## 2 Methodology
### Phase 3. Land Cover/Use Change Model
#### 2.4.2 Steps for Generating a Land-Use Model
On the contrary, any positive or negative value indicates that the analyzed variable affects the observed land change. Positive values indicate an association and negative values show repulsion. It is considered statistically significant with a 95% probability if \(|C|>1.96 SD(C)\). Step 3. Correlation analysis. The WoE and contrasts are provided for each transition and factor. The only assumption the factors must meet is that they are independent, verified by the Cramer Index, considering less than 0.3 as no association tolerance [40]. In this work, the following degrees of association are taken into account to make a decision:  
* 1 : There is a complete association between variables. * \([0.75-1[\): There is a strong association between variables. * \([0.5-0.75[\): There is a moderate association between variables. * \([0.25-0.5[\): There is minimal and very poor association between variables. * \([0-0.25[\): There is no association between variables  
In our case, we need to study the association between all pairs of variables formed among the three categorical variables and each of the created ranges of the continuous variables. Step 4. Building, calibrating, executing and validating the simulation model. A model is built based on cellular automata where each cell (or pixel) will depend on the states of neighboring cells. In particular, a change probability allocation mechanism is used for each one. Subsequently, cells expand or contract (changing to another land type) depending on what was determined in the previous steps conditioned by such a probability. Here, two complementary transition functions can be used: (1) expansion/contraction of cell groups (expander) of a given category and (2) generation of new cell groups (patcher). Control parameters of the cell group's size and shape, such as their average size, size variance and isometry, can be modified. Increasing the size of the cell group allows obtaining groups of cells that are less distributed in space, increasing the size variance of the most diverse cell groups, and increasing the isometry by 1 makes it possible to generate more isometric cell groups. The formation of groups of cells can be canceled by setting the group size to 1, and the variance to 1 will not allow the formation of new groups [31]. Subsequently, a validation of the simulated map with the observed map is carried out. This validation uses fuzzy similarity indices, which allow comparing the simulated and observed land-use change maps, considering the spatial coincidence under different tolerance levels (different window or pixel sizes). These indices focus on the areas of change, considering not only the classification of one pixel but also its neighboring pixels [41]. It is suggested that obtaining values above 50% similarity between the compared maps would be satisfactory to validate the model. Step 5. Projecting to the future. Once the model's ability to satisfactorily predict changes has been determined, it can generate future maps that provide valuable information on growth and development trends. These maps allow understanding and anticipating changes to improve decision-making.