Polynomial regression quality assessment

polynomial-regression-quality-assessment

Summary

Evaluate the goodness-of-fit of a polynomial calibration model by computing and validating the coefficient of determination (R²) against a predefined threshold, ensuring that the m/z–drift-time–CCS relationship meets required accuracy standards for collision cross section calibration.

When to use

After fitting a polynomial calibration model to tunemix reference data in DEIMoS, assess whether the model explains sufficient variance in the m/z–drift-time–CCS relationship. Use this skill when you have established a tunemix calibration object with fitted coefficients and need to verify that the R² value meets or exceeds the ≥0.99997 threshold for positive or negative ion mode data before applying the calibration to unknown samples.

When NOT to use

• Input is a feature table or aligned features rather than tunemix reference standards; R² assessment applies only to reference calibration data with known CCS values.
• Calibration model has not yet been fitted; R² is undefined before model.fit() is called.
• Goal is to evaluate prediction accuracy on held-out test samples rather than reference data; this skill assesses fit quality on the training set, not generalization.

Inputs

• fitted DEIMoS calibration object (ccs_cal) with tunemix reference data
• known CCS values and m/z-to-CCS mapping for tunemix standards
• positive or negative ion mode tunemix data (e.g., example_tune_pos.h5 or equivalent)

Outputs

• R² metric (scalar, range 0–1)
• pass/fail validation result against 0.99997 threshold
• fitted calibration coefficients (retained from calibration object)

How to apply

Following calibration model fitting via deimos calibration.fit(), extract the R² metric from the fitted model by squaring the correlation coefficient (ccs_cal.fit['r'] ** 2). Compare the computed R² value directly against the threshold of 0.99997; if R² is equal to or greater than this threshold, the model is acceptable for downstream CCS prediction. The high threshold (≥0.99997) reflects the need for precise m/z–drift-time–CCS mapping in ion mobility-mass spectrometry workflows. Document both the R² value and its comparison outcome for each ion mode separately (positive and negative), as the calibration performance may differ between modes.

Related tools

• DEIMoS (Python API and command-line tool for calibration object initialization, model fitting, and R² extraction from fitted polynomial coefficients) — http://github.com/pnnl/deimos
• Python (Programming language for arithmetic operations (squaring correlation coefficients) and threshold comparison logic)
• numpy (Numerical library for array operations and statistical calculations underlying R² computation)

Examples

tune_pos = deimos.load('example_tune_pos.h5', key='ms1'); ccs_cal = deimos.CCSCalibration(tune_pos, known_ccs_values); ccs_cal.fit(); r_squared = ccs_cal.fit['r'] ** 2; print('R-squared:', r_squared); assert r_squared >= 0.99997, f'Calibration failed: R² = {r_squared}'

Evaluation signals

• R² value is a scalar between 0 and 1 (inclusive) with no NaN or inf values.
• R² ≥ 0.99997 for positive ion mode tunemix data and R² ≥ 0.99997 for negative ion mode tunemix data independently.
• R² values computed from the same tunemix dataset are reproducible (same fitted coefficients yield identical R² on repeated extraction).
• R² is derived from a fitted polynomial model that maps m/z and drift_time to CCS using tunemix reference standards with known CCS values.
• Pass/fail decision is documented separately for each ion mode, confirming calibration quality before applying the model to unknown samples.

Limitations

• R² measures goodness-of-fit on the training data (tunemix reference set) and does not directly assess generalization to unknown samples or different ion types.
• The 0.99997 threshold is specific to DEIMoS tunemix calibration and may not be appropriate for other calibration approaches or reference standards.
• R² is sensitive to polynomial degree; lower-degree polynomials may yield lower R² even if the relationship is adequately captured for practical purposes.
• Separate tunemix datasets (positive vs. negative ion mode) are required; a single ion mode's calibration cannot be directly applied to the other without re-assessment.

Evidence

• [results] R-squared threshold and ion mode specificity: "Does the DEIMoS tunemix calibration function produce collision cross section (CCS) calibration coefficients that achieve R-squared values ≥0.99997 when applied to positive and negative ion mode tune"
• [results] Observed R² values meeting threshold: "The DEIMoS tunemix calibration routine applied to positive ion mode tune mix data yields R-squared = 0.9999784552958121, and to negative ion mode yields R-squared = 0.9999784552958134, both exceeding"
• [results] Extraction method from fitted model: "Extract and record the R-squared value from the fitted model (ccs_cal.fit['r'] ** 2) to verify it meets the threshold of ≥0.99997."
• [results] Calibration workflow context: "Fit a polynomial calibration model to the tunemix data using the calibration.fit() method to establish the m/z–drift-time–CCS relationship."
• [readme] DEIMoS calibration capability: "Functionality includes feature detection, feature alignment, collision cross section (CCS) calibration, isotope detection, and MS/MS spectral deconvolution"