de Bie, Kees
5. Logistic regression
In section 4.1, it was discussed that a Poisson distribution denoting ‘yield’ (16x)
versus ‘no yield’ (29x) can be estimated through logistic regression. The
established linear prediction (LP) part of the logistic model with a probability for all
coefficients below 1096, and a McFadden's Rho? of 62%, reads:
LP = 2.73 - 0.89*SLO + 0.085*SLO? - 4.20*TXT - 3.35*TER + 2.88*WHC - 10.13*HPI + 3.14*PRU
* 3.24*YEA + 3.27*NPK - 4.00*TRA
Where:
SLO = Slope (%) within the orchard
TXT = 1 if top-soil texture is LS or SL (not C, SC, or SCL)
TER = 1 if terrain is terrace (not hill or footslope)
WHC = 1 if reported water holding capacity (by the farmer) is poor (not fair or good)
HPI = 1 if hose-pipes / tubes for irrigation purposes were present in the orchard (otherwise 0)
PRU = 1 if pruning of trees is done (otherwise 0) J
YEA = 1 if relatively a good year and -1 if relatively a bad year
NPK = 1 if mineral fertilizers applied
TRA = 1 if weeding with a tractor (not manual)
The model's sensitivity (response prediction accuracy) is 87% and specificity (non-
response prediction accuracy) is 77% (Figure 10). The model suggests that the
probability to expect yield (assumed mechanisms for ‘flower initiation’ according to
a “0,1” Poisson distribution) is higher if orchards are:
e Situated on finer textured soils on steeper slopes located in hills and footslopes
with poor water holding capacity, and
e not watered by hose-pipe, fertilized by NPK, pruned, and weeded by tractor.
Figure 10 shows that the prediction is prone to errors and that the normal
distribution lines of the two groups overlap, i.e. estimates are not all zeros and
ones. The model is thus not conclusive. Most likely, used independents have an
indicative behavior and not necessarily a causal one.
1.0 T T T T T T ue K T T T T ! c 3 T T T T T T T T
0.9- tT | |- $ [ without actual yield 1
0.8f t ia Bl |
L I] i a r 7
_ 07 | y S abs x |
> 0.61 | ii f T + error quadrant,
8 o5 & Ii 1 $3 E rr
& 0.4- | | it ox 2S. f with actual yield q
os} | + ed unns " 7
02 || 1 oy 1 s À
E | $ 1 1
0.1r Lr: dp 7 = L error quadrant j
0.0 Ei l = L I 3 b lal Lu à
so 20 10 0 10 20 30 0 0.2 0.4 0.6 0.8 1.0
a. Count (no yields) ^ Count (with yields) b. Probability to produce yield
Figure 10. Group-wise comparison of logistic model results:
a: Probability to expect mango yield.
b: Z-scores of mango yield probabilities.
332
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B7. Amsterdam 2000.
