# Split100

### From ObjectVision

The transition potential calculation variant Split100 differs from Mnl100 by the replacement of the Multi Nomimal Logit transformation of \( S_ij \) and \( N_ijt \) respectively by a binomial logit transformation .

\( SuitabilityLogit_{ij} \) is defined by `Rules/SuitabilityLogitExpr`

as the logit of \( v_{ij} \).

And furthermore

here is defined by `Rules/DynamicNeighbourLogitExpr`

as the logit of \( N_{ijt} \), the linear combination of neighbourhood data.

For the rest, all definitions are equal to those for Mnl100.

Split100 most closely resembles the calculation of transition potentials in DynaClue, especially when Neighbourhood Enrichment would be reactivated. The definitions of Mnl100 and Linear100 more closely reproduce what has been estimated by the logistic regressions on suitability factors and neighbourhood enrichment or potential.

Thus, The resulting Transition Potential \(TP_{ijt}\) for allocatable land unit \(i\), allocatable land use type \(j\) and time step \(t\) is defined as

- if not \(Allow_{ijt}\) then \(-5[EUR/m^2]\)
- if \(Allow_{ijt}\) then \((1-W_j)*S^{L}_{ij} + W_j * N^{L}_{ijt}\) with \(W_j\) is the j-th entry of the scenario parameter vector Neighbourhood/Weight.

\(S^{L}_{ij}\) is defined by `Rules/SuitabilityLogitExpr`

as \( exp(v_{ij}) \over {1 + \exp(v_{ij})}\)

\(v_{ij}\) is defined by `Rules/SuitabilityExpExpr`

as `min_elem(MakeDefined(SuitabilityData_ij, -1000000.0), 80.0)`

which means that undefined SuitabilityData is replaced by a very negative value and very positive values are capped to a maximum of 80 to prevent numeric overflows in the exponential function.

`SuitabilityData_ij`

is defined by `alloc1.txt`

as a linear combination of factor map data.

\(N^{L}_{ijt}\) is the combined neighbourhood value, which is defined by `Rules/DynamicNeighbourLogitExpr`

as
\( \exp(N_{ijt}) \over {1+\exp(N_{ikt})} \)

\(N_{ijt}\) is defined by `Rules/DynamicNeighbourExpExpr`

as `min_elem(Alloc2/ConstWeight_j + DynamicNeighbourData_ijt, 80.0)`

which means that very positive values are capped to a maximum of 80 to prevent numeric overflows in the exponent function.