Automated Valuation Modeling (AVM) for Beginners – How to Prep a Non-Numeric Variable for a Regression Model – ChatGPT Weighs in!

 

Sid: The median sale price of a single-family home in Town 14 is $220,900, while in Town 15 it is $260,000. However, both towns' median sale price per square foot (SPSF Median) is quite similar. On the other hand, even though Towns 15 and 17 have the same median sale price of $260,000, their weighted average sale price per square foot (SPSF Wgt Avg) differs significantly. Can you study the data in this table and help me understand why there are such discrepancies without honing in outside factors?

ChatGPT: Based on the given data, let's analyze the differences in the metrics to understand the discrepancies observed. 

1. Living Area (SF): The total living area of Town 15 is significantly higher than Town 14, Town 16, and Town 17. This means that the homes in Town 15 are generally larger in size compared to the other towns. 

2. SP Count: Town 15 has the highest number of sales (794), followed closely by Town 16 (778). Town 14 has the lowest number of sales (196). This difference in sales count could be a contributing factor to the differences in median sale prices. 

3. SP Sum: Town 15 has the highest total sale price sum ($232,856,009), followed by Town 16 ($213,846,709) and Town 17 ($195,983,709). Town 14 has the lowest total sale price sum ($45,631,509). This indicates that despite having fewer sales, Town 15 has higher-priced homes, which is reflected in its higher total sale price sum. 

4. SPSF: Towns 15, 16, and 17 have similar median sale price per square foot (SPSF) values, with Town 15 having the highest value (170), followed by Town 17 (184) and Town 16 (168). Town 14 has the lowest SPSF value (167), indicating slightly lower pricing per square foot compared to the other towns. 

5. SPSF Wgt Avg: The weighted average sale price per square foot (SPSF Wgt Avg) takes into account the total sale price and living area of each town to calculate an average value. Even though Towns 15 and 17 have the same median sale price, their SPSF Wgt Avg values differ significantly. This difference could be attributed to the distribution of sales across different living areas in each town. 

In summary, the observed discrepancies in median sale prices and SPSF metrics can primarily be attributed to the size of the homes, the number of sales, and the distribution of sales across different living areas in each town. Additional factors such as location, condition, amenities, and market demand can further explain the differences but have been excluded from the given data. 

Sid: Should I use SPSF Median or SPSF Wgt Avg for target encoding the "Town" variable in a regression model to improve its efficiency and predictability? 

ChatGPT: When using target encoding to encode the "Town" variable in a regression model, it is generally recommended to use the weighted average sale price per square foot (SPSF Wgt Avg) rather than the median sale price per square foot (SPSF Median). 

The main reason for this is that the weighted average takes into account both the sale price and the living area of each town, providing a more comprehensive representation of the pricing patterns. It considers the distribution of sales across different living areas, which helps capture the overall pricing trends more accurately. 

Using the SPSF Wgt Avg for target encoding can potentially improve the efficiency and predictability of the regression model as it incorporates information about the size of the homes and the distribution of sales in each town. It provides a more nuanced understanding of how town affects the sale price per square foot. 

However, it is important to note that other factors such as location, condition, amenities, and market demand can also impact the sale price and should be considered in conjunction with the target encoding. Additionally, it is always recommended to validate the model's performance and assess its predictive power through appropriate evaluation metrics and techniques. 

Sid: Since the sale price or time-adjusted sale price will be the dependent variable in the regression model, either the SPSF Median or SPSF Wgt Avg will transfer the influence of the dependent variable, which is against the regression assumptions. Can you suggest which will transfer lesser influence if used to target encoding? Is there a better alternative to target encoding the “Town” variable? 

ChatGPT: You are correct that using the SPSF Median or SPSF Wgt Avg for target encoding would transfer the influence of the dependent variable to the "Town" variable, potentially violating regression assumptions. 

If you want to avoid this issue and still include the "Town" variable in your regression model, there are alternative encoding techniques that you can consider: 

1. One-Hot Encoding: This method involves creating binary dummy variables for each unique category of the "Town" variable. Each town would have its own dummy variable indicating its presence or absence. This approach avoids transferring the influence of the dependent variable to the "Town" variable and allows for independent interpretation of each town's effect on the sale price. However, note that this can result in a high number of additional variables depending on the number of unique towns. 

2. Frequency Encoding: In this method, you replace each category of the "Town" variable with the frequency of occurrence of that category in the dataset. This encoding technique preserves the information about each town's occurrence without transferring the influence of the dependent variable directly. However, it may not capture specific pricing information about each town. 

3. Target Mean Encoding: Instead of using SPSF Median or SPSF Wgt Avg, you can consider target mean encoding, which involves replacing each category of the "Town" variable with the mean sale price for that specific town. This encoding technique captures specific pricing information for each town while minimizing the transfer of influence from the dependent variable. Target mean encoding can be more informative than frequency encoding but should be used with caution, especially with small sample sizes or highly correlated categories. 

It's worth noting that there is no one-size-fits-all solution, and the choice of encoding technique may depend on the specific characteristics of your dataset and the goals of your regression model. It is important to carefully evaluate and compare the performance of different encoding methods through appropriate validation and evaluation techniques to ensure the reliability and predictive power of the regression model.

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