Statistical Modelling › Limitations and Considerations

While the metrics and techniques discussed provide powerful tools for model evaluation, they come with important caveats that practitioners should understand. R-squared and RMSE only measure prediction accuracy on the specific data we have. They say nothing about whether our model will work on fundamentally different populations or whether it has captured causal relationships that remain stable under interventions. A model with excellent metrics might still fail catastrophically if deployed in a context that differs from the training environment.

Cross-validation assumes that the data points are independent and identically distributed. This assumption breaks down in many real-world scenarios. Time series data exhibits temporal dependencies that violate independence, requiring specialized cross-validation strategies that respect temporal order. Hierarchical or clustered data where observations within groups are correlated requires cluster-aware cross-validation to avoid overoptimistic performance estimates.

The choice of evaluation metric matters enormously and should align with the costs and benefits in the application domain. RMSE weights all errors equally after squaring, but in many applications, different types of errors have vastly different consequences. Predicting that a disease is absent when it is present might be far more costly than the reverse error. In such cases, specialized metrics or cost-sensitive evaluation frameworks provide more appropriate assessments.

Cross-validation provides honest performance estimates but doesn't eliminate the fundamental challenge of limited data. If we have only a small dataset, even carefully cross-validated performance estimates will have high uncertainty. No amount of clever evaluation can substitute for collecting more data when the training set is too small to support the complexity of the model we're trying to build.

Finally, all these techniques assume we've properly prepared our data and chosen appropriate model architectures. No evaluation framework can rescue a model built on the wrong features, with serious data quality issues, or using an architecture fundamentally unsuited to the problem. These tools help us evaluate and compare models, but they don't replace the need for domain knowledge, careful feature engineering, and thoughtful model design.