A new approach in regression analysis for modeling adsorption isotherms

Area of Science:

• Environmental Chemistry
• Chemical Engineering
• Physical Chemistry

Background:

• Isotherm parameter estimation is crucial for understanding adsorption processes.
• Numerous regression methods exist, but their performance under varying noise conditions is unclear.
• Experimental validation of these methods is time-consuming.

Purpose of the Study:

• To compare numerical approaches for isotherm parameter estimation.
• To evaluate methods based on different noise structures in analytical measurements.
• To identify robust regression techniques for adsorption modeling.

Main Methods:

• Monte Carlo simulation was employed to generate large datasets.
• Six homoscedastic and five heteroscedastic noise models were simulated.
• Performance was assessed using median percentage error and mean absolute relative error.

Main Results:

• For single experiments with homoscedastic noise, ordinary least squares is the preferred method.
• For single experiments with heteroscedastic noise, orthogonal distance regression or Margart's percent standard deviation are recommended.
• When experiments are repeated three times, weighted least squares performs comparably to orthogonal distance regression.

Conclusions:

• The choice of regression method significantly depends on the noise characteristics of the experimental data.
• Weighted least squares offers a computationally efficient alternative to more complex methods when replicate data is available.
• Accurate isotherm parameter estimation requires careful consideration of analytical method precision.