Residual Constraint Approach (RCA)
Sales Comparison Approach: The Residual Constraint Approach or RCA for short, is a term I give to the following method for the Sales Comparison Approach. This method could also be called the Intangible or Subjective Value Approach. The method is designed to give appraisers the capability to produce opinions of value with much higher degrees of precision than with standard methods, by:
- Using a high-quality regression tool such as Salford Systems MARS or R-Language Earth.
- Controlling the total adjustments for subjective or qualitative features through a multi-stage regression and scoring process.
General
RCA is a way to contain or limit the over- and under-valuation of subjective features that require the subjective assignment of scores to subjective property features such as view, condition, and quality.
The procedure can be divided into three stages:
Stage I
The first stage of the RCA method is to use a high-quality regression tool such as MARS from Salford Systems or earth from R-Language, to model as much of the price variance as possible, based on objective quantitative features, typically provided by tax assessor and MLS data, such as gross living area (GLA), lot size, room sizes and counts, roofing type, foundation type, and location. This method works best when this initial regression model can account for at least 70-80% of the price variance based on such data. However, lower values are certainly usable – at the expense of accuracy. Appraisers simply do the best they can with the data they have. It can be argued that regression is as good or better than any other method available, even in the worst-case scenarios.
Stage II
The remaining price variance, the difference between the actual sale price and the estimate provided by the regression model, called the residual, is assumed to be the result of variables that are either unknown or must be scored through subjective judgment. The most important of the latter group of variables are those referred to as ‘qualitative’. These qualitative variables have values that can only be represented through subjective judgment, as they cannot be objectively measured using commonly accepted scientific measurement standards. For example, we might judge the condition of a home-based on the percentage of homes in the subject neighborhood that we consider, subjectively, to be in worse condition; and with this method of scoring, we might give a score of 0-100%, rounded to the nearest whole percent. However, it is often the case, that more accuracy is required, and I typically use 0.0-100.0%. These latter cases occur when we are dealing with properties near the bottom or top of the value curve, where the slope is steep, and values change quickly with minor variations in the score. For example, a neighborhood of older homes might have just 2% in the category of “fixers”. A home with a score of 1.5 might need some moderate repair work on the order of $20,000, while a home with a score of 0.4 might as well be demolished at a cost of $250,000. Likewise, homes “overbuilt” with expensive features often tend to have values that skyrocket in the upper 1% of scores.
The residual is a single quantity and is a basket value for all of the variables or features not input into the regression software. All of the sales analyzed by the regression software can be ranked by their residuals obtained by subtracting the estimates provided by the Stage I model from their sale prices. ( If one wants a higher degree of accuracy, he can “massage” the sale prices to remove buyer concessions, but this would be a lot of work, if, for example, there are 300 sales to analyze. However, if there are relatively few sales with such concessions in the market, this may be possible, depending on whether such data is reliably flagged by the MLS. )
The ranked residuals can be scored by percentage above or
below in the ranking. So, if we were to
use percentage below, the score with the greatest negative residual would get a
score of 0 and the one with the highest score would get 99, base on an integer
score from 0-99. (One can make this
score more accurate by using 0.0-99.9.)
Next, the regression can be run against the residual score as the single predictor variable against the sale residual to get a model for the residuals. This is really just a function of score vs residual. If you add the price predicted by the Stage 1 model, to the residual predicted by the residual score, you should come very close to the sale price for the sales comparables. And if you apply this to your estimate of the residual score for the subject – you should have a very good estimate for the hypothetical sale price of the subject property.
Stage III
The two above models can be combined into a single model and coded into a computer program for calculation. Six to a dozen or so comps, if reasonably similar to the subject, can be entered into the computer, along with the subject feature values, to calculate the adjustments and adjusted sales prices, which are in turn averaged to provide an estimate sale price for the subject. There should be the option of weighting the sales comparables by the degree of similarity to the subject if that makes sense.
Final Issues
It may be necessary, because of reporting requirements, to split the residuals into component values. In particular, the Condition, Quality, and View may need to be separated out. How this is done, is largely the discretion of the appraiser. The constraint is that for each sale comparable, the adjustments for the qualitative variables must add up to the residual. A house with an average score in these features has a residual near 0. Thus, we expect, as features deviate from the average, the residual becomes more positive (for the above characteristics) or more negative (for inferior characteristics). Thus if a sales comparable has a residual of -50,000, is in average condition and is of average quality, with a poor view, we might expect to assign all of that $50,000 to the poor view. It doesn’t really matter how that $50,000 is distributed to various qualitative features in computing the final adjusted value. The mathematics ensures the adjusted value remains the same. The distribution does, however, provide an explanation to the reader of the appraisal as to why the adjusted price is what it is.
An interesting problem is how to divide up the estimated residual for the subject property. In fact, since the appraiser has inspected the subject, he is in a good position to make a reasonable division of the estimated residual across the available “residual features.”