de Bie, Kees
Table 1. Count of surveyed mango orchards in Phrao by terrain unit
Hills Footslopes Terraces Total
Mango alone 8 13 2 23
Mango + Lychee 1 1 2 4
Mango + Longan 5 3 3 11
Mango + Lychee + Longan 2 3 6 11
4.1 Yields
Middlemen buy the produce before harvest, i.e. on the tree, and arrange the actual
harvesting (April-June) between themselves. Thus, when interviewed, farmers
could only report the ‘farm gate’ lump sum received for their crop. The bargaining
skills of the farmer and middleman, the total quantity involved, and the quality of
the fruit, all influence the price. In 1993, farm-gate mango prices varied from 10-30
Bath/kg (40-120 US-$ cents/kg)”.
Yield data from 47 orchards were available? for analysis; they were expressed in
'000 Bath/ha. Yield data were estimates by dividing the proceeds by mango sales
by the orchard size and the fraction of mango trees per orchard. In 18 orchards
surveyed, there was "0" mango yield. The many zero yields and many cases with
low yield resulted in a non-normal distribution of the yield data. Figure 3^ shows
the Z-scores. In theory, a lognormal distribution fits well to such data and to data
that cannot assume negative values (such as yields). To establish data normality
as required for linear regression, logarithmic data transformation is applied. Figure
3^ shows the results of a natural log transformation. The “0” yields are all omitted;
the Z-scores of the 29 remaining yield data show a linear pattern. Testing the
Ln(yield) data for normality by the 2-tail Kolmogorov-Smirnov test provided a P-
value of 62.3%, which is acceptable. Adding the 18 “0” yields by using the arbitrary
Ln(Yield+1) transformation (Figure 3°) provided Z-scores that were partly linear,
partly non-linear; when tested together, the transformed data were not normally
distributed (Figure 3%). Transformations like aY" (with n<0) did not result in further
improvement because of the large number of “0” yields.
Initial models proposed were based on the observation that certain orchards
produced fruit (according to a lognormal distribution), while others did not. They
were (see sections 5 and 6):
e A model assuming a “0,1” Poisson distribution indicating “when yields can be
expected”, and estimated through logistic regression. Estimated is the S-
shaped model: Yield probability 7 e / (14 e), where ‘Ip’ stands for the linear
prediction: a - b.X4 + c.Xa+...z.X; (a to z are coefficients and X, to X,
independents; Jongman ef al. 1987).
e A model, established through linear multiple regression, assuming normal
distribution of logarithmic transformed yields for the “1” population.
The highest reported yield was 250,000 Bath/ha. At 10 Bath/kg this translates into 25 t/ha.
2 Farmers could not provide reliable yield information.
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B7. Amsterdam 2000.
325
