CHAPTER 7 NOTES Flashcards
Steps for Building MRA Models
Building an MRA model requires a systematic step-by-step approach. The Advanced Computer-Assisted Mass Appraisal text listed as a recommended reading outlines this process in great detail in Chapter 3. There are two main phases in model building: (a) model specification and (b) model calibration. Model specification involves selecting the variables to be considered and defining their relationships to value and to each other. Model calibration means attaching numbers to the specified model, solving for the coefficients attached tothevariables of interest.
A part of model calibration is testing to ensure the model will create the estimated value with the desired accuracy. In this testing, the model’s results are compared to real-world examples to see if the model can provide accurate estimates. If not, then the model must be re-specified and re-calibrated until it produces acceptable results.
In this lesson, the modeling process will be explained in nine steps:
• Steps 1 to 6 are model specification; • Step 7 is model calibration; and
• Steps 8 and 9 are testing.
We will illustrate these steps through their practical application in developing a model. However, before this practical application, we will first briefly outline some background on these steps.
Steps for Building MRA Models
Building an MRA model requires a systematic step-by-step approach. The Advanced Computer-Assisted Mass Appraisal text listed as a recommended reading outlines this process in great detail in Chapter 3. There are two main phases in model building: (a) model specification and (b) model calibration. Model specification involves selecting the variables to be considered and defining their relationships to value and to each other. Model calibration means attaching numbers to the specified model, solving for the coefficients attached to the variables of interest.
A part of model calibration is testing to ensure the model will create the estimated value with the desiredaccuracy. In this testing, the model’sresults are comparedto real-world examplestoseeifthemodelcan provide accurate estimates. If not, then the model must be re-specified and re-calibrated until it produces acceptable results.
In this lesson, the modeling process will be explained in nine steps:
• Steps 1 to 6 are model specification; • Step 7 is model calibration; and
• Steps 8 and 9 are testing.
We will illustrate these steps through their practical application in developing a model. However, before this practical application, we will first briefly outline some background on these steps.
Steps for Building MRA Models
As outlined in Lesson 6, the first step is to describe an appropriate general model. The Advanced Computer-Assisted Mass Appraisal textbook describes several general model structures in Chapter 3. In selecting an appropriate model structure, you need to consider:
• the available data and its general format;
• the available software programs that can be used to calibrate the model – i.e., it does not make sense to specify a complex hybrid regression model when all that is available for calibration is a simple spreadsheet program; and
• good economic and appraisal theory.
For most of the uses in this course, we will apply the simple additive regression model as follows:
y = b0 + b1x1 + b2x2 + b3x3 + b4x4 +… + bnxn
The dependent variable (y) is the variable you are trying to estimate – usually market value. The independent variables (x) representtheattributes orcharacteristics of thesold propertiesinthedatabase(e.g.,squarefootage, number of bedrooms). The coefficients (b) are the numbers assigned by the regression to each independent variable (e.g., dollars per square foot, dollars per bedroom).
Steps for Building MRA Models
As outlined in Lesson 6, the first step is to describe an appropriate general model. The Advanced Computer-Assisted Mass Appraisal textbook describes several general model structures in Chapter 3. In selecting an appropriate model structure, you need to consider:
• the available data and its general format;
• the available software programs that can be used to calibrate the model – i.e., it does not make sense to specify a complex hybrid regression model when all that is available for calibration is a simple spreadsheet program; and
• good economic and appraisal theory.
For most of the uses in this course, we will apply the simple additive regression model as follows:
y = b0 + b1x1 + b2x2 + b3x3 + b4x4 +… + bnxn
The dependent variable (y) is the variable you are trying to estimate – usually market value. The independent variables (x) representtheattributes orcharacteristics of thesold propertiesinthedatabase(e.g.,squarefootage, number of bedrooms). The coefficients (b) are the numbers assigned by the regression to each independent variable (e.g., dollars per square foot, dollars per bedroom).
Steps for Building MRA Models
Additive multiple regression is the most common form of regression as it conforms to the concepts of value and expectations of most market participants.It does not require a level of complexity beyond simple transformations and most statistical software packages (e.g., Excel,SPSS, NCSS) are capable of carrying out additive regression analysis.In terms of statistical procedures, additive regression is reasonably straight forward and the coefficients assigned to variables are understandable –in many cases,they can beexplained in dollar terms,such as so many dollars per square foot of living area. Additive regression is the only method of model calibration that will be used in this lesson and the next. Multiplicative regression is another method for calibrating models which is more complex and less easy to explain. It is useful in some situations, but because of its limited application we will leave this topic to the more advanced model building discussed in BUSI 444.
Steps for Building MRA Models
Additive multiple regression is the most common form of regression as it conforms to the concepts of value and expectations of most market participants.It does not require a level of complexity beyond simple transformations and most statistical software packages (e.g., Excel,SPSS, NCSS) are capable of carrying out additive regression analysis.In terms of statistical procedures, additive regression is reasonably straight forward and the coefficients assigned to variables are understandable –in many cases,they can beexplained in dollar terms,such as so many dollars per square foot of living area. Additive regression is the only method of model calibration that will be used in this lesson and the next. Multiplicative regression is another method for calibrating models which is more complex and less easy to explain. It is useful in some situations, but because of its limited application we will leave this topic to the more advanced model building discussed in BUSI 444.
Steps for Building MRA Models
The second step in the modeling process is to review the variables in the database in order to identify which may be suitable to use as independent variables for the model we are building. Up until now, we have used all of the variables provided in the databases, but in real applications you have to sort through many unsuitable variables and choose between alternative variables that may be all seem suitable but cannot be used together (e.g., multicollinear variables). In order to choose an appropriate model, you need to become familiar with the variables available in the database. For example.
• What property characteristics are represented?
• Do these characteristics fit better with an additive or multiplicative model structure?
• Are there several alternate forms for the same characteristic?
• If the form of the variable is not appropriate for the model structure, can a transformation be developed to put the variable into the correct form?
This is the data analysis phase, outlined in steps three and four below.
The third step, and one of the most important, is to examine the data in the database using the techniques described in Lessons 3, 4, and 6. Tools such as graphic analysis, crosstabs, compare means, and correlation analysis can help identify how variables are related to the dependent variable and also relationships between any independent variables. Multicollinearity was touched on in the previous lesson but will be described in more detail later in this lesson.
Steps for Building MRA Models
The second step in the modeling process is to review the variables in the database in order to identify which may be suitable to use as independent variables for the model we are building. Up until now, we have used all of the variables provided in the databases, but in real applications you have to sort through many unsuitable variables and choose between alternative variables that may be all seem suitable but cannot be used together (e.g., multicollinear variables). In order to choose an appropriate model, you need to become familiar with the variables available in the database. For example.
• What property characteristics are represented?
• Do these characteristics fit better with an additive or multiplicative model structure?
• Are there several alternate forms for the same characteristic?
• If the form of the variable is not appropriate for the model structure, can a transformation be developed to put the variable into the correct form?
This is the data analysis phase, outlined in steps three and four below.
The third step, and one of the most important, is to examine the data in the database using the techniques described in Lessons 3, 4, and 6. Tools such as graphic analysis, crosstabs, compare means, and correlation analysis can help identify how variables are related to the dependent variable and also relationships between any independent variables. Multicollinearity was touched on in the previous lesson but will be described in more detail later in this lesson.
Steps for Building MRA Models
In the fourth step, we need to identify any variables that may, in our appraisal judgement, be useful in the model, but are not useable in their current form - these require transformation. For example, in the MRA model for selling price developed in Lesson 6, let’s say we had a new variable that indicated the quality of each condo unit. This would likely be of use in the model, since purchasers tend to review quality in determining price. However, this new variable is coded as poor, fair, average, good, very good, and excellent, descriptions that are of no use in a mathematical regression model - e.g. , what might 812.35 times “excellent” work out to? We need to translate these descriptions into numerical equivalents, so we transform poor to 0, fair to 1, average to 2, up to excellent as 5. Thus, 812.35 times 5 (for excellent) makes arithmetic sense and would add over $4,000 to the selling price of the condo.1 This process is called transformation and is the fourth step in the process.
Steps for Building MRA Models
In the fourth step, we need to identify any variables that may, in our appraisal judgement, be useful in the model, but are not useable in their current form - these require transformation. For example, in the MRA model for selling price developed in Lesson 6, let’s say we had a new variable that indicated the quality of each condo unit. This would likely be of use in the model, since purchasers tend to review quality in determining price. However, this new variable is coded as poor, fair, average, good, very good, and excellent, descriptions that are of no use in a mathematical regression model - e.g. , what might 812.35 times “excellent” work out to? We need to translate these descriptions into numerical equivalents, so we transform poor to 0, fair to 1, average to 2, up to excellent as 5. Thus, 812.35 times 5 (for excellent) makes arithmetic sense and would add over $4,000 to the selling price of the condo.1 This process is called transformation and is the fourth step in the process.
Steps for Building MRA Models
The fifth step is to repeat Step 3 with any transformed variables - re-evaluating the potential variables for the model to see which offer the best suitability. If necessary, variables can be transformed again.
The sixth step is listing the final group of potential independent variables.
Steps for Building MRA Models
The fifth step is to repeat Step 3 with any transformed variables - re-evaluating the potential variables for the model to see which offer the best suitability. If necessary, variables can be transformed again.
The sixth step is listing the final group of potential independent variables.
Steps for Building MRA Models
The final three steps (7 through 9) are:
create the model using the specified variables and statistical software, which will determine the coefficients for the regression equation;
test and evaluate the model, finding how well it performs in terms of estimating the dependent variable or describing each variable’s contribution towards explaining the value of the dependent variable; and finally
• state your conclusions as to the quality of the model - in other words, describe (ideally in plain English that a layperson can understand!) what you did and why, and how well your model achieves its intended results.
Steps for Building MRA Models
The final three steps (7 through 9) are:
create the model using the specified variables and statistical software, which will determine the coefficients for the regression equation;
test and evaluate the model, finding how well it performs in terms of estimating the dependent variable or describing each variable’s contribution towards explaining the value of the dependent variable; and finally
state your conclusions as to the quality of the model - in other words, describe (ideally in plain English that a layperson can understand!) what you did and why, and how well your model achieves its intended results.
Steps for Building MRA Models
For model calibration, in valuation work models are primarily calibrated to produce either predictive or explanatory results.
Predictive Model: developed to produce the highest quality overall prediction of market value - for example, achieve the best possible estimate of selling price, but not necessarily the most reliable estimates for the individual coefficients.
Explanatory Model: developed primarily to explain the value that each variable contributes to market value - for example, the value per square foot of living area. In other words, rather than focussing on the outcome of the
model overall, this type of model focuses on developing the most accurate possible values for the coefficients.
Steps for Building MRA Models
For model calibration, in valuation work models are primarily calibrated to produce either predictive or explanatory results.
Predictive Model: developed to produce the highest quality overall prediction of market value - for example, achieve the best possible estimate of selling price, but not necessarily the most reliable estimates for the individual coefficients.
Explanatory Model: developed primarily to explain the value that each variable contributes to market value - for example, the value per square foot of living area. In other words, rather than focussing on the outcome of the
model overall, this type of model focuses on developing the most accurate possible values for the coefficients.
Steps for Building MRA Models
In a good explanatory model, the variable coefficients could be used as adjustments in a direct comparison approach or as market-derived costs in a cost approach. In an explanatory model, the model builder wants to maximize the accuracy of the values of the coefficients. As discussed in Lesson 6, the significance of the coefficients is indicated by the t-statistic and its associated significance level. Higher t-statistics and lower significance levels increase the reliance the model builder can place on the statistical significance of the coefficients. A high t-statistic leads to the acceptance of the hypothesis that the coefficient is significantly different than zero, meaning you are confident the coefficient number is accurate. As mentioned in the previous lesson, the criteria for this is usually to have a t-statistic over 2 and a significance level of less than .05. This would indicate that the probability of this coefficient being equal to zero is 5 % or less, meaning you are confident it is a reliable result.
Steps for Building MRA Models
In a good explanatory model, the variable coefficients could be used as adjustments in a direct comparison approach or as market-derived costs in a cost approach. In an explanatory model, the model builder wants to maximize the accuracy of the values of the coefficients. As discussed in Lesson 6, the significance of the coefficients is indicated by the t-statistic and its associated significance level. Higher t-statistics and lower significance levels increase the reliance the model builder can place on the statistical significance of the coefficients. A high t-statistic leads to the acceptance of the hypothesis that the coefficient is significantly different than zero, meaning you are confident the coefficient number is accurate. As mentioned in the previous lesson, the criteria for this is usually to have a t-statistic over 2 and a significance level of less than .05. This would indicate that the probability of this coefficient being equal to zero is 5 % or less, meaning you are confident it is a reliable result.
Steps for Building MRA Models
On the other hand, a good predictive model can be used to directly estimate sales prices. In a predictive model, the model builder wants to ensure the R-square is high and the standard error of the estimate is minimized.
This is normally achieved by including all variables that reduce the model’s standard error, regardless of the t-statistics or significance levels for the variables. This leads to a model with the lowest overall error possible, but it does not necessarily produce reliable individual variable coefficients.
Steps for Building MRA Models
On the other hand, a good predictive model can be used to directly estimate sales prices. In a predictive model, the model builder wants to ensure the R-square is high and the standard error of the estimate is minimized.
This is normally achieved by including all variables that reduce the model’s standard error, regardless of the t-statistics or significance levels for the variables. This leads to a model with the lowest overall error possible, but it does not necessarily produce reliable individual variable coefficients.
Steps for Building MRA Models
Depending on which goal is emphasized, the actions taken in the variable selection and calibration processes will vary. As this is an introductory course, the procedures described will tend to follow a middle course which allows for both a good prediction of market value and variable coefficients which are reasonable and rational from an appraisal perspective.
During the modeling process illustrated in this lesson, we will briefly demonstrate how these different approaches vary in procedures and outcomes.
Steps for Building MRA Models
Depending on which goal is emphasized, the actions taken in the variable selection and calibration processes will vary. As this is an introductory course, the procedures described will tend to follow a middle course which allows for both a good prediction of market value and variable coefficients which are reasonable and rational from an appraisal perspective.
During the modeling process illustrated in this lesson, we will briefly demonstrate how these different approaches vary in procedures and outcomes.
Illustration of MRA Model Building
Model Data
For this lesson, we will continue to focus on the Regina condominium sales data. The database we will use in this lesson is “Regina3”. This contains the same 120 sales used in previous lessons, but with 15 additional variables. You can download this database from the course website under “Online Readings”
There are 22 variables in the “Regina3” database. These are listed below:
Illustration of MRA Model Building
Model Data
For this lesson, we will continue to focus on the Regina condominium sales data. The database we will use in this lesson is “Regina3”. This contains the same 120 sales used in previous lessons, but with 15 additional variables. You can download this database from the course website under “Online Readings”
There are 22 variables in the “Regina3” database. These are listed below:
Illustration of MRA Model Building
Model Data
STEP 1: Specifying the Model
We will be developing an additive model to estimate the value of condominiums (condos) based on the variables given in the “Regina3” database.
Again, the additive general model that is often applied to residential property is:
MV = LV + BV
where
MV = estimated market value (or selling price); LV = land value; and
BV = building value.
However, because we are dealing with condos, land value will be ignored. Given the list of variables available in our database, we will produce the following general model for the market value:
MV = bo + (bi X LIVINGAREA) +E(bi x LOCATION VARIABLE)+ (b; x AMENITY)
where
MV = is the estimated condo value or the estimated market value (or selling price);
bo = constant;
bi, = coefficients of the independent variables;
LIVINGAREA = total living area in the condo;
LOCATION VARIABLES = any variable associated with the location of the condo (e.g., floor number); AMENITY; = any variable associated with condo amenities (e.g., underground parking or a pool in the complex).
Illustration of MRA Model Building
Model Data
STEP 1: Specifying the Model
We will be developing an additive model to estimate the value of condominiums (condos) based on the variables
given in the “Regina3” database. Again, the additive general model that is often applied to residential property is:
MV = LV + BV
Illustration of MRA Model Building
Model Data
STEP 2: Reviewing the Variables
The next step in the model development process is to review the variables available in the database and group the variables according to the factor the characteristic represents in the general model (e.g., in this case living area, location, or amenities). Very often, some characteristics to be included in the model will be represented by more than one variable and sometimes it is necessary to use a combination of more than one variable to correctly represent the characteristic or factor needed in the model.
Illustration of MRA Model Building
Model Data
STEP 2: Reviewing the Variables
The next step in the model development process is to review the variables available in the database and group the variables according to the factor the characteristic represents in the general model (e.g., in this case living area, location, or amenities). Very often, some characteristics to be included in the model will be represented by more than one variable and sometimes it is necessary to use a combination of more than one variable to correctly represent the characteristic or factor needed in the model.
Illustration of MRA Model Building
Model Data
STEP 2: Reviewing the Variables
For our database, the variables can be sorted as follows:
FACTOR VARIABLES
Living Area Total_Area
Location Topflr, Floor#, Abutting
Amenities Directio, Bedrms, Bath#, FullBath, Tqrbath, Halfbath, Patiofl, Balc#, Parkug, Parksurf, Parkdgar, Pool
Before making choices among variables or making changes to the database (Step 4: Transformations), you should familiarize yourself with the characteristics of the variables. In the next step, we will examine the variables to see which are best suited to be included in the modeling process (Step 6: List the Variables for Calibration).
Illustration of MRA Model Building
Model Data
STEP 2: Reviewing the Variables
For our database, the variables can be sorted as follows:
FACTOR VARIABLES
Living Area Total_Area
Location Topflr, Floor#, Abutting
Amenities Directio, Bedrms, Bath#, FullBath, Tqrbath, Halfbath, Patiofl, Balc#, Parkug, Parksurf, Parkdgar, Pool
Before making choices among variables or making changes to the database (Step 4: Transformations), you should familiarize yourself with the characteristics of the variables. In the next step, we will examine the variables to see which are best suited to be included in the modeling process (Step 6: List the Variables for Calibration).
