Chapter 2
Data Issues Involved with the Application of
Automated Valuation Methods: A Case Study
and
Chapter 3
The Modified Comparable Sales Method as the
Basis for a Property Tax Valuation System and its
Chapter 2 Overview
• Addresses Real World Issues
– Data quality – temporal effects
– Market stratification
– Actual models and variables
• Valuable Resource for
– those who are entering the field of AVM
modelling
Valuation Accuracy Over Time
Median and COD - Butler County
0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 20020120020 3 2002052002072002 09 2002112003 01 2003032003 05 20030720030 9 2003112004012004032004052004 07 2004092004 11 2005012005 03 20050520050 7 20050920051 1 2006012006032006052006072006 09 20061120070 1 20070320070 5 Sale Month CO D 95.00 96.00 97.00 98.00 99.00 100.00 101.00 102.00 103.00 Me d ia n r at io COD Median
Degradation of Data Quality Between Reval
Cycles
• COD plotted vs. sale month for 2002 through mid 2007 time
frame … sales between sexennial reval cycles
• CODs for first three years averaged 9.66
• CODs for last year and a half averaged 12.54
• Why the increase?
– 2005 was a triennial reval year so the 2002-2004 sales were
reviewed in conjunction with the determination of the triennial
factors for the 2005 update (but no inventory review)
– Sales for 2005 on had not been reviewed in conjunction with
valuation work
– Property changes occurring over the 2002-2007 were only
A Pragmatic Market Stratification
Model Description
Model Description
1
Rural - Lowest Value Nbhds
11
Hamilton - Lowest Priced Nbhds
2
Rural - Modest Priced Nbhds
12
Hamilton - Moderate Priced
3
Rural - Moderate Priced Nbhds
13
Hamilton - Higher Priced
4
Rural - Lower Priced Condos
14
Hamilton - Lower Priced Condos
5
Rural - Moderate Priced Condos
15
Hamilton - Moderate Priced Condos
6
Fairfield - Lowest Priced Nbhds
16
Middletown - Lowest Priced Nbhds
7
Fairfield - Moderate Priced
17
Middletown - Moderate Priced
8
Fairfield - Higher Priced
18
Middletown - Higher Priced
9
Fairfield - Lower Priced Condos
19
Middletown - Lower Priced Condos
10
Fairfield - Moderate Priced Condos 20
Middletown - Moderate Priced Condos
Major Components of the Model
• Land and Structural Features
• Date of Sale and Age Factors
Var
No. Name Var Freq M Comment
14 CalcAc 9 Land size computed from land breakdown information,
expressed as number of acres (43,560 sq ft) … while land size is accounted for in the land value this tests for potential added value reflected in the market.
38 Bedrms 3 Number of bedrooms, typically included in condominium models
43 TotFix 17 Total plumbing fixtures, typical full bath has 3, half bath has 2. 51 Recrom 17 Recreation room area in basement, lower quality finish
Var
No. Var Name M Freq Comment
The following terms are date of sale spline terms which adjust for six month period from July 2007 on back. 94 RDS*SF 13 Date of sale for full sales span from January 2002 to
current. July 2007 = 0, June 2007 = 1, etc.
Reverse data of sale (RDS) term is multiplied by SFLA 95 DS-6SF 10 Date of sale for December 2006 on back … Dec 2006 = 1,
Nov 2006 = 2, etc. After Dec 2006 value is 0.
DS-6 term above is multiplied by SFLA (living area) 96 DS12SF 12 Date of sale for June 2006 on back
Selected Land
and Structural
Details
Selected Date of
Sale, Age and
Quality
adjustments
Var No. Var Name M Freq Comment
131 BiLevl 7 SFLA, if dwelling style is Bi-Level 132 Split 7 SFLA, if dwelling style is Split 133 Ranch 7 SFLA, if dwelling style is Ranch 134 TwnHse 1 SFLA, if dwelling style is Townhouse 135 2S-O/S 5 SFLA, if dwelling style is 2story Old Style
Predicting Estimation Accuracy
Excluding the low priced houses, the log linear model of COD
performance is generated regressing ln (COD) against average Age,
ln (average price/150,000) and flags for Condo and Rural models
Multiple R 0.7692 R Square 0.5917 Adjusted R 0.4284 Standard Error 0.2104 Observations 15 ANOVA Df SS MS F Significance F Regression 4 0.6414 0.1604 3.6229 0.0449 Residual 10 0.4426 0.0443 Total 14 1.0841
Coefficients Std Error t Stat P-value Lower 95% Upper 95% Intercept 2.2129 0.1358 16.2937 0.0000 1.9103 2.5155 Condo -0.4135 0.1729 -2.3919 0.0378 -0.7987 -0.0283 ln(Pr/150K) -0.3602 0.1993 -1.8074 0.1008 -0.8043 0.0838
Benefits/Importance of this Chapter
• Makes sure that the importance of data
quality is understood
• Is a real world example of market
stratification and model formulation
• Illustrates the usual richness of detail in an
assessment database
Chapter 3 Overview
• Full description of the comparables sales method
(CSM) used in mass appraisal
• Description of spatially regressive/autoregressive
model
• The relationship between the spatial model and a
modified comparable sales method (MCSM)
• Comparison of CSM and MCSM to several
competing model structures including
– Geographically weighted regression
– Response surface models
Develops the Rationale for Expressing CSM
as a Weighted Residual Error Method
ˆ
ˆ
( )
(
)
CSM S
=
X
β
+
CW Y
−
X
β
Again, in words this says that the estimate for
the subjects is equal to the MRA estimate
modified by the weighted residual errors of
the comparables
Describes the Spatially Lagged Weight
Matrix Model
The value of a property is related to values of nearby
properties
Y
=
ρ
WY
+
ε
W
is a spatial weights matrix
The relationship is called a spatial lag or autoregressive
model
Adding in a bit more complexity
The value of a property is a function of its characteristics
(MRA) and nearby properties (spatial lag)
(
)
Y
=
X
β ρ
+
W Y X
−
β
+
ε
Provides the Link Between CSM and Spatial
Model
ˆ
(1
)[
ˆ
(
ˆ
)]
Y
=
α β
X
+ −
α
X
β
+
W Y
−
X
β
ˆ
(1
) (
ˆ
)
Y
=
X
β
+ −
α
W Y
−
X
β
Consider a linear Combination of MRA and Comps. For example
Value = .2*MRA+.8*Comps
*
ˆ
(
ˆ
)
Y
=
X
β ρ
+
W Y
−
X
β
This is analogous in form to the spatially regressive/autoregressive model
(
)
Y
=
X
β ρ
+
W Y X
−
β
+
ε
The Relationship is Exploted to Obtain
Improved Accuracy
COD vs. rho - Fairfax
