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and time. We then generate multiple variables from these data (number of consecutive dry days, number of days with temperature above a certain threshold, total
rainfall accumulated, etc.). We also use variables related to the terrain and soil. The
Plackett-Luce model picks the best predictor and determines the best point where to
split the data (for example, making a group with less than four consecutive dry days
and another group with more than 4 days).
In our second example, the model splits the set of farmers in two equal groups.
In the simulation, 250 farmers were assigned to each condition. It correctly identifies the drought resistant varieties—Varieties 6 and 10—which jump out in the right
part of the graph. The graph also shows 95% confidence intervals around the parameter estimations, which give an idea of the certainty we have that the varieties are
really different.
The results of our simulation illustrate how the tricot approach can distinguish
between different varieties and has the power to evaluate the variety by climatic
conditions. In a simulation of different environmental conditions, it is clear that the
performance of the different varieties varies based on those basic climatic conditions. This influences the evaluation of the farmers, who provide different
feedback.
11.3 Deriving Variety Recommendations from On-Farm
Trials
The outputs from the Plackett-Luce model and the Plackett-Luce tree are shown on
a log-scale in reference to winning from a particular variety. These values are a bit
abstract, but as shown in Fig. 11.2, the values are linearly related to the underlying
trait values. The PL model can also produce probabilities of winning from all other
varieties for each of the varieties, which are easier to interpret. These values can be
used to construct portfolios of varieties.
We illustrate variety portfolio construction with an example. To construct robust
portfolios, we use theory from financial asset management, adapting the method of
Dembo and King (1992) to relative losses (probabilities of being the best). The
method is closely related to Conditional Value at Risk (Testuri and Uryasev 2004).
This is a state-of-the-art metric now widely used in banks, which was previously
applied by Sukcharoen and Leatham (2016) to variety portfolio construction.
For simplicity, we focus on a smaller example, with four varieties in two seasonal climate scenarios. In Table 11.1 we show a possible output from a PlackettLuce tree, which can be interpreted as a payoff matrix for the construction of robust
portfolios.
We generated another table from this, Table 11.2, showing the relative opportunity loss. We obtained these values by dividing the values by the highest value in
each column, to first get the so-called competitive ratio. We subtract the competitive
ratio from 1 to get relative opportunity loss values. Different types of seasonal
C. Fadda and J. Etten
and time. We then generate multiple variables from these data (number of consecutive dry days, number of days with temperature above a certain threshold, total
rainfall accumulated, etc.). We also use variables related to the terrain and soil. The
Plackett-Luce model picks the best predictor and determines the best point where to
split the data (for example, making a group with less than four consecutive dry days
and another group with more than 4 days).
In our second example, the model splits the set of farmers in two equal groups.
In the simulation, 250 farmers were assigned to each condition. It correctly identifies the drought resistant varieties—Varieties 6 and 10—which jump out in the right
part of the graph. The graph also shows 95% confidence intervals around the parameter estimations, which give an idea of the certainty we have that the varieties are
really different.
The results of our simulation illustrate how the tricot approach can distinguish
between different varieties and has the power to evaluate the variety by climatic
conditions. In a simulation of different environmental conditions, it is clear that the
performance of the different varieties varies based on those basic climatic conditions. This influences the evaluation of the farmers, who provide different
feedback.
11.3 Deriving Variety Recommendations from On-Farm
Trials
The outputs from the Plackett-Luce model and the Plackett-Luce tree are shown on
a log-scale in reference to winning from a particular variety. These values are a bit
abstract, but as shown in Fig. 11.2, the values are linearly related to the underlying
trait values. The PL model can also produce probabilities of winning from all other
varieties for each of the varieties, which are easier to interpret. These values can be
used to construct portfolios of varieties.
We illustrate variety portfolio construction with an example. To construct robust
portfolios, we use theory from financial asset management, adapting the method of
Dembo and King (1992) to relative losses (probabilities of being the best). The
method is closely related to Conditional Value at Risk (Testuri and Uryasev 2004).
This is a state-of-the-art metric now widely used in banks, which was previously
applied by Sukcharoen and Leatham (2016) to variety portfolio construction.
For simplicity, we focus on a smaller example, with four varieties in two seasonal climate scenarios. In Table 11.1 we show a possible output from a PlackettLuce tree, which can be interpreted as a payoff matrix for the construction of robust
portfolios.
We generated another table from this, Table 11.2, showing the relative opportunity loss. We obtained these values by dividing the values by the highest value in
each column, to first get the so-called competitive ratio. We subtract the competitive
ratio from 1 to get relative opportunity loss values. Different types of seasonal
C. Fadda and J. Etten