For an OLS model the mean squared error can be used to assess the fit of the trained model on the validation data.

What is the equivalent for a logistic regression model? Can I simply use the following residual sum of squares function?

$RSS=\Sigma^N_{i=1}(y_i-{\hat p})^2$

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    $\begingroup$ How about using classification rate? $\endgroup$ – pe-perry May 10 '16 at 16:19

What you propose is equivalent to using the Brier score which is a proper scoring rule. So it is certainly OK to use it for cross-validation.

See also logistic regression predictive modeling.

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