Mass Appraisal
Modeling Using GIS
by Josh Myers
Josh Myers Valuation Solutions
About Josh
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Josh Myers is president of Josh Myers Valuation
Solutions LLC. In addition to consulting, Josh has
experience working at the local jurisdiction level and at
the CAMA software vendor level. He holds a Masters
Degree in Statistics from the University of Virginia. Josh
has given about twenty major conference
presentations. His article, co-authored with Wayne
Moore, PH.D, "Using Geographic-Attribute Weighted
Regression for CAMA Modeling," was published in the
Journal of Property Tax Assessment and Administration
in 2010 and won the 2011 IAAO Bernard L. Barnard
Outstanding Technical Essay Award. Josh is also a
member of the IPTI/IAAO Editorial Review Board. He
resides in Chesapeake, Va., is a volunteer staff member
at his Church, and helps coach a high school baseball
General Notes
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The goal today is education through less formulas
and more concepts.
Feel free to raise your hand and ask short questions
as we go along.
During the question and answer period at the end,
feel free to ask me a question about any topic that
you wish, whether we cover it today or not.
The Importance of
Software
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Software is the key to changing the mass appraisal
industry.
This is because people will not implement good
ideas until it is feasible to do so; only software grants
them that power.
Unless good ideas are included in software in an
easy-to-use way, then they will never get adopted by
the industry at large. We can present on them at
conferences, publish papers about them, and place
them in the standards, but none of that matters if
they aren’t included in software.
To AVM or not to
AVM?
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What are the benefits and drawbacks of using a
Statistical Mass Appraisal Model (AVM) instead of a
More “Manual” Approach? (Remember, the marketadjusted cost approach is only partially manual).
Here are a few things to consider. First, models
make mistakes just as humans do, so they are not
infallible. Second, people love to have the
perception of control, even if the results are not
optimal.
To AVM or not to
AVM?
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Pros of the AVM: has the potential to be highly
accurate; usually results in huge time savings;
usually removes many of the problems resulting
from human biases.
Cons of the AVM: can be hard to explain to
appraisers and/or taxpayers; can produce some
wildly-incorrect estimates; results are only as good
as the modeler.
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To AVM or not to
AVM?
The Cons of the AVM are greatly exasperated when
they are implemented improperly or without the
sufficient involvement of the appraisal staff.
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A knowledgable modeler is needed to create and
manage the AVM.
Staff should be trained in how to understand the
AVM and their key role in the process should be
clearly explained.
After the AVM has been run, results should be
reviewed by appraisal staff to check for wildlyincorrect estimates.
Using Subjective
Factors in Modeling
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Quality appraisers are critical to the application of
subjective factors to real property.
In modeling, subjective factors are usually qualitative
variables and often times have to be converted to a
set of binary variables or linearized as a continuous
variable.
It is important to have consistent applications of
subjective factors in your offices because they can
lessen the effectiveness of any mass appraisal
model, especially AVMs.
How do I Tell which
• Model is Better?
Usually, people only compare CODs of competing
models to see which is better, but does this make
sense?
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No, for several reasons:
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Model coefficient values should be compared to
see if they are equally interpretable.
A statistical test for the equality of the CODs is
needed to tell if the CODs are statistically
significantly different.
A more detailed comparison of the different types
of inequity in the competing models must be
undertaken.
There needs to be analysis to see how equitably
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How do I Tell which
Model is Better?
Additionally a separate set of sales (prediction sales
set) needs to be established to use to accurately
compare competing models apart from using the
sales used in the modeling (model-building sales
set).
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It is important to compare model results under
realistic conditions, namely, the forward prediction
of sale prices, because that is what we do in mass
appraisal.
It is important to compare models using the exact
same conditions (same model-building sales set,
same prediction sales set, and same rules).
Use of Location in
Modeling
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It is highly important for accuracy to incorporate
location into Mass Appraisal Models. This is
important for all types of models. Remember,
location, location, location!
Example: Charlottesville, Va. vs. Chesapeake, Va.
How does a mass
appraisal model use
GIS?
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Mass Appraisal Models use GIS through parcel
centroid coordinates.
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Each parcel in GIS is a polygon.
Centroid coordinates are simply the middle point in
the polygon of the parcel.
Accurate centroid coordinates can be determined
from any polygon in GIS, even ones that are not
rectangular.
Example:
(x,y)
Two Concepts in
Spatial Modeling
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Spatial Autocorrelation - the spatial clustering of
similar sale prices.
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Simple Example: The houses beside the mall sell
for around $200,000, but the houses beside the
park sell for around $300,000.
Spatial Heterogeneity - the spatial clustering of
similar market rates.
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Simple Example: The houses beside the river go
for about $150 per square foot, but the houses
downtown go for about $75 per square foot.
Two Types of GIS
Mass Appraisal
Models
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We can’t cover everything today, but I wanted to show
you two of the best mass appraisal models out there
that use GIS.
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MRA + Comparable Sales
GWR/GAWR
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MRA + Comp Sales
Multiple Regression Analysis (MRA) is used here to arrive
at the adjustments made in the comparable sales
approach.
GIS coordinates are used to determine the distance
between the subject property and the comparable sale
properties, and this distance is used to determine the
weight the individual comparable sales have in the
determination of the value estimate for the subject.
After some math the relationship reduces to the following:
Estimate = MRAs + w1*r1 + w2*r2 + w3*r3 + w4*r4 +
w5*r5, where MRAs is the MRA estimate of the subject
property, w1 through w5 are the set of weights determined
by the distance, w1 + w2 + w3 + w4 + w5 = 1, and r1
through r5 are the MRA residuals for the five comparable
GWR/GAWR
• GWR essentially runs one separate weighted MRA model
for every subject property, with the weighting done by
geographic distance. Sale properties nearer to a given
subject property are given more weight in each regression
than those farther away.
• GAWR is the same as GWR but with the weighting done
by both geographic distance and attribute similarity. Now
sale properties nearer and more similar to a given subject
property are given more weight in each regression than
those farther away and more dissimilar.
GAWR
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A more in-depth presentation of GAWR is available on
my website.
On the next slide, we see GAWR performing best in
comparison to a host of other models, produced by
both practitioners and academics, using the large
Fairfax County, Va. Test Dataset.
One Caveat: no model performs best in every dataset
100% of the time, so different models must be tested
and compared with each set of data.
GAWR
Wait a second...
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You may be thinking, “wait a second, there are other
ways to use location in modeling like neighborhoods,
market areas, or sub-market areas - what makes you
so sure that GIS coordinates are better? Is it really
worth making things this complicated?”
Let’s investigate this further.
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The Importance of
Coordinates in
Modeling
Do GIS parcel coordinates add any locational
explanatory power over simply having locational
binary variables (like the neighborhood, sub-market,
or market area for the parcel)?
Wayne Moore and Josh Myers did a research
project on this in 2010. In short, the project
compared the results of several top modelers, with
only neighborhood binary variables used to account
for location, to GWR and GAWR models, with parcel
coordinates used to account for location.
Here are some results from that research.
The Importance of
Coordinates in
Modeling
The Importance of
Coordinates in
Modeling
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The Importance of
Coordinates in
Modeling
First, as an aside, the project was able to conclude
that there were statistically significant differences
among AVM methodologies. Therefore, it is false to
believe the choice between models does not matter.
In addition, results of the project actually conclude
that the GAWR model, using attribute weighting in
addition to distance weighting, is a statistically
significantly better model than all of the models
without parcel coordinates. The GWR model barely
misses this distinction, so technically parcel
coordinates alone were not proven, with this dataset,
to be statistically significantly able to improve
performance.
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The Importance of
Coordinates in
Modeling
However, the test that we used was not as powerful
as the one I now use for my solo work. With that
more powerful test, GWR would have been
statistically significantly able to improve performance,
meaning that the addition of parcel coordinates could
be said to improve performance.
Bolstering the case for the efficacy of GAWR, these
results also show that GAWR, with or without using
the RCN, is the statistically best model when
compared to a host of others (although not statistically
significantly better, under our original test, than
GWR).
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Summary
We first discussed some general topics: the importance of
software, the pros and cons of AVMs, the use of subjective
factors in modeling, and how to tell if one model is superior
to another.
Next we discussed why location is important in modeling,
the fact that parcel centroid coordinates are the part of GIS
that is used in modeling, and some key spatial modeling
concepts like spatial autocorrelation and spatial
heterogeneity.
Next, two types of mass appraisal models that use GIS
coordinates were discussed: MRA + Comp Sales and
GWR/GAWR. Promising results were given from GAWR.
Finally, additional GWR/GAWR results were used to show
the importance of using coordinates over locational market
Thank You For
Attending!
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We have time for questions. Ask me anything - it can
be related or unrelated to something we said today.
Go to my website:
www.joshmyersvaluationsolutions.com to get a PDF
copy of this presentation. This web address is also
available on my business card (available up front).