Zed Langston
May 12, 2015
Assignment 5: Evaluating Model Uncertainty Through Sensitivity Analysis

Description: 

This project will use a previously completed model of urban development structure to examine the how model parameters influence emergent patterns through a sensitivity analysis.  The base model was created in assignment 4 and modified by adding the nearest neighbor distance (nnd) patch and global variable.  In addition, a plot and monitor were added to the interface.  Each parameter in the model will go through 10 iterations per parameter setting to test how the parameter changes effect the nnd.  To complete this objective, a parameter sweep will be conducted where the aesthetic, the distance to service and the neighborhood density parameters will be adjusted, using the settings 0.0, 0.5, and 1.0, over many iterations (810) to see how the change in parameter values influence the emergent patterns.  The parameter sweep will be conducted using the parameter sweep tool (within the behavior space) using the nnd variable to report the distance among an agent and the next closest agent data over time of the parameters of the model within NetLogo.  The data will be visually displayed using Excel to chart the data results (below).  The graphs show, in order of appearance, the distance to service preference parameter, the aesthetic quality preference parameter and the neighborhood density preference parameter.  Each of these time-series graphs were produced from the parameter sweep tool using the settings mentioned above and the iterations correspond to each of the parameters for all three graphs.  This mean that at any iteration number, the graphs could be compared to see the parameter set point used and would also apply to the other two time-series graphs.  The image sets and the graphs were completed at different times and do not correspond directly.  Rather the image sets could fit into the time-series graphs as a subset and are presented as supplemental findings.  The reason it is important to do the parameter sweep (over many iterations) is to account for the stochastic component (n-test) of the model that can obscure results of different parameter setting with only a few runs.

Questions:

1)  The difference between a variable (left: global and patch variables) and parameters (right: green) is that a parameter represents a characteristic of a variable, a value that remains static during the simulation, although in some may be changed by the user during the iteration.  A variable is a container or model state (an address in memory) and may change during a procedure or as part of the procedure (within brackets) without a user command during the iteration.  A NetLogo model may have global, patch, link and/or turtle variables while a parameter might represent a set of data values (range) that can be used as an input for a model iteration.  The parameter is set or specified, remaining static during the iteration.  In this instance, the parameter is the input values (criteria) assigned to the variable that will be used in the weight calculation (four of the parameters).

2) The parameter that the nnd is most sensitive to is the distance to service preference parameter because the parameter determines how close the agents will develop to a service center, starting with the initial service center and adding a service center with every 20 developments.  A very important factor is the initial service center that directly corresponds with distance to service center preference.  This then becomes a more suitable area for development creating a feedback that leads to path dependence.  The feedback that leads to path dependence acts to reinforce the area near the service center causing more agents to develop close to this region creating a clustered spatial distribution that increase as the distance to service preference parameter increases.  This spatial phenomena can be seen in the lower image set.  A high distance to service preference parameter setting will result in much closer agent development (lower image set) and a low parameter setting will result in agents that maintain more distance from each other in the structural development patterns (top image set).  Looking at the three sets of images, there is some variation in the final nnd (plot value) when the focus parameter was changed from 0.2, 0.6 and 1.0 and all other parameters remaining constant.  Looking at the graphic of the parameter sweep tool, the peaks and valleys do correspond to the parameter changes 0, 0.5 and 1.0 and, with some exceptions, appear to be lower when the parameter is at 1.0.  Because of the stochastic component within the model this factor is highlighted by the parameter sweep.  It should be noted that when looking at the image sets the highest initial nnd value at the left side of the plot is typically a much larger value because, initially, there are very few developments making the nnd very high at first.  In most of the iterations when this parameter is higher, the nnd is lower and the nnd peaks correspond to a lower parameter value.

3) The parameter that the nnd is least sensitive to is the neighborhood density preference parameter because the parameter determines how close the agents prefer to be to other agents in developed neighborhoods in the simulation.  A high parameter setting will result in agent development in dense neighborhoods but because of the n-test agents will have to choose the most suitable location for development (based on calculated weight) from 16 randomly selected locations.  Looking at the three sets of images, there is not much variation in the final nnd (plot value) even though the parameter was changed from 0.2, 0.6 and 1.0.  Looking at the graphic of the parameter sweep tool, it is easy to see that the peaks and valleys do not correspond to the parameter changes 0, 0.5 and 1.0.  The image sets (top and middle) use a neighborhood density of 0.2 and 0.6 respectively, with all other parameters staying constant and the nnd goes down, but is higher with the lower image set using a neighborhood density of 1.0 indicative of the stochasiticty within the model.  The graph  shows little difference with an increase from 0.5 to 1.0 also leading to the general conclusion that the nnd is least sensitive to this parameter.

4) The reason that nnd is might be important to homeowners is because it describes the average spatial distance between one residential building and the next closest residential building.  That factor would be important so that you know if the neighbor’s house would be visible or within reach through the window.  Many people would prefer to have a little space between their house and the neighbors house.  Another reason that this spatial information might be important is for agents that are looking to develop in the local area so that they know what kind of neighborhood structure that exists before choosing to develop.  Another metric that could be use is average distance to the points of attraction.  It is different from the nnd because it would be the distance from each of the points in the neighborhoods included divided by the number of buildings within the neighborhoods.  Another metric that could be use is the number of service centers that are within a certain distance from each neighborhood.  It is different from the nnd because it would be the number of service centers within a specified distance from the neighborhoods.

5) The model emulates how preferences and suitability for development within an urban area lead to specific patterns over space and time. Developers make decisions about where to develop based on available site locations. Site locations are chosen at random to introduce the real-world variability that developers have when choosing a site for development. The model describes how preferences lead to the spatial structural development of a built urban environment over time.  The model describes how decisions and potential available site locations can lead to variations of that built urban environment.  The model describes how the distance to a service center, distance to points of attraction, neighborhood density (how close agents want to be to other agents) and development density in any particular neighborhood can influence agent decisions to develop and how the results of those decisions lead to specific spatial structures over time.  Decisions are based on a specific number of potential available site locations and the suitability of those locations for the developer. Overall, the model describes how autonomous agent decisions (micro-motives) lead to emergent patterns over time and space because of agent interactions, path dependence and feedback from agent decisions and new development.