indicator for malnutrition, are:

// Proximal determinants only: both binary indicators
stunting ~ water + sanitation

// Distal determinants only: both categorical indicators
stunting ~ i.education + i.poverty

// Both proximal and distal determinants
stunting ~ water + sanitation + i.education + i.poverty


I am surprised to find that the r-squared value of the second model is higher than the third model, as calculated by the correlation between the predicted and actual values (stata):

predict predicted, xb
corr predicted stunting
local rsq = r(rho)


While I expected the strength of the relationship and statistical significance of the more proximal causes to decrease (as they were soaked up by the distal causes), I expected the combined model to have higher explanatory power (as measured by r-squared). Does anyone have any explanation as to why the second model has the most explanatory power? Let me know if I can provide additional information for answering this question.

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Regarding R-squared and logistic regression, you may want to take a look at this post: stats.stackexchange.com/a/3562 –  Tim Aug 24 '12 at 16:43
Just a quick check: do any of the independent variables have missing values? If so, that alone can cause the r-squared statistics to be incomparable. –  whuber Aug 24 '12 at 17:14
They certainly do, thanks. –  mike Aug 26 '12 at 16:39