The Role of Quantitative Variables in Automated Valuation Modeling (AVM)

Target Audience: New Graduates/Analysts

In statistics, a quantitative variable represents numeric values that can be measured and compared in magnitude. The three main types of quantitative variables are continuous, ratio, and discrete.

Continuous variable: A continuous variable can take any numerical value within a range. For example, in an AVM, the sale price is a continuous variable because it can take on any value within a specific range, such as $100,000 or $200,000. This variable type helps measure variation and compares different values along a continuum.

Ratio variable: A ratio variable, like the adjusted sale price per square foot (SP/SF), is a powerful tool in property valuation. It has a true zero point, meaning a value of zero indicates the absence of the thing being measured. This precision allows for meaningful comparisons in ratios and proportions, enhancing the accuracy of property valuation.

Discrete variable: A discrete variable, such as the median monthly sale prices, is a versatile tool in property valuation. It takes on specific numerical values that are separate and distinct from each other, allowing for counting and representing distinct categories or events. This versatility makes it adaptable to various property valuation scenarios.

In an AVM, using these three types of quantitative variables – sale price (continuous), SP/SF (ratio), and median monthly sale prices (discrete) – will help capture different aspects of the housing market in a specific county. By incorporating these variables, analysts can provide a more comprehensive and accurate valuation of properties based on various metrics and factors.

Continuous vs. Ratio Variable

Suppose you are developing an AVM for a specific county with arms-length sales from the recent nine quarters. Before starting the regression modeling, you must understand the adjusted sale price's nuances in raw and normalized (SP/SF) forms. Here is how to compare and contrast their statistical measures.

1. Mean:

• Adjusted Sale Price Mean: $436,481
• SP/SF Mean: $218.99

Comparison: The mean provides the average value of the data. It is a central measure that can help understand the general value of properties in the dataset.

Contrast: While the adjusted sale price gives an overall average value of properties sold, the SP/SF mean gives a measure of value standardized by the property size. This can help in comparing properties of different sizes.

2. Standard Error:

• Adjusted Sale Price Standard Error: $1,415
• SP/SF Standard Error: $0.44

Comparison: The standard error indicates the variability or uncertainty in the mean estimate. A smaller standard error suggests a more precise estimate.

Contrast: The standard error for adjusted sale price and SP/SF helps assess the reliability of the mean estimates. Understanding the accuracy of the valuation predictions is particularly important in AVMs.

3. Median:

• Adjusted Sale Price Median: $401,962
• SP/SF Median: $214.26

Comparison: The median represents the middle value of the dataset when arranged in order. It is a robust measure that is not affected by extreme values.

Contrast: Using the median alongside the mean provides a more complete picture of the data distribution. It can help identify any skewness or outliers impacting the valuation model.

4. Mode:

• Adjusted Sale Price Mode: $381,196
• SP/SF Mode: $194.89

Comparison: The mode is the most frequently occurring value in the dataset. Understanding common pricing trends can be useful.

Contrast: While the mean and median provide central measures, the mode gives insight into popular price points. This information can be valuable in identifying pricing patterns and preferences in the housing market.

5. Standard Deviation:

• Adjusted Sale Price Standard Deviation: $153,531
• SP/SF Standard Deviation: $48.26

Comparison: The standard deviation measures the dispersion of the data points around the mean. A higher standard deviation indicates greater variability in the dataset.

Contrast: Understanding the standard deviation for both adjusted sale price and SP/SF helps assess the spread of property values and can aid in determining the level of risk associated with valuation estimates.

6. Kurtosis:

• Adjusted Sale Price Kurtosis: 1.02213
• SP/SF Kurtosis: 9.4649

Comparison: The kurtosis value for adjusted sale price is around 1.02213, close to a normal distribution with moderate tailedness.

Contrast: However, the SP/SF kurtosis value of 9.4649 suggests a highly peaked distribution or heavy tails, indicating a departure from normality and the potential presence of outliers or extreme values.

7. Skewness:

• Adjusted Sale Price Skewness: 1.10514
• SP/SF Skewness: 1.8910

Comparison: Both the adjusted sale price and SP/SF skewness values are positive, indicating right-skewed distributions where the tail is on the right side of the peak.

Contrast: The skewness values suggest that the data is skewed toward higher values, with the SP/SF distribution exhibiting slightly higher skewness than the adjusted sale price.

In essence, each of these statistical measures provides valuable insights into the distribution, variability, and central tendencies of the property values in the dataset. By accounting for different aspects of the data distribution, incorporating these measures in an AVM can enhance the accuracy and reliability of the valuation predictions.

Important to Understand

Analyzing the sale price per living square foot (SP/SF) as a normalized ratio can provide additional insights and a more meaningful perspective in understanding the local housing market for several reasons:

1. Standardization: SP/SF makes comparing properties of differing sizes easier. This allows for a more direct comparison (apples to apples) based on the property's value relative to its size.

2. Fair Comparison: SP/SF provides a fair comparison between properties with different sizes. This can help evaluate properties' value propositions irrespective of their size.

3. Market Analysis: SP/SF can help identify trends in pricing per unit area over time. It can reveal whether there are specific patterns in how prices change based on property size, which can be valuable for market analysis.

4. Understanding Value: Analyzing the SP/SF can provide insights into the value buyers place on living space. It can help understand preferences for larger or smaller properties and their corresponding price points.

5. Property Valuation: SP/SF is a standard metric real estate professionals use for appraisals and property valuation purposes. It allows for a standardized approach to assessing property values.

However, it's important to note that while SP/SF offers several advantages, it should not be the sole metric for analyzing the local housing market. Raw sale prices may still be relevant, especially when considering other factors such as location, amenities, market conditions, and property features. Both metrics provide valuable insights, and a comprehensive analysis should consider a combination of normalized and raw prices to understand the local housing market.

Discrete Quantitative Variable

A discrete variable is a quantitative variable that can take on a finite number of distinct and separate values; for instance, if we have the median sale prices for each month from January to December, each month (e.g., January, February, March, etc.) represents a discrete value for the median sale price.

These values can be measured, counted, and analyzed numerically, fitting the criteria of a discrete quantitative variable.

The variable doesn't exist on a continuous spectrum. There aren't "in-between" months or quarters, so one can't have a 1.3rd quarter or July and a half. There are distinct categories (months or quarters) with clear boundaries. Even though it's not continuous, the variable represents numerical values. One can order the months (1st, 2nd, 3rd...) or quarters (Q1, Q2, Q3, Q4) in a sequence.

In summary, while month and quarter are categories, they have a defined order and can be used in calculations, making them discreet quantitative variables.

Example

The breakdown of the median sale price and median SP/SF by quarter creates discrete quantitative variables. Discrete variables can take on a finite number of values within a specific range. In this case, the number of possible values for the median sale price and median SP/SF is limited by the number of quarterly sales.

Here’s an analysis of the breakdown of the two variables in the table you provided:

    1) Median Sale Price: There is a seasonal pattern to the median sale price, with higher prices in the second and third quarters (Q2 and Q3) and lower prices in the first and fourth quarters (Q1 and Q4). This could be due to several factors, such as buyer behavior or the availability of listings. For example, more people may be looking to buy a house in the spring and summer months, which could increase prices. Additionally, sellers may be more motivated to sell their homes before the end of the year, which could lead to lower prices in Q4.

   2) Median SP/SF: The median SP/SF also shows a seasonal pattern, with higher prices in Q2 and Q3 and lower prices in Q1 and Q4. This suggests that the seasonal pattern in the median sale price is likely due to changes in the types of properties sold rather than changes in the overall housing price in the county. For example, a higher proportion of larger homes may be sold in Q2 and Q3, which would drive up the median SP/SF.

Overall, the breakdown of the median sale price and median SP/SF by quarter, leading to a discreet variable, can help understand the seasonal trends in the housing market. This information can also help build a more accurate AVM by considering when a property is sold.

In conclusion, understanding the different types of quantitative variables empowers analysts to leverage the data effectively. Combining continuous, ratio, and discrete variables provides a comprehensive view of the housing market, making AVM a valuable tool for property valuation.

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