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If we then take an independent sample of validation data from the same population as the training data, it will generally turn out that the model does not fit the validation data as well as it fits the training data.
The size of this difference is likely to be large especially when the size of the training data set is small, or when the number of parameters in the model is large.
In this situation the misclassification error rate can be used to summarize the fit, although other measures like positive predictive value could also be used.
When the value being predicted is continuously distributed, the mean squared error, root mean squared error or median absolute deviation could be used to summarize the errors.
The disadvantage of this method is that some observations may never be selected in the validation subsample, whereas others may be selected more than once. This method also exhibits Monte Carlo variation, meaning that the results will vary if the analysis is repeated with different random splits.
For each such split, the model is fit to the training data, and predictive accuracy is assessed using the validation data. The advantage of this method (over k-fold cross validation) is that the proportion of the training/validation split is not dependent on the number of iterations (folds).It can be used to estimate any quantitative measure of fit that is appropriate for the data and model.For example, for binary classification problems, each case in the validation set is either predicted correctly or incorrectly.The process looks similar to jackknife; however, with cross-validation one computes a statistic on the left-out sample(s), while with jackknifing one computes a statistic from the kept samples only. In the holdout method, we randomly assign data points to two sets d.