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Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
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Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least...
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The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
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One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

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This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
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Related Experiment Video

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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Modified partial least square structural equation model with multivariate adaptive regression spline: Parameter

Hendra H Dukalang1,2, Bambang Widjanarko Otok1, Purhadi1

  • 1Department of Statistics, Institut Teknologi Sepuluh Nopember, Surabaya, 60111 Indonesia.

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|June 18, 2025
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Summary
This summary is machine-generated.

This study introduces Multivariate Adaptive Regression Splines Partial Least Square (MARSPLS) to address nonlinearities in Partial Least Squares Structural Equation Modelling (PLS-SEM). MARSPLS enhances predictive accuracy for complex latent variable relationships.

Keywords:
Behaviour intentionMARSMARSPLSMaximum likelihood estimationMultivariate Adaptive Regression Spline Partial Least SquareOrdinary least squaresPLS-SEM

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Area of Science:

  • Statistics
  • Machine Learning
  • Behavioral Science

Background:

  • Partial Least Squares Structural Equation Modelling (PLS-SEM) often yields biased results due to its linear assumptions.
  • Capturing nonlinear and interaction effects between latent variables is a significant challenge in existing PLS-SEM models.

Purpose of the Study:

  • To propose a novel model, Multivariate Adaptive Regression Splines Partial Least Square (MARSPLS), to overcome the limitations of PLS-SEM in handling nonlinear relationships.
  • To enhance the predictive accuracy of structural equation modeling by incorporating the flexibility of Multivariate Adaptive Regression Splines (MARS).

Main Methods:

  • The MARSPLS model integrates MARS within the PLS-SEM framework to capture nonlinear and interaction effects.
  • Parameter estimation for MARSPLS is detailed using Maximum Likelihood Estimator (MLE) and Ordinary Least Squares (OLS).
  • The model's performance is validated using simulated data and empirical data on e-wallet behavioral intention from 385 Indonesian respondents.

Main Results:

  • MARSPLS with interaction demonstrated superior predictive accuracy compared to traditional methods.
  • The model achieved a higher R² value of 54.08% and lower information criteria (AIC, AICc) and Root Mean Square Error (RMSE).

Conclusions:

  • MARSPLS offers a novel approach for PLS-SEM when latent variable relationships are nonlinear or unknown.
  • The proposed method effectively models complex relationships involving four exogenous and one endogenous latent variable, without moderation or mediation effects.