## 2 Data and Methods
### Analysis
Results of the constrained model showed few pixels with values below 0 or above 1 and a mean RMS error of 5.538 indicating that the selected endmembers effectively characterized the landscape. An inspection of RMS distribution revealed the highest error pixels concentrated in areas that seasonally inundate with water, however the magnitude of error was not considered serious enough to warrant modification of the model. The library of candidate predictors utilized in the logit model consisted of six difference variables (one for each band pair, 1-5, and 7) and four fraction images. Predictor values were extracted at the sampled locations and collated (Operation 8, Figure 2). The type of error that we detect within subgroups is always commission error. Our logit models are used to identify misclassified pixels of the commissioned category, assigning a value of 1 to cases associated with the latter category and 0 to cases associated with the primary category to which the subgroup has membership. For example, we wanted to identify misclassified savanna within the _cropland_3_ subgroup, correcting the commissioning of savanna by cropland, so an outcome value of 1 was assigned to savanna cases and outcome value of 0 to cropland. The 10 candidate predictors were input to the logit model using backward stepwise selection (Operation 9, Figure 2). The significance level for removal was set at 0.10 and classification cutoff at 0.5. Overall fit of the model was evaluated using scalar measures of fit, such as log-likelihood, as well as information based measures [(70)]. The likelihood ratio test (\(G^{2}\)) compares the log likelihoods of the full and constrained model (_i.e._, a model with all coefficients but the intercept constrained to zero), and is reported as a chi-square statistic, with degrees of freedom and a statistical significance level. The likelihood ratio test allowed us to test the hypothesis that all model coefficients except the intercept were zero. Common pseudo-R square measures, such as [PERSON]'s R\({}^{2}\) and Nagelkerke R\({}^{2}\) were used to assess the adequacy of the model. We also used the [PERSON]'s goodness-of-fit test to compare predicted to observed frequencies, whereby a test with a large p-value indicates a good fit between the model and the  
Figure 4: **(Left)**: Location of selected endmembers in scatterplot where Landsat TM band 4 is assigned to the y-axis and band 7, the x-axis. Values of X and Y-Axes are at-surface reflectance. (**Right**): Endmember pixel boundaries mapped and overlaid on high-resolution imagery (Google Earth). data. Finally, to compare full (non-nested) to nested models we employ information measures of fit. Comparisons were made between the full, or non-nested (10 predictor), and nested (4 predictor) models using the difference in the Bayesian Information Criterion (BIC) measures for the two models (where an absolute difference of 2-6 suggests positive evidence, 6-10 indicates strong evidence, and a difference greater than 10 suggests very strong evidence in favor of the nested model [70]. Using Erdas IMAGINE's _Model Builder_, parameters returned from the nested logit model were applied to the predictor layers, utilizing the subgroup thematic map to restrict the operation to the spatial extent of the strata of interest (Operation 10, Figure 2). Pixels within the subgroup were recoded to the appropriate land cover based on a threshold probability of 50% (Operation 11, Figure 2). Operations 5, 8-11 (Figure 2) were repeated for the remainder of high error subgroups. Once all high error subgroups were addressed, validation was performed using the dataset generated in (Operation 3, Figure 2).