Assignment 4
Why is it important to test each of your sub models independently? Explain how you tested the sub-components of the main model using images and text to illustrate your methods and explain how your diagnostics conformed (or not) to your expectations.
My sub-models are:
-
model of aesthetic quality (+ visualisation)
-
calculation of displaying the distance form servce centers (+ visualisation)
-
calculation of utility function (+ visualisation, firstly without and with development)
-
(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, Brown et al. 2005)
-
It is important to test each submodel independently to verify its rightness of calculation and its function, as they are principal parts of the subsequent calculation of Utility. Equally I can easier learn how to interpret the color scales. The parameters of attractivity or existence of initial-center are stable, but the utility funtion is recalculating following the different preferencies and addition of new houses at each time step.
1. model of aesthetic quality (show_aesthetic_quality)
we have created 2 points of interest [25,25] and [75,75] to heterogenize the world. Equally we defined that with increasing euclidean distance from these points the patches' attractivity will decrease. Using visualisation we can easily verify our expectation. The
pcolor scale-color green aesthetic_quality aes_min aes_max
assigne that (by NetLogo dictionnary):
scale-color color number range1 range2
If range1 is less than range2, then the larger the number, the lighter the shade of color. But if range2 is less than range1, the color scaling is inverted.
Accordingly, the patches with lower attractivity (farther from the points of attractivity) will be displayed as darker and vice versa. The areas at the upper left and lower right are not black because possibilty of 'world wrapping', so possible calculation over the world edges.
Visualisation of attractivity. Lighter color = higher attractivity, darker color = lower attractivity, points of interest = yellow
2. model of services distances (show_distance_to_service)
in this sub-model, the SWITCH initial-center? is added.
i) Initial-center? OFF
there is not center so all patches in the world are homogenous (no patches closer/farther away from the service center).
Visualisation of distance to services, with no initial center. World is homogenous. Points of interest = yellow but their have no influence on the disance to service calculation
ii) Initial-center? ON
The patch with [50,50] is created with the status 'center' and with color green. Subseqently the calculation of the dstance_to_service can be calculated in manner alike the attractiveness. We expect the visualisation of 'show_distance_to_service to have the lighter patches color nearer to the center and darker colors (farther away) on the corner. The visualisation meet the expectations.
Visualisation of distance to services with initial center in the center of the world [50,50]. Lighter color = higher attractivity, darker color = lower attractivity, points of interest = yellow
3. model of utility (show_utility)
In this model, the previous sub-models are implemented in it calculation. Final visualisation are in scale of blue, equally representing higher utility values by lighter colors and vice versa.
In this final model, the preferences for the services/aesthetic quality or neighborhood_density are included in final equation. Accordingly the final utility values depends on preferences. If all preference sliders are set on 0.00, the final utility is 1 for all patches, with initial-center? ON and OFF the resuls is the same.
Visualisation of utility values, with all preferences values put to 0,0,0. Equally the utility is the same for all patches. Initial-center? ON
Visualisation of utility values, with all preferences values put to 0,0,0. Equally the utility is the same for all patches. Initial-center? OFF
The methods for calculating the components of utility are deterministic in this model. How is stochasticity implemented in the model? What parameter influences the degree of stochasticity?
The stochasticity, (personally I think this is one of the best ideas in Brown et al. paper) is implemented by the existence of subsets of possible new development sites of the world's patches. This situalion is reflecting the reality that nobody can really made its choise of house placing from every available spots. It is every time form the 'subset' of whole landsacape.
In the model, this subset is represented by the variable in input box n_test and it 'represents the number of randomly chosen vacant cells presented to a developer at each time step.' Accordingly, every new house is placed on the patch with the highest utility value from the subseted patches. If the number is set 16
Visualisation of different placement of subsets (rose) of development sites at each time step (left, right). The final placement of house (red) is located on the patch with the highest utility value from this subset. Every time step the different subset of patches is taken.
n_test = 16 in both cases.
If the n_test value is high (9000), the 9000 from 10 000 available patches are selected so it is more likely that the cell with the highest utility value (in this case the closest to service center) will be included in the subset and thus uset for development.
Visualisation of subset of placement (rose) if n_test = 9000.The placement of new house (red) is placed near to city center (green), on the patch with the highest utility value from this subset.
How is initial environmental heterogeneity implemented in this model and what parameter or parameters determine its importance? Do you think that greater environmental heterogeneity corresponds to greater variability among replicate model runs, and why? Support your argument with evidence from replicate simulations with and without initial environmental heterogeneity.
Environmental heterogeneity is implemented by two points of attaction located at [25,25] and [75,75]. It's importance is determined by parameter aesthetic_quality_preference. Althought I suppose that existence of initial center and mostly habitants' preferences to be closer to this center equally produce some king of environmental heteregeneity because they influence the placement of first habitants. If both preference values (for service proximity, distance to points of attraction) are put on 0, there is no influence of these variables on the final Utility value.
Final utility valuee of te world in the preferences to service distances and to points of attraction is set to 0.
From the theory we conclude that more spatial homogeneity lead to greater path dependance because the following houses development is more influenced by the locations of first habitants (as mentionned higher). The last one is totally random as they have not preferences to proximity of services/points of attractions. Sunsequently, the location of the later habitants is influenced by the preference values to neighborhood density preferences. If the neighborhood density preference is > 0, the clusters of habitations will be created.
For homogenous space, with no points of attraction, there is the greater path dependance. As the location of first habitants are not attracted to exact location (determined by i.e. points of attraction), they could be placed over the world and the next habitants will follow their location.
To discover the influence of environment (points of attraction, existance of initial center) on path dependance we have to run the development process several times (here only 3 runs are published) and finally compare the final development.
As parameters I will use environmental_variability reference (proximity to service center, points of attractions) and habitat preferences (neighborfood density preferences, ideal_density) put on 0 and 1 values and their combination.
results of 3 runs with different references to environmental heteregeneity and to neighbor_density. Without no preferences to environmental variability (or without no environmental variability) the location is more patch dependant bacause we can predict the location of the first arrivals. With more heteregenous space we can assume more likely the placement of the first arrivals.
3 runs of environmental preferences (1) and habitat preference (1). The development is placed closed to the one of the points of attraction/service center. The variability among among runs still highly depend on the locations of the firts arrivals but we can expect localisain on first arrivals. With higher preferences values and higher environment variability we suppose to obtain bigger invariant region.
3 runs of environmental preferences (1) and habitat preference (0). The development is placed closed to the one of the points of attraction/service center, however the clusters of habitations are not created. The variability among runs is caused by
3 runs of environmental preferences (0) and habitat preference (1). The development is randomly clustered because of high habitat_density_preference but we couldn't predict placement of the first habitants. There is strong patch dependance because the later development location are strongly dependant on location of early arrivals.
3 runs of environmental preferences (0) and habitat preference (0). The development is not clustered because of no habitat_density_preference. This is the lovest path dependant but equally it is absolutely random.
Describe at least two of the model assumptions or simplifications and how they could influence your interpretation of model results. Despite these assumptions and limitations, what can we learn from this model?
Despite all these assumptions and simplifications we can conclude and understand that the same process don't lead necassarilly to the same spatial pattern over time. Throught models we can understand the underlying process, however understanding the process doesnt lead directly to the exact spatial prediction.
Two simplification were crucial for me:
heteregenisation of the space using only 2 point of attraction and number of the subset of early-arrivals. If the number (n_test) will be hight, we can certainly predict the locatisation of new arrival - to to patches with the highest utility values.
Utility values (no neighborhood preferences) for n_test 16 (left) and 9000 (right). In both cases the new haitats are locating the patch with the higher utility value. Althought if the n_test is large (9000) there is more probability that subsetted patches will be placed on the patchech with utility closed to 1 (the highest) so the early-arrivals wil be placed on the best positions (between points af attraction and service, left )
The model can teach us that same process can lead to different spatial results, mostly if there are possibility of path dependance, accordingly if the actual decisions are influenced by the past decision, which is the everyday true. Equally, understanding of the process can lead to better adjustment policy rules, or laws if we are already aware that is impossible to acuratelly predict the outcome. Throught different laws or policy we can set more rule to influence the process and equally influence the results. and make uncertainty lower.
*
*
*
The first hypothesis was that a model (and a system) with more and stronger feedbacks would be more path dependent that a model with fewer and/or weaker feedbacks, because feedbacks, both positive and negative, are a primary cause of non-linearities, path dependance, and multiple equilibria in complex systems.
Second hypohesis was that where the environment is relatively homogeneous, land-use histories would be more path dependant where the environmet is variable.