The Cluster Analysis by Using Nonparametric Cubic B-Spline Modeling for Longitudinal Data


  • Noor Nawzat Ahmed
  • Suhail Najm Abdullah



البيانات الطولية ، نموذج الشرائح B-spline التكعيبية اللامعلمية ، التحليل العنقودي ، طريقة الاتجاه المتناوب لخوارزمية المضاعف ADMM., Longitudinal Data, Nonparametric Cubic B-Spline, Cluster Analysis, The Alternating Direction Method for Multiplier Algorithm ADMM.


Longitudinal data is becoming increasingly common, especially in the medical and economic fields, and various methods have been analyzed and developed to analyze this type of data.

In this research, the focus was on compiling and analyzing this data, as cluster analysis plays an important role in identifying and grouping co-expressed subfiles over time and employing them on the nonparametric smoothing cubic B-spline model, which is characterized by providing continuous first and second derivatives, resulting in a smoother curve with fewer abrupt changes in slope. It is also more flexible and can pick up on more complex patterns and fluctuations in the data.

The longitudinal balanced data profile was compiled into subgroups by penalizing the pairwise distances between the coefficients of the cubic B-spline model using one of the common penalize functions, the Minimax Concave Penalty function (MCP). This method, in turn, works to determine the number of clusters through one of the model selection criteria, Bayesian information criteria (BIC), and we used optimization methods to solve their equations. Therefore, we applied the alternative direction method of the ADMM multiplier algorithm to reach approximate solutions to find the estimators of the nonparametric model using R statistical software.
Longitudinally balanced data were generated in the simulation study, as the number of subjects was 60 and the number of repeats (time) was 10 for each subject. The simulation was iterated 100 times, and it showed that employing the MCP partial methods on the cubic model can group profiles into clusters, which is the aim of this paper.


Paper type: Research paper.


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Statistical Researches

How to Cite

“The Cluster Analysis by Using Nonparametric Cubic B-Spline Modeling for Longitudinal Data” (2023) Journal of Economics and Administrative Sciences, 29(138), pp. 147–160. doi:10.33095/jeas.v29i138.3045.

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