  In recent years, many non-traditional classification methods, such as Random
Forest, Boosting, and neural network, have been widely used in applications.
Their performance is typically measured in terms of classification accuracy.
While the classification error rate and the like are important, they do not
address a fundamental question: Is the classification method underfitted? To
our best knowledge, there is no existing method that can assess the
goodness-of-fit of a general classification procedure. Indeed, the lack of a
parametric assumption makes it challenging to construct proper tests. To
overcome this difficulty, we propose a methodology called BAGofT that splits
the data into a training set and a validation set. First, the classification
procedure to assess is applied to the training set, which is also used to
adaptively find a data grouping that reveals the most severe regions of
underfitting. Then, based on this grouping, we calculate a test statistic by
comparing the estimated success probabilities and the actual observed responses
from the validation set. The data splitting guarantees that the size of the
test is controlled under the null hypothesis, and the power of the test goes to
one as the sample size increases under the alternative hypothesis. For testing
parametric classification models, the BAGofT has a broader scope than the
existing methods since it is not restricted to specific parametric models
(e.g., logistic regression). Extensive simulation studies show the utility of
the BAGofT when assessing general classification procedures and its strengths
over some existing methods when testing parametric classification models.
