# Mnl100

### From ObjectVision

Mnl100 is a calculation schema in the EuClueScanner for calculating dynamic transition potentials that is defined in ModelTraits.dms. Alternative ModelTraits are: Linear100 and Split100.

Its main characteristic is that the linear combination of suitability factors (as defined by alloc1.reg) and the linear combination of DynamicNeighbourData factors (as defined by alloc2.reg) are each fed to the exponential function and then rescaled separately by the sum for all land use types to a 0..1 value and then combined using the neighbourhood weight value \( W_j \).

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 \((1-W_j)*S^{MNL}_{ij} + W_j * N^{MNL}_{ijt}\) with \(W_j\) is the j-th entry of the scenario parameter vector Neighbourhood/Weight.

\(Allow_{ijt}\) is based on the allowed matrix combined with age dependent bottom-up rules.

\(S^{MNL}_{ij}\) is defined by `Rules/SuitabilityMnlExpr`

as \(\exp(v_{ij}) \over {\sum\limits_{k}exp(v_{ik})}\)

\(v_{ij}\) 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.

\(N^{MNL}_{ijt}\) is defined by `Rules/DynamicNeighbourMNLExpr`

as
\( \exp(N_{ijt}) \over {\sum\limits_{k}\exp(N_{ikt})} \)

\(N_{ijt}\) 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.

`DynamicNeighbourData_ijt`

represent either linear combinations of Neighbourhood Potentials or linear combinations of the Neighbourhood Enrichment depending on the definition of Rules/DynamicNeighbourExpr2, which can refer to Rules/DynamicNeighbourExpr0 that define linear combinations of the non-scaled PotentialData factors or Rules/DynamicNeighbourExpr1 that define the linear combinations of EnrichmentData factors. In the EUCS100, PotentialData has been used as until 28-03-2013 there was a bug in the definition of Mean Enrichment calculation resulting in Neighbourhood Enrichments that were SUM(Kernel)=88 times too high.