**by Mark Linne, MAI, Steven Kane, and George Dell
**

Published by the Appraisal Institute, 2000

Copyright © 2000 Property Valuation Advisors, Newburyport, MA

**W**ith friendlier software programs and large on-line databases of sale properties, Appraisal Valuation Modeling or AVM is becoming more popular.

Initially, AVMs or statistical valuation techniques were used in the assessment or mass appraisal field. The main difference had been that the traditional appraisal method of selecting three to five comparable sales discarded the least useful data in favor of the most similar comparable sales. AVMs, on the other hand, used a large universe of sales and squeezed out whatever information existed.

Some traditionalists look at AVMs as information overload and call it data smog. On the other hand, AVM proponents cite the few comparable sales and the subjectivity used by traditional appraisers.

The author believes that when similarity exists among properties, then AVMs provide the quickest, least costly answer. When property characteristics vary and comparable data is sparse, however, loads of judgments are necessary and traditional methods lead to better results. So each technique has its strengths and weaknesses.

The author investigates the biases inherent in the methods. Traditional appraising introduces bias inadvertently or intentionally. Adjustable AVMs assumptions are concealed yet the analysis is reproducible. Fixed AVMs (expert systems or neural networks) algorithms or formulas are secret and can have application bias.

Reliability depends on the person who is performing the appraisal or creating the AVM. One goal of the AVM is to introduce more science and less art. Secondarily, it is to deliver less labor intensive, less costly, and quicker results.

Statistics embraces probabilities, measurement, forecasting, and risk. Analysis can be descriptive, or inferential. Statistical analysis allows one to measure the reliability and accuracy of the results. Valuation models attempt to predict, replicate, or explain the market value of properties from real estate data.

The three components of statistical analysis are:

- Identification - Identification of elements of comparison that control value: thus choosing the specific variables that will be analyzed.
- Quantification - Measuring the variables and calculating their impact.
Data can be A) Nominal (Ex: census tracts, building type, zoning type); B) Ordinal - order without regard to the magnitude of the relative difference of each item (Ex: quality, condition, utility); C) Interval - allows adding and subtracting but not multiplying or dividing (Ex: time in years and months), or D) Ratio (Ex: sale price, size of building, age of building).

- Interpretation - Regression analysis can provide an estimate of value for the property as a whole or on a unit basis. It also can be used to analyze the marginal value of attributes such as a garage, fireplace, or overall condition of a property.

Inferential statistics can explain the possible association between an independent and dependent variable. The independent variable (property characteristics) cause the dependent variable (the sale price of a property) to behave in particular way. A valuation model can value the entire property or one element of a property.

To get the best results, 1) the analysis should be as free from bias as possible, 2) the association of the variables analyzed should be strong, and 3) the causal associations should be consistent in different but similar market areas.

More of X should be shown to cause more of Y (if all else is equal). In the end, the causal relationship should be rational and make appraisal and economic sense.

How many sales are enough? In a purely scientific endeavor, 25 to 30 samples are required for reliable results. With real estate valuation, the necessary sample size will vary depending on the similarity of the sale properties. The author recommends that at least six hits (sale properties of a certain type) be used for a particular property characteristic to be adequately represented.

An important term of which to be aware is collinearity. This is a common error whereby two variables interact with one another. An example is the relationship between the number of rooms and amount of square feet.

How many valuation variables are too many or too few? When property is purchased, usually several factors define the sale price: location, type, size, quality, condition, and functionality. Secondarily, amenities may further influence the price, but usually in smaller increments. In some instances, governmental assessment analysts grapple with statistical models containing more than 30 variables to predict market value. The author believes this is too many. On the other hand, one or two variables (other than in extremely homogeneous properties) will be too few. About six variables should explain a large part of the value of most properties. Only variables that significantly affect value should be included.

... location, type, size, quality, condition, and functionality.

A model evaluates the relative importance of the variables to value and then creates a valuation formula that has the smallest distance between the estimated sale price and the actual sale prices of the sample. A regression analysis is often based on the least squares method. This can be diagrammed in a scatter plot. Graphically, a line best fits the relationship of the variables. An example of a simple valuation formula is as follows:

Appraised Value = value constant + ($50 x SF of living area) + ($25 x SF of basement area)

A comparison of the expected sale price versus the actual sale price generates a reliability indicator known as the R^{2} (coefficient of determination). This determines how good the fit of the model is. The higher the number (between 0.00 and 1.00), the better the model. A model with an R^{2} of .60 or greater explains a lot.

Other accuracy indicators are the COV (coefficient of variation) and the COD (coefficient of dispersion). Both are explained in the text.

A frequent problem is that not enough sales may exist in the present market. So using older sales may be required. An analysis can be conducted to see if the older sales need adjustment for time (a change in market conditions since the sale occurred). It is best to adjust the selling prices for time before analyzing other variables in the model.

Uses for AVMs range from instantaneous property valuation for lending purposes to portfolio valuations for asset management. The author through examples answers the questions: how does one analyze, interpret, and present data effectively using an AVM. Examples are primarily residential in nature, although the principals can be applied to commercial property.

In a simple case, popular spreadsheets can be used. For more power, and with larger databases, statistics packages such as SPSS will be more robust and full-featured.

The author brings the reader through the process of creating a regression-based appraisal valuation model. In the case study, the property type was simple: a vacant house lot. Therefore, no building component existed. The method used was OLS (ordinary least squares). Variables that explained the most variation in value were lake frontage, westerly views, and lot size. A regression analysis determined the best coefficients or adjustments for each variable. These were applied to the constant to provide a value estimate for the subject lot.

The booklet also contains a glossary defining many statistical terms such as collinearity, correlation, coefficient, R^{2}, and standard deviation, etc.

If you are looking to develop valuation models, you may want to invest further in statistics texts, particularly economics statistics texts, or texts on property assessment with more breadth and depth. If, however, you are looking for a quick and easy introductory booklet on the topic, this is a good place to start.

The book above, A Guide to Appraisal Valuation Modeling, is available on-line at Amazon Books.

*Stephen Traub, ASA, the reviewer, is
chief commercial appraiser for Property Valuation Advisors, 63 Hill St., Newburyport, MA 01950.
He is a certified general appraiser in NH, ME, and MA.*

To contact the author of this review, e-mail to: straub@shore.net or contact him at the address above, or call 978-462-4347.

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