ASSIGNMENT 5: EVALUATING MODEL UNCERTAINTY THROUGH SENSITIVITY ANALYSIS
Objective: Perform a sensitivity analysis to evaluate model parameters that are most influential in determining emerging patterns.
Use: NetLogo's parameters sweep tool called the Behavior space
Part 1: Creating a measurable emergent outcome - by new patch variable called nearest-neighbor-distance, as global variable nnd
Part 2: Perform a sensitivity analysis - by Tools-> Behavior space, create New Experiment
Part 3: Analyze results: Graph the time series of nearest neighbor distance values for the different parameter settings.
Part 4: Discussion
What is the difference between a variable and a parameters?
A variable represents a model state, and may change during simulation. A parameter is commonly used to describe objects statically. A parameter is normally a constant in a single simulation, and is changed only when you need to adjust your model behavior. (Source: http://www.anylogic.com/anylogic/help/index.jsp?topic=/com.xj.anylogic.help/html/data/Parameters%20and%20Variables.html)
In NetLogo, a 'variable' p.ex. 'distance_services_preference' presents the range of available values which could possibly 'vary' during the simulation run. A 'parameter' represents the only 1 value from the range of variable values which is stable in that moment.
Statistical characteristics of NND (nearest neighbor distance)
Summary of NND for all tested parameters:
NND
Min. 1st Qu. Median Mean 3rd Qu. Max.
1.215 1.420 1.532 1.616 1.664 3.532
runs: 7680
tested characteristics:
A initial_center. TRUE FALSE
B neighborhood_density_preference 0.00 0.25 0.50 0.75
C ideal_density 0.5 0.6 0.7 0.8 0.9 1.0
D aesthetic_quality_preference 0.00 0.25 0.50 0.75
E distance_services_preference 0.00 0.25 0.50 0.75
Sensitivity analysis for all tested parameters for nearest-neighbor distance
initial_center
neighborhood density preference
ideal density
aesthetic quality preference
distance services preference
Which parameter is the nearest-neighbor distance most sensitive to? Why do you think this is the case?
Which parameter is the nearest-neighbor distance least sensitive to? Why do you think this is the case?
I suppose to conclude than nnd is more/less sensitive to parameters if it is changing with decreasing/increasing parameters values.
Analysing above plots I assume that nnd is the most variable at low values of ideal_density (0.5) but remains unchainged with higher ideal_density values. The same pattern I can observe at 0 aesthetic quality preferences. From values > 0.25 preferences, nnd is not changing over time.
NND is onstantly decreasing with icreasing neighborhood density preference so the higher % of neighbor reference leads to lower NND values, so more clustered housing emergent pattern.
However, for aesthetic quality preference, at 0 values the NND could be close to each ther of far away, equaly from 0.25 the preferences for aesthetic values are not playing a significant roles in NND changes.
To conclude, the NND si most sensitive (most variable) to aesthetic quality preference and the least sensitive to existence of initial center. To idetify these influence it could be useful to create another experiment for Aesthetic quality and Ideal density and with more details in 0 - 0.25 and 0.5 - 0.6 preferences values, respectivelly. The distance_service_preferences shows interesting behavior, because with increasing preferences, the NND can increase leading to more dispersed habitations, not to more clustered, over the services centers, not close to neighbors.
In our parameter sweep we used the mean nearest-neighbor-distance as an output descriptive statistic. Describe why nearest-neighbor-distance may be important to homeowners. List at least one other measurement that we could have used and explain how it differs from mean nearestneighbor-distance.”
This values ins important determination of existing clusters and how far away are houses from one to another. However, this measure mx the reality - with only this measure we cant really deduce the occupation of landscape. I suppose that the density of houses/parcelle can be better way how to decribe occupation of cpace. If the NND will be same for all houses, that means that they are randomly distributed over space. Now we conclude that they are clustered, however we coudn't identify these clusters positions in space. Mean nearest neighborhood distance will not provide information about the space clustering. The same mean value can be obtained from highly clustered housed far away from each another with several houses between them and by randomly distiributed, non clustered houses (Figure below). In this reason we assume that another clusters characteristics are needed (number of direct neighbors, % of clustered houses from all houses, buffer direction of points of attraction, services centers...)
Equally, the total temporal development of NND (decreasing over time as the number of houses is increasing) is not recover. Finally we didn't examine the influence of preference values over time on NNDbut the final state of housing location.
Exemple of clustered/random habitation and the same NND obtained
Provide a 100 word summary of what the model describes with regards to how residential decision making leads to specific patterns of urban growth.
Residential decision making depends on their preferences to
-
services’ distances
-
aesthetic quality
-
Neighborhood density.
Following this preferences values, the Utility value is calculating:
u_xy= q_xy^(α_q )×〖sd〗_xy^(α_sd )×(1-|β_nd-〖nd〗_xy |)^(α_nd )
where q_xy^(α_q ) is the aesthetic quality weighted by the parameter aesthetic_quality_preference, 〖sd〗_xy^(α_sd ) is the preference for proximity to service centers weighted by distance_services_preference, and (1-|β_nd-〖nd〗_xy |)^(α_nd ) is the neighborhood density weighted by neighborhood_density_preference.
Every new arrival is settled to patch with the highest Utility value. The count of available patches for new settlement is however subsetted from all worlds’ patches. The new arrivals don’t dispose the overall view of the area. The Environmental variables as aesthetic quality and existence of Initial center are more important for the settlement of the new habitants. If the preferences for these environmental characteristics are put to 0, the specific pattern of urban growth depends more on placement of first habitants because the environment as considered as homogenous and thus is more random. If the preferences for environmental values are >0, we can more precisely predict location of first habitants into areas with highest Utility value – close to service center and to points of attractions.