by Ossama Kettani & Muhittin Oral

There are basically three approaches to property valuation, although initially there were eight. The survivors are: (1) the market value approach, (2) the cost approach, and (3) the income approach. The most challenging of these seems to be the market value approach. In the case of market value approach, the general tendency is usually to employ multiple regression analysis or a method of comparison. Multiple regression analysis is a popular one because it is a well known and accepted approach in many areas and disciplines. It has some shortcomings and the main one is to bury the subject property in a large group of properties through a sample, whether they are comparables or not with the subject property. The method of comparison is an attempt to eliminate such a central tendency valuation and to concentrate only on “comparables”. However, the latter lacks a formal and rigorous valuation methodology.

Kettani and Oral (2014) has developed an new real estate appraisal method named “analogical regression” that retains the advantages of both multiple regression analysis and method of comparison but avoids their shortcomings. *Analogical regression *is based on *analogical reasoning*. In very simple terms, analogical reasoning has the following structure: (1) ** A** has the characteristic

**; (2)**

*X***shares that characteristic**

*B***; (3)**

*X***has also characteistic**

*A***; (4) Because**

*Y***and**

*A***share characteristic**

*B***, we conclude that what is not known,**

*X***shares charateristic**

*B***as well. That reasoning fits very nicely for the purpose of estimating the market value of any subject property. To activate the analogical reasoning within the context of real estate appraisal we need the following data: (1) identification of comparables of the subject property, (2) the actual market prices of the comparables, (3) the characteristics of both the subject property and its comparables. The unknown is the market prices of the subject property and that is the one to be estimated using all the available data just listed above. The identification of comparables is done using an index called “comparability index.” Through such a process all the irrelevant properties are dropped from consideration in the appraisal process, simply because it does not make sense to relate the subject property to those that are not comparable. The set of comparables, not any sample from the population of all properties, is the basis of analogical regression. The number of comparables usually varies between 4-6 properties.**

*Y*Any statistical method, including multiple regression analysis, uses one kind or another an optimization technique. For instance, the paramaters of multiple regression model are estimated employing the ordinary least square (OLS) method to minimize the sum of the squared errors. The purpose is to get an estimate as close as possible to actual value. However, in the case of multiple regression analysis, one has to pay attention to whether the number of observations is sufficiently larger than the number of parameter to be estimated. If not, then multiple regression analysis is not an appropriate method to be employed. Especially, when there are 4-5 comparables (observations) and 2-3 parameters to be estimated, conventional multiple regression model is not much of a help. Therefore, we need another method and this another method is analogical regression.

Although the set of comparables includes similar properties one cannot however expect that every single property has exactly the same score with respect to every attribute or characteristics. For instance, 4-5 comparables may be in the same location but their ages (8 years old apartment versus 10 years old one) or living area sizes (100 m^{2} versus 125 m^{2}) might be somewhat different. Then the market price variation of the comparables can be considered as a consequence of these score differences. Not knowing the market value of the subject property but willing to estimate it, we need to find how the score differences can affect the market values of properties.

Analogical regression model works as follows: The actual market price of each comparable is adjusted according to the score differences. For instance, consider the table below:

Table 1: A Numerical Example Leading to Analogical Regression Model

Characteristics | Adjustment Rate | SubjectProperty | Comparable 1 | Comparable 2 | Comparable 3 |

Market Price | $ 100,000 |
$ 98,000 | $ 100,000 | $ 93,500 | |

Living Area | $ 300 per m^{2} |
100 m^{2} |
90 m^{2} |
110 m^{2} |
85 m^{2} |

Age | $ 1,000 per year |
9 Years |
8 Years | 12 years | 11 Years |

Adjusted Market Values | $ 100,000 |
$ 100,000 |
$ 100,000 |

Adjustment rate in Table 1 is a monetary worth corresponding to the common contribution of an attribute to the market prices of the comparables and the subject property. We have two adjustment rates to be determined: for “living area” and for “age.” The objective is to determine those adjustment rates that will make the subject property as identical to the comparables in terms of “adjusted market values.” Consider the adjustment rates as: $ 300 per m^{2} for living area and a negative rate – $ 1,000 per year for the age. Applying these rates, we find the same adjusted market value for the subject property relative to all the comparables considered: $ 100,000. Hence we conclude that the adjusted market value of the subject property is $ 100,000 relative to the actual market prices of all comparables. The reasoning behind these calculations works as follows. Take Comparable 1 and compare it with the subject property. Comparable 1’s living area is 90 m^{2}, 10 m^{2} smaller. This suggests that the subject property, being 10 m^{2} larger, should sell for more than $ 98,000, to be precise, for ($ 98,000+ $ 300×10 = $ 101,000). But, the age of the subject property is 1 year older than Comparable 1, hence we have to deduct $ 1,000 from the amount $ 101,000, which results in $ 100,000. When this very same logic is applied to the cases of other two comparables, we again obtain $ 100,000 as the adjusted value for the subject property. We, therefore, conclude that the adjusted market value of the subject property is $ 100,000 given the group of these three comparables and their characteristics when associated with those of the subject property.

Some remarks are in order. First, finding adjustment rates by trial and error is next to impossible, for there are infinitely many trial rates that can be considered in such a process, even for one single subject property. In the presence of millions of real estates, this process of determining the adjustment rates becomes even a more forbidding task. Therefore, we need a method by which we can optimally determine adjustment rates that will put the subject property and its comparables on equal footing with respect to market values. Analogical regression model just does this using “goal programming” approach. Second, in the numerical example above, there were only two property attributes (living area and age) for which the adjustment rates are to be calculated. This number might be easily greater than two attributes in practice, thus demanding a computer-assisted method that is extremely efficient and really implementable.

The interested readers in analogical regression model are refrerred to Kettani and Oral (2014) for the details.