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Table 1 Proposed models

From: Genomic Bayesian functional regression models with interactions for predicting wheat grain yield using hyper-spectral image data

Method Model Type
M1 \(\hat{\mu }_{ij} = E_{i} + g_{j} + \gamma_{ij}\) Conventional
M2 \(\hat{\mu }_{ij} = E_{i} + g_{j} + gE_{ij} + \gamma_{ij}\) Conventional
M3 \(\hat{\mu }_{ij} = E_{i} + g_{j} + \mathop \sum \limits_{k = 1}^{p} x_{ijk} \beta_{k} + \gamma_{ij}\) Conventional
M4 \(\hat{\mu }_{ij} = E_{i} + g_{j} + gE_{ij} + \mathop \sum \limits_{k = 1}^{p} x_{ijk} \beta_{k} + \gamma_{ij}\) Conventional
M5 \(\hat{\mu }_{ij} = E_{i} + g_{j} + \mathop \int \limits_{392}^{851} x_{ij} \left( k \right)\beta_{1} \left( k \right)dk + \gamma_{ij}\) Functional Bayesian B-splines
M6 \(\hat{\mu }_{ij} = E_{i} + g_{j} + \mathop \int \limits_{392}^{851} x_{ij} \left( k \right)\beta_{1} \left( k \right)dk + \gamma_{ij}\) Functional Bayesian Fourier
M7 \(\hat{\mu }_{ij} = E_{i} + g_{j} + gE_{ij} + \mathop \int \limits_{392}^{851} x_{ij} \left( k \right)\beta_{1} \left( k \right)dk + \gamma_{ij}\) Functional Bayesian B-splines basis
M8 \(\hat{\mu }_{ij} = E_{i} + g_{j} + gE_{ij} + \mathop \int \limits_{392}^{851} x_{ij} \left( k \right)\beta_{1} \left( k \right)dk + \gamma_{ij}\) Functional Bayesian Fourier basis
M9 \(\hat{\mu }_{ij} = E_{i} + g_{j} + \mathop \sum \limits_{k = 1}^{p} x_{ijk} \beta_{k} + \mathop \sum \limits_{k = 1}^{p} x_{ijk} \beta_{ki} + \gamma_{ij}\) Conventional
M10 \(\hat{\mu }_{ij} = E_{i} + g_{j} + gE_{ij} + \mathop \sum \limits_{k = 1}^{p} x_{ijk} \beta_{k} + \mathop \sum \limits_{k = 1}^{p} x_{ijk} \beta_{ki} + \gamma_{ij}\) Conventional
M11 \(\hat{\mu }_{ij} = E_{i} + g_{j} + \mathop \int \limits_{392}^{851} x_{ij} \left( k \right)\beta_{1} \left( k \right)dk + \mathop \int \limits_{392}^{851} x_{ij} \left( k \right)\beta_{2i} \left( k \right)dk + \gamma_{ij}\) Functional Bayesian B-splines basis
M12 \(\hat{\mu }_{ij} = E_{i} + g_{j} + \mathop \int \limits_{392}^{851} x_{ij} \left( k \right)\beta_{1} \left( k \right)dk + \mathop \int \limits_{392}^{851} x_{ij} \left( k \right)\beta_{2i} \left( k \right)dk + \gamma_{ij}\) Functional Bayesian Fourier basis
M13 \(\hat{\mu }_{ij} = E_{i} + g_{j} + gE_{ij} + \mathop \int \limits_{392}^{851} x_{ij} \left( k \right)\beta_{1} \left( k \right)dk + \mathop \int \limits_{392}^{851} x_{ij} \left( k \right)\beta_{2i} \left( k \right)dk + \gamma_{ij}\) Functional Bayesian B-splines basis
M14 \(\hat{\mu }_{ij} = E_{i} + g_{j} + gE_{ij} + \mathop \int \limits_{392}^{851} x_{ij} \left( k \right)\beta_{1} \left( k \right)dk + \mathop \int \limits_{392}^{851} x_{ij} \left( k \right)\beta_{2i} \left( k \right)dk + \gamma_{ij}\) Functional Bayesian Fourier basis