You’re correct that you could use the advanced feature called spatial multipliers to capture the spatial (and temporal) effect of income on the probability of transition from forest to urban. Spatial multipliers let you adjust the probability of transition in any cell on your landscape at any time and take the form of a raster by timestep. The transition probability of a given cell on your landscape from one state to another is the product of the spatial multiplier raster and your base transition probabilities. If you set your base transition probabilities all to 1 (in your Pathway Diagram), you can enter the actual value of your probabilities as multipliers. You could go so far as to have a spatial multiplier raster for each transition and each timestep.
If you have rasters of projected income in 2025 and 2050, you can use them to generate spatial multipliers for those years. To generate spatial multipliers, you would need to know the relationship between income and transition probability. This gets to your question of whether ST-Sim is able to run a spatial regression in order to determine the relationship between income and transition probability based on historic data. We use R for this type of statistical analysis as there are many excellent packages that allow you to use frequentist or Bayesian methods to estimate regression coefficients. You could use any language or program you like to run the spatial regression, e.g. Python or ArcGIS. The nice thing about using R is that you can use the rsyncrosim R package to interface with ST-Sim which lets you both prepare ST-Sim inputs, such as spatial multipliers, and run ST-Sim models all from within the same platform. There is always the possibility of developing an ST-Sim Add-On which would perform the spatial regression to generate spatial multiplier rasters internally but there hasn’t been a demand for this to date as most of our advanced users like to script and customize these input preparation steps themselves.
One last note is that the spatial multipliers can be generated dynamically during the course of a simulation in response to changes in the landscape. For example, ST-Sim can pause every 10 years and feed information on the state of the landscape to an R script which would then calculate new spatial multipliers and pass them back to ST-Sim and the simulation would continue.