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On the sensitivity of linear discriminant analysis to sampling variation and analytical errors
1Department of Clinical Chemistry, State University Hospital, Rigshospitalet, Copenhagen, Denmark.
Summary
Analytical errors can skew results for linear discriminant functions, especially in high dimensions. Evaluating performance on an independent test set is crucial for accurate error rate estimation.
Area of Science:
- Statistics
- Analytical Chemistry
- Machine Learning
Background:
- Linear discriminant functions (LDFs) are widely used for classification.
- Analytical errors, including inaccuracy and imprecision, can impact model performance.
- Understanding these impacts is vital for reliable data analysis.
Purpose of the Study:
- To investigate the influence of analytical inaccuracy and imprecision on LDFs.
- To assess how analytical shifts affect error rate estimation.
- To determine the best practices for evaluating LDF performance.
Main Methods:
- Simulated analytical shifts and imprecision were introduced.
- LDFs were trained and evaluated on both training and independent test sets.
- Impact on group and overall error rates was quantified.
Main Results:
- Analytical shifts during training lead to spuriously low error rates, particularly in high-dimensional data.
- Post-establishment inaccuracy significantly alters individual group error rates but moderately affects overall rates.
- Imprecision reduces group separation similarly to univariate cases.
Conclusions:
- Evaluating LDF error rates on an independent test set provides realistic performance estimates.
- Relying solely on training set evaluation or split-sample principles can be misleading.
- Independent testing is essential for robust discriminant function analysis.