Assignment 4

For this assignment, we assembled a model with several sub-models. The model discusses land use, and where homes are placed based on distance to resources, aesthetic quality, and neighborhood density. It is based on “Path dependence and the validation of agent-based spatial models of land use” by Brown, so the model takes path dependence and feedbacks into account when discussing the land use and development.

 

1. 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.

It is important to test each of the sub models independently because only by testing them independently can one see how each variable affects the model. I tested the sub components of the main model by first setting all of the preferential settings to 0.

Then I would scoot up each setting to see how each one affected the model.

 

Base Model:

With everything set to not affect the model, I expected the placement of homes and service centers to be random. Indeed, initially, with everything set to 0, there wasn’t a distinct pattern of anything. The houses (pink) are all spread out, not in clusters with each other. The service centers (green) are randomly placed. Nothing is clustered around the service centers or the maximum aesthetic quality points (yellow).

 

Distance to Services only:

Upping just the distance to services preference to 1 instead of 0 changed the model significantly. I was not sure how this variable would affect the model, but a higher setting means that the houses will be placed closer to service centers as opposed to “not caring” and being placed anywhere in the model. With the preference set to 1, the houses all began to cluster around the service center (which in this case was set to the middle), and additional service centers were also built in the middle of the model.

 

Aesthetic Quality only:

Raising the aesthetic quality preference from 0 to 1 changed the model significantly as well. I expected that raising the desired aesthetic quality would put homes closer to the aesthetic maximums (yellow). Indeed, the houses clustered around the aesthetic maximums, and additional service centers were built there. Despite the initial service center being in the middle, no houses were built there.

Neighborhood Density only:

Raising the neighborhood density preference from 0 to 1 did not seem to change the base model. I thought it would have some kind of effect. Everything is still spread out and the service centers also seem to be positioned randomly. This was with the ideal density set to 0.5.

I hypothesized that changing the ideal density would give some changes. Indeed, with the neighborhood density at 1 and the ideal density upped to 1, the homes begin to cluster together to fulfill the expected neighborhood density changes:

 

2. 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?

Deterministic models refer to models where no randomness comes into play in determining how the model develops over time. Stochasticity is when a model can be influenced by a random variable.

While the components above are all calculated in a deterministic way, there is a stochastic element – where the houses are placed. In each time step, 16 random lots open up, and those are the only lots available to place houses in. The settings above will determine which lot gets chosen of the 16 available lots, but which 16 lots become available in the first place is the stochastic parameter.

 

3. 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.

Initial environmental heterogeneity is implemented in this model with the aesthetic quality. Each patch has a different aesthetic quality that affects the outcome – if it is a factor that is set to come into play.

A few factors are important to consider on whether the environmental heterogeneity corresponds to greater variability or not. If aesthetic quality is important in the model, there will be less “choices” from the random 16 patches that open up on each time step. The models will look very similar over many runs, because there is more of a constraint (aesthetic quality) to where things should go (closer to the aesthetic maximums).

If the aesthetic quality is less important in the model, the homes will not tend to group towards the aesthetic maximums, and things can turn out very differently across runs.

Examples:

(for the examples I set “distance services preference” to 0.5, “neighborhood density preference” to 0.5, “ideal density” to 0.5, and “initial center” (resource) on.

Aesthetic quality very important (“aesthetic quality preference” = 1):

These three runs turns out very similarly, the homes are clustered around the aesthetic maximums, with additional resource centers being built there as well.

 

Aesthetic quality not important (“aesthetic quality preference” = 0):

These three models turned out rather differently. The homes did cluster some around the initial central resource center, but things were able to become more random, too, because the aesthetic values had no effect. The shapes of the overall group of homes turned out very differently, and where the resource centers ended up is also rather different as well.

 

4. Explain the roles of feedbacks and path dependence in this model. How are the two concepts related? How do the three parameters for preference relate to feedbacks and path dependence? What parameter settings would you use to eliminate any effect of feedbacks or path dependence?

Feedbacks can be thought of as “positive” or “negative”. Positive feedbacks reinforce and “add to” the model over time, and negative feedbacks dampen or “take away from” a model over time. Path dependence means that early events narrow the possibilities of future events. Feedbacks and path dependence are related concepts in that both take earlier conditions and drastically affect the model over time based on those conditions.

In this model, aesthetic quality preference, distance to resources, and desired neighborhood density all act as constraints. Because this version of the model will always end up with the same number of homes and resource centers, it is difficult to say whether we are seeing positive or negative feedback – but path dependence is definitely occurring.

If aesthetic quality preference is higher, the homes will be built closer to the aesthetic maximums, and result in layouts like my first few runs in question 3.

If homes need to be closer to resources, they will cluster around the first resource built (whether it is set to initial center or not will affect the pattern). This clustering means that the homes will end up blobbed together close to where the first resource was built. Any “outliers” that don’t end up in the main blob would only be there because that is the vacant lot closest to the blob – which, because the 16 lots are random, will not always be in the blob itself:

The density desired factor doesn’t have an impact in the similar way that aesthetic quality and distances to resources do, but it does strongly affect how the homes are clustered together. It is a more obvious component of path dependence – because homes already exist in earlier time steps, homes built in later time steps will cluster closer to the earlier homes (if the option presents itself in the form of an available nearby vacant lot).

Feedbacks and path dependence will come into play in some form with all of these settings. Other than having a completely random model (see question 1, in the base model), I’m not sure that these things can be fully eliminated using these factors.

 

5. 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?

There are a few assumptions made in this model worthy of note:

a. That all of the agents would have the same preferences in terms of desired aesthetic quality, neighborhood density, and distance to resources.

Some people truly enjoy “fancier” neighborhoods – some don’t. Some people love living in the big city – some don’t. Some people love being in walking distance to shops – some don’t. This model assumes that all agents have the same desires. Financial differences play a big role in these categories specifically. It would pose some serious limitations of simulating a realistic city, because it wouldn’t be able to take into account the various possible configurations of housing based on these factors.

 

b. That aesthetic quality, neighborhood density, and distance to resources are the only things taken into account when building new homes.

Though these are important considerations, they are not the end of the story when it comes to simulating housing distributions. If someone played with this model with the goal of creating the biggest cluster of people in one area, the factors used (desired density, distance to resources, and perhaps clustering around aesthetic maximums) may not be the factors that would work to create a large cluster of people in the real world.

 

Even with these assumptions taken into consideration, we can still learn a lot from this model because it does do a very good job of showing us the way that aesthetics, distance from resources, and desired density can affect the configuration of homes, and it does teach us a lot about path dependence, heterogeneity, multiple variable models, and models within models.