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However, it was pointed out that these models require strong assumptions with regard to the non-effect of the removed variable and therefore, this solution may be not appropriate in many situations.
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We attempted to address this by consecutively adding or removing variables, and analysing subsets of individuals (extensive sensitivity analyses).
Entering and removing variables and interaction terms alters the overall goodness of fit of a model and changes the AIC.
Model reduction was performed by stepwise backward elimination, removing variables and interactions not significant at P < 0.05.
For multiple regressions, a backward elimination procedure used log-likelihood criteria with p > 0.1 for removing variables and p < 0.05 for entering variables.
Variables from each of the submodels were then included in the complete models, which were again reduced iteratively by considering [1] the Hosmer and Lemeshow test for goodness of fit, [2] the drop in Nagelkerke's R when removing variables, and [3] the significance of the association of each variable in the model with endometriosis (dropping variables from P>.5 down to P>.2).
Prior to fitting the models, we identified a limited set of strongly collinear variable groups with an r>0.779 (Supplementary Fig. 12) and removed variables within these groups that were deemed less likely to be influential for woody cover change.
We controlled for multicollinearity by checking tolerance scores of variables; where tolerance was <0.2, we considered bivariate relationships with Spearman rank correlation and removed variables of lesser ecological relevance.
We applied a backward stepwise removal procedure (Grafen & Hails, 2002) to avoid problems from including nonsignificant terms (Engqvist, 2005) and the removed variables were re-entered one by one to the final model to obtain relevant statistics.
Data were radiometrically corrected to remove variable acquisition gains, power levels, insonification area and grazing angles, whereas geometric corrections were applied to compensate for the slant range.
VNNotExist Replace by non-existing variable name D. Variable value 1. VVRemove Remove variable value 2.
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