# Land Development Model of SMARTPLANS

The land development model of SMARTPLANS predicts the total amount of developed floorspace that is available to be occupied by land use activities type *L*. Land use activities could represent households, people, or firms, etc. Let *FS _{iL}(t)* be the amount of floorspace of type

*L*in zone

*i*. Also, let

*FS*be the region-wide total amount of floorspace type

_{L}(t+1)*L*. The predictions for the land development model depend on running two integrated models:

**Building demolition model**: This model is used to calculate the probability (or proportion),*PD*, of certain floorspace_{iL}*L*being demolished in zone*i*at time*t*+ 1. The probability is formulated as the following logistic regression model:where betas are the estimated parameters to be inputted in the model for type

*L*, and*X*is a set of_{ki}*k*zonal characteristics found to have significant influence on the likelihood of that floorspace*L*being demolished.-
**Floorspace location choice model**: This model is used to calculate the probability of allocating developed floorspace type*L*to zone*i*at time*t*+ 1. To account for the heterogeneity that might exist within the one type of floorspace, the location choice model is setup in a way that allows the user to define certain classes*C*within type*L*. Here, the user must specify the share*P/*for each class_{C|L}*C*within*L*exogenously. The logit probability for class*C*belonging to floorspace*L*to be allocated to zone*i*at time*t*+ 1 is formulated as follows:*V*is a linear-in-parameter systematic utility function observed by class_{iL|C}*C*of land use type*L*and attributes of the zone*i*.

## Floorspace Simulation Formula

Floorspace of type *L* in zone *i* at time *t* + 1 is calculated as follows:

where *FR _{iL}(t+1)* represents the amount of floorspace type

*L*in zone

*i*that was not demolished by time

*t*+ 1,

*FN*is the amount of newly developed floorspace type

_{iL}(t+1)*L*in zone

*i*at time

*t*+1,

*PF*is the previously defined logit probability used to allocate newly developed floorspace that is available to class

_{iL|C}*C*within type

*L*to zone

*i*at time

*t*+1,

*P*is an exogenous value representing the share of class

_{C|L}*C*within type

*L*. The amount of floorspace type

*L*that was not demolished by time

*t*+ 1 is calculated as follows:

where *PD _{iL}* is the probability of floorspace type

*L*being demolished in zone

*i*by time

*t*+1 (outcome of the building demolition model). Finally,

*FN*is calculated as follows:

_{iL}(t+1)