# Development of a mixed-effects longitudinal spline regression method for growth data analysis
> Bangsawang I.L.

URL kanonis: https://discover.unhas.ac.id/publications/pub_scopus_105050716460
Jurnal / Konferensi: Methodsx
Tahun terbit: 2026
DOI: https://doi.org/10.1016/j.mex.2026.104164
ISSN: 22150161
Kuartil SJR: Q1
Citations: 0

## Authors
- Bangsawang I.L.

## Abstract
Conventional parametric regression in longitudinal studies frequently violates the homoscedasticity and linearity assumptions. Moreover, in practice, it is common to observe data patterns that are not defined by any specific parametric functional form. As a result, the parametric longitudinal regression model risks a biased estimation. Therefore, this study proposes the development of a mixed-effects longitudinal model that incorporates a spline estimator. The proposed method is applied to analyze the growth of children's weight based on age and height. This method simultaneously accommodates the fixed effects of predictors, random effects across individuals, and flexible curve estimation without distributional constraints. The optimal model obtained a cubic spline with three knot points, yielding a minimum Generalized Cross Validation (GCV) value of 0.980 and evaluated with the Root Mean Square Error (RMSE) value of 0.612. The individual and time random effects are found to be statistically significant (p < 0.05). The findings indicate that the proposed mixed-effects spline offers flexibility in capturing complex trajectories without parametric assumptions. Some highlights proposed in this method are:•The proposed method integrates truncated spline multivariable estimator within the mixed-effects regression function.•The parameter estimation uses maximum likelihood method.•The data uses continuous responses in longitudinal structure.

## Keywords
- Spline (mechanical)
- Mathematics
- Estimator
- Homoscedasticity
- Smoothing spline
- Statistics
- Parametric statistics
- Regression
- Regression analysis
- Growth curve (statistics)
- Polynomial regression
- Nonparametric statistics
- Contouring
- Parametric equation
- Parametric model
- Mean squared error
- Kriging
- Longitudinal data
- Semiparametric regression
- Nonparametric regression
- B-spline
- Thin plate spline
- Semiparametric model
- Computer science
- Applied mathematics
- Local regression
- Restricted maximum likelihood
- Estimation theory
- Linear regression
- Random effects model
- Generalized method of moments
- Flexibility (engineering)

---
Sumber: Discover Unhas — RIMS Universitas Hasanuddin.
Saat mengutip, gunakan DOI bila tersedia atau URL kanonis di atas.