This contribution explores the application of mixed effects smooth models, as introduced in [1], to the analysis of real-world data with missing observations. These models combine P-splines with linear mixed models, allowing robust and interpretable predictions while providing control over the smoothness of the resulting curves through penalization. We first validate the functionality of the proposed approach on simulated data and subsequently apply the theoretical framework described in [1] to a dataset describing the relationship between light reflectance and wavelength in trees. One of the main challenges in this dataset was the presence of missing values, which we addressed using a one-stage prediction approach that incorporates both observed and unobserved data. The results include smooth and accurate predictions, together with confidence intervals that reflect the variability of the predictions and provide additional information on the behaviour of the model and the uncertainty of the predictions.

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Prediction with Mixed Effects Smooth Models by using P-Splines

  • Veronika Šmajserová,
  • Jitka Machalová

摘要

This contribution explores the application of mixed effects smooth models, as introduced in [1], to the analysis of real-world data with missing observations. These models combine P-splines with linear mixed models, allowing robust and interpretable predictions while providing control over the smoothness of the resulting curves through penalization. We first validate the functionality of the proposed approach on simulated data and subsequently apply the theoretical framework described in [1] to a dataset describing the relationship between light reflectance and wavelength in trees. One of the main challenges in this dataset was the presence of missing values, which we addressed using a one-stage prediction approach that incorporates both observed and unobserved data. The results include smooth and accurate predictions, together with confidence intervals that reflect the variability of the predictions and provide additional information on the behaviour of the model and the uncertainty of the predictions.