# Table 1 Proposed models

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