A method for determining groups in nonparametric regression curves: Application to prefrontal cortex neural activity analysis

Javier Roca-Pardiñas; Celestino Ordóñez; Luís Meira Machado; Javier Roca-Pardiñas; Celestino Ordóñez; Luís Meira Machado

doi:10.3934/mbe.2022302

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 7: 6435-6454. doi: 10.3934/mbe.2022302

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A method for determining groups in nonparametric regression curves: Application to prefrontal cortex neural activity analysis

1.
Department of Statistics and Operational Research, Vigo University, Vigo 36310, Spain
2.
Department of Mining Exploitation and Prospecting, Geomatics and Computer Graphics Lab, Oviedo University, Mieres 33600, Spain
3.
Center of Mathematics, Minho University, Braga 4704-553, Portugal

Academic Editor: Wandi Ding

Received: 03 March 2022 Revised: 21 March 2022 Accepted: 28 March 2022 Published: 24 April 2022

Generalized additive models provide a flexible and easily-interpretable method for uncovering a nonlinear relationship between response and covariates. In many situations, the effect of a continuous covariate on the response varies across groups defined by the levels of a categorical variable. When confronted with a considerable number of groups defined by the levels of the categorical variable and a factor‐by‐curve interaction is detected in the model, it then becomes important to compare these regression curves. When the null hypothesis of equality of curves is rejected, leading to the clear conclusion that at least one curve is different, we may assume that individuals can be grouped into a number of classes whose members all share the same regression function. We propose a method that allows determining such groups with an automatic selection of their number by means of bootstrapping. The validity and behavior of the proposed method were evaluated through simulation studies. The applicability of the proposed method is illustrated using real data from an experimental study in neurology.
- clustering of regression curves,
- factor-by-curve interaction,
- generalized additive model,
- multiple regression curves,
- nonlinear regression,
- number of groups
Citation: Javier Roca-Pardiñas, Celestino Ordóñez, Luís Meira Machado. A method for determining groups in nonparametric regression curves: Application to prefrontal cortex neural activity analysis[J]. Mathematical Biosciences and Engineering, 2022, 19(7): 6435-6454. doi: 10.3934/mbe.2022302

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Abstract

Generalized additive models provide a flexible and easily-interpretable method for uncovering a nonlinear relationship between response and covariates. In many situations, the effect of a continuous covariate on the response varies across groups defined by the levels of a categorical variable. When confronted with a considerable number of groups defined by the levels of the categorical variable and a factor‐by‐curve interaction is detected in the model, it then becomes important to compare these regression curves. When the null hypothesis of equality of curves is rejected, leading to the clear conclusion that at least one curve is different, we may assume that individuals can be grouped into a number of classes whose members all share the same regression function. We propose a method that allows determining such groups with an automatic selection of their number by means of bootstrapping. The validity and behavior of the proposed method were evaluated through simulation studies. The applicability of the proposed method is illustrated using real data from an experimental study in neurology.

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