## 2 Data and Methods
### Analysis
Reclassification was iterative, each iteration addressing commission error within a particular high-error subgroup and restricted to the spatial extent of same. There were, overall, five subgroups reclassified within the footprint (Path: 172 Row: 071) but only four subgroups directly affected error in the primary cropland class: two cropland and two settlement. We limit our description of method and models to these subgroups, describing the approach to reclassification in detail using one of the cropland subgroups and one of the settlement groups as examples. Commission error within the _cropland_3_ class resulted in 13 known areas of savanna misclassified as cropland (Table 2), indicating a data high degree of spectral confusion between savanna and cropland within this strata. We randomly sampled 200 locations within the _cropland_3_ thematic subgroup and assigned a land cover label (Operation 5, Figure 2). Land cover was interpreted for 176 observations with high confidence, the remainder were eliminated from the analysis. The assessment indicated that classification error was distributed between two primary land cover categories (e.g., cropland and savanna) within subgroups; the binary outcome allowed us to use logistic regression to estimate the probability that one of the two particular land covers was present given a set of predictors. The binary logistic regression model has the form:  
\[ln\left(\
icefrac{{p}}{{(1-p)}}\right)=a+b_{1}x_{1}+b_{2}x_{2}+\ldots b_{n}x_{n}, \tag{1}\]  
where \(p=\) probability of a case belonging to category 1; \(p/(1-p)=\) odds; \(a=\) constant; \(n=\) number of predictors; \(b_{1}...b_{n}=\) regression coefficients; and \(bx_{1}...x_{n}=\) regression predictors  
Logit models are used as the basis for pixel reclassification for a number of reasons. First, logistic regression does not assume a linear relationship between predictors and the outcome variable. Second, accuracy assessment of the subgroup thematic map indicates that the dependent variable is dichotomous. Third, there are no predictor requirements for normality, linearity, or equal variance within primary categories of subgroups. Fourth, the primary categories are mutually exclusive and exhaustive. Last, logit models provide an efficient way of testing classification outcomes and offer a flexible interface for evaluating the contribution of any given predictor, or set of predictors. Predictors for the logit model were generated from the original multi-spectral data, incorporating elements of phenology and sub-pixel composition of land cover. Multi-temporal data is utilized to capture variability in phenology which has been demonstrated to enhance differentiation between cropland and surrounding natural land cover [59, 64, 65, 66] as well as among crop type [67, 68]. Temporal intra-band differencing (e.g., B1\({}_{\text{T}}\)-B1\({}_{\text{T}2}\)) was adopted to measure change in phenological states within the unique spectral windows of each band, between date 1 (T\({}_{1}\)) and date 2 (T\({}_{2}\)) (Operation 6, Figure 2). Quantitative subpixel information of surface components was estimated using SMA to spectrally unmix one image of the seasonal image pairs (Operation 7, Figure 2). We selected the Landsat image acquired during the harvest season since spectral separation between cropland and the surrounding natural savanna was slightly greater than that found in the preseason scene. No discernible advantage in separation between cropland and settlement was detected between scenes. A Sequential Maximum Angle Convex Cone (SMACC) [69], utilizing a residual minimization model, was used to identify a _pseudo_ set of image endmembers that were displayed in a scatterplot amongst all pixels in the TM image as reference locations that would guide endmember selection. The set of four endmembers used in this analysis was selected through iterative testing of candidate pixels at reference locations, representing photosynthetic vegetation (PV), soil, non-photosynthetic vegetation (NPV), and shade components(Figure 4).