130
way. In Example 1, farmers draw random values from a normal distribution separated by a small interval and rank the varieties based on these values (see Fig. 11.1).
This simulates the error that farmers make, following our findings on the accuracy
of farmer observations in these trials for a relatively difficult trait (Steinke et al.
2017). An interesting feature of this ranking approach is that it also works for more
elusive traits that depend on farmers’ preferences, such as the taste of the product or
farmers’ overall evaluation of each variety, which is eventually what determines
variety adoption.
In Fig. 11.2, the results of the first simulation can be seen. The original input
values of the simulation are on the x axis and the Plackett-Luce model estimates are
on the y axis. As the graph shows, the PL model is able to reconstruct the values
very closely, with a correlation of 0.994 with the original values. In a few cases, the
model does not retrieve the right order. Variety 13 is ranked lower than Variety 12
and Variety 18 is ranked lower than Variety 17. In other words, only 10% of the
varieties are shifted by one position. There is very little information loss. However,
there are important features that reveal the limitations of the PL model. The y scale
represents the log-odds of winning from Variety 1, the variety arbitrarily chosen as
our reference. The scale of the model parameters does not have an absolute zero.
Variety 1 has a parameter value of zero, but any other variety can be chosen as the
reference variety. In reality the underlying mean value for Variety 1 is 4. The original value cannot be retrieved from the model. In other words, the index given by the
PL model has a meaning only relative to the other varieties, even though there is a
strong linear relationship with the underlying latent variable.
In Example 2, we added a complication in that 250 of the 500 farmers experienced a drought condition, which made two varieties increase their mean. However,
there is also an error in the measurement of the drought condition. We then applied
a Plackett-Luce tree model to this artificial dataset, to visualise how it distinguishes
between the two groups of farmers and their variety rankings. Also, we show how to
derive variety recommendations from the model outputs to respond to climate risk.
0
2
4
6
8
10
0.0 0.1 0.2 0.3 0.4
Simulation input value
Probability density
Fig. 11.1 Probability distributions used for the simulation for 20 varieties. Normal distributions
with standard deviation of 1 and means separated by an interval of 0.185 (value from Steinke et al.
2017 for “challenging trait”)
C. Fadda and J. Etten
way. In Example 1, farmers draw random values from a normal distribution separated by a small interval and rank the varieties based on these values (see Fig. 11.1).
This simulates the error that farmers make, following our findings on the accuracy
of farmer observations in these trials for a relatively difficult trait (Steinke et al.
2017). An interesting feature of this ranking approach is that it also works for more
elusive traits that depend on farmers’ preferences, such as the taste of the product or
farmers’ overall evaluation of each variety, which is eventually what determines
variety adoption.
In Fig. 11.2, the results of the first simulation can be seen. The original input
values of the simulation are on the x axis and the Plackett-Luce model estimates are
on the y axis. As the graph shows, the PL model is able to reconstruct the values
very closely, with a correlation of 0.994 with the original values. In a few cases, the
model does not retrieve the right order. Variety 13 is ranked lower than Variety 12
and Variety 18 is ranked lower than Variety 17. In other words, only 10% of the
varieties are shifted by one position. There is very little information loss. However,
there are important features that reveal the limitations of the PL model. The y scale
represents the log-odds of winning from Variety 1, the variety arbitrarily chosen as
our reference. The scale of the model parameters does not have an absolute zero.
Variety 1 has a parameter value of zero, but any other variety can be chosen as the
reference variety. In reality the underlying mean value for Variety 1 is 4. The original value cannot be retrieved from the model. In other words, the index given by the
PL model has a meaning only relative to the other varieties, even though there is a
strong linear relationship with the underlying latent variable.
In Example 2, we added a complication in that 250 of the 500 farmers experienced a drought condition, which made two varieties increase their mean. However,
there is also an error in the measurement of the drought condition. We then applied
a Plackett-Luce tree model to this artificial dataset, to visualise how it distinguishes
between the two groups of farmers and their variety rankings. Also, we show how to
derive variety recommendations from the model outputs to respond to climate risk.
0
2
4
6
8
10
0.0 0.1 0.2 0.3 0.4
Simulation input value
Probability density
Fig. 11.1 Probability distributions used for the simulation for 20 varieties. Normal distributions
with standard deviation of 1 and means separated by an interval of 0.185 (value from Steinke et al.
2017 for “challenging trait”)
C. Fadda and J. Etten