withinsample

Within-sample, often written as within-sample or simply in-sample, refers to data that are used to fit, calibrate, or estimate a statistical model. Predictions, residuals, and performance metrics computed on the same dataset that was used to train the model constitute within-sample evaluation. This is in contrast to out-of-sample evaluation, where predictions are assessed on data not used during fitting.

In-sample metrics commonly reported include measures such as R-squared, mean squared error, or log-likelihood. While these metrics describe how well the model explains or fits the data it was built on, they can be biased upward due to overfitting, especially when model complexity grows without adequate regularization or validation. Consequently, strong in-sample performance does not guarantee similarly strong predictive performance on new data.

To mitigate optimistic bias, practitioners separate data into training and validation or testing sets, or use cross-validation and nested cross-validation. In time-series contexts, care is taken to preserve temporal order, using methods like rolling-origin or walk-forward validation to obtain more realistic out-of-sample assessments. Although within-sample diagnostics can aid model understanding and selection, they should be interpreted alongside out-of-sample evaluation to gauge generalizability.

In summary, within-sample evaluation measures a model’s fit on the data used for estimation, but it is not a substitute for out-of-sample testing. Reporting both perspectives helps provide a balanced view of model performance.