DA is a technique, which discriminates among k classes 
(objects) based on a set of independent or predictor variables. 
The objectives of DA are to (1) find linear composites of n 
independent variables which maximize among-groups to 
within-groups variability; (2) test if the group centroids of the k 
dependent classes are different; (3) determine which of the n 
independent variables contribute significantly to class 
discrimination; and (4) assign unclassified or “new” 
observations to one of k classes (Lowell, 1991). The variates 
for a discriminant analysis, also known as the discriminant 
function takes the following form: 
Y, 2a*fiXy t foXot...t fX, (4) 
where 
Y; = discriminant Y score of discriminant function j 
for object (class) k 
a = intercept 
J = discriminant weight for independent variable i 
X5, 2 independent variable i object (class) k 
3.5 Model validation 
Model validation (evaluation) can be done by split-sample 
validation, as mentioned previously. For each model, predict 
the response of the remaining data, and calculate the error from 
the predictions and the observed values (De'ath and Fabricius, 
2000). We also used overall accuracy and kappa coefficient to 
assess models, because overall accuracy only include the data 
along the major diagonal and excludes the errors of omission 
and commission, kappa incorporates the non-diagonal elements 
of the error matrix as a product of the row and column marginal 
(Lillesand et al., 2008). 
4. Results and Discussion 
For the base models shown in Table 1, the accuracy of 
MAXENT (kappa value 0.84) was the best in SS-1, followed 
by GLM (0.7) and GARP (0.6), and DA (0.55) was the worst. 
The kappa values of non-parametric algorithms, MAXENT 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B7, 2012 
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia 
   
(0.46) and GARP (0.12) in SS-2, dropped sharply, while 
parametric GLM (0.7) and DA (0.55) dropped slightly in SS-2 
as tested by independent samples from the Kuandaushan-trail, 
with 076 km away from aforementioned two training sites in 
Huisun. For the first data-merged models in SS-3, the kappa 
values of four models lifted back to almost the same values as 
those in SS-1 from SS-2 or even better, and the four models 
still kept the same order in accuracy as that in SS-1. As the 
first data-merged models built in SS-3 were applied to a larger 
area in SS-4 including Tong-Mao Mountain, with 10 km away 
from the three sites at Huisun, the kappa values of MAXENT 
and DA declined to near zero, as well as GARP and GLM 
could not work possibly due to a limit on the size of data layer, 
a big difference in the domain values of predictor variables 
between Huisun and Tong Mao, or some other possible 
unknown factors which we will figure out later. In contrast, 
the kappa value of MAXENT in SS-5 rebounded strikingly as 
the second data-merged models built in SS-5 were applied to 
the same area as that in SS-4 (Table 2), while that of DA rose 
back slightly. Consequently, it was unlikely to accurately 
extend spatial patterns of CFs from the Huisun area to 
Tong-Mao Mountain area with 10 km gap or to the entire study 
area encompassing Huisun by predictive models merely based 
on topographic (indirectly operating) variables. 
The models, either base models in SS-1 or the first data-merged 
models in SS-3, accurately predicted the potential habitats of 
CFs in Huisun, and substantially reduced the area of field 
survey to less than 10% of the entire study area, even less than 
2.5% with MAXENT (Tables 3 and 4 and Figure 2). In 
Huisun study area, all the potential CF habitats predicted 
occurred in the Kuan-Dau watershed, and none occurred in the 
Tong-Feng watershed because of remarkable differences in 
humidity and solar illumination between them. The outcome 
had been proved true by field surveys through which almost no 
cycad-ferns were found in the Tong-Feng watershed. In 
contrast, neither the first data-merged models in SS-3 nor the 
second data-merged models in SS-5 could not accurately 
extrapolated CF spatial patterns when they were applied to the 
larger area encompassing Ton Mao Mountain. Consequently, 
they could not reduce the area of field survey to less than 10% 
of the entire study area, even greater than 25% with DA (Tables 
5 and 6 and Figure 3). 
  
  
  
  
Class MAXENT GARP GLM DA 
SS] SS)  SS3 SS] SS? SS3 SSL SS2 SS3 .SS|I SS2 M SS3 
Training Overall (%) 97 97 96 88 88 95 95 95 95 86 86 87 
Kappa .89 .89 38 62 ‚62 27 .83 .83 85 63 .63 68 
Test Overall (%) 95 90 95 88 78 91 96 92 92 85 84 85 
Kappa S4 46 2% 60 12 77 J0 .70 77. .00  .55 .62 
  
Table 1 SS-1, SS-2, SS-3: the accuracies of the models with elevation, slope, and terrain position variables for predicting 
the potential habitat of CFs. 
  
  
  
  
Class MAXENT GARP GLM DA 
SS4 SSS SS4 SSS Ss4 SS5 SS4 SS5 
Training Overall (26) 86 91 — zz — — 70 69 
Kappa ‚64 15 = m» — i 34 33 
Test Overall (%) 82 91 — — — 64 66 
Kappa .06 73 — — — a. .05 0.25 
  
Table 2 SS-4 and SS—5: the accuracies of the models with elevation, slope, and aspect variables for predicting 
the potential habitat of CFs.