Net         1.0722         $\alpha=0.05$, $\lambda=6.57e^{-4}$             1170
  Component Lasso     0.8775         $\alpha=0.05$, $\lambda=2.45e^{-5}$, $noc=37$   564
  **Environment 3**                                                                  
  Lasso               0.8216         $\lambda=7.23e^{-3}$                            28  
  Naive Elastic Net   1.1087         $\alpha=0.05$, $\lambda=4.89e^{-4}$             1170
  Elastic Net         1.1249         $\alpha=0.05$, $\lambda=1.20e^{-3}$             1125
  Component Lasso     0.8830         $\alpha=0.05$, $\lambda=1.62e^{-3}$, $noc=17$   303
  **Environment 4**                                                                  
  Lasso               0.8068         $\lambda=6.8e^{-3}$                             27  
  Naive Elastic Net   1.0487         $\alpha=0.05$, $\lambda=5.18e^{-4}$             1157
  Elastic Net         0.9349         $\alpha=0.05$, $\lambda=2.75e^{-3}$             1081
  Component Lasso     0.8200         $\alpha=0.05$, $\lambda=3.36e^{-5}$, $noc=33$   564

  : *Test MSE, parameters, and number of non-zero predictors for the real data set.* []{data-label="table:real"}

The component lasso achieves the lowest test MSE in environments 1 and 2 by splitting the variables into 29 and 37 connected components respectively. The lasso achieves the lowest MSE in environments 3 and 4. In this dataset, splitting the genomic markers into correlated groups helped improve the accuracy in certain environments. Sorting the predictors according to the connected components chosen by the component lasso and plotting the heat map of the sample covariance matrix reveals the block-diagonal structure of the genomic markers. The corresponding connected components can be seen in Figure \[fig:realheat\].

![*Heat map of the sample covariance matrix corresponding to the wheat data.*[]{data-label="fig:realheat"}](heat_real.png)

This example illustrates that the component lasso can provide improved prediction accuracy and interpretability in some 