Predicting Residential Home Prices in Ames, IA
Which factors contribute to the sale price of a house? There are plenty of answers: size matters, as do the building materials. Location is important. Does it have a backyard? A swimming pool? What’s the garage size like? How old is it? As you can see, the number of ways you can assess a house’s price quickly gets out of hand. It’s nearly impossible to accurately and heuristically judge a house given a large set of variables. But is there a way to look at those variables simultaneously and quantitatively to accurately predict the market sale price?
The answer is yes. The power of machine learning provides us with the tools we need to look at a large data set and spit out a predicted value. Using a dataset containing information on houses in Ames, Iowa, our team leveraged different machine learning techniques to predict respective sale prices.
Upon receiving the dataset, we first performed an exploratory data analysis to assess the completeness of the data, and to see if any variables needed to be altered so that they would be usable by our models. For example, categorical variables would need to be dummified or converted to ordinal format, and certain numerical variables might need to be transformed to ensure a usable distribution.
Next, we identified or engineered important features and conversely dropped variables which did not strongly correlate with sale price.
With a condensed dataset, we then began applying different types of machine learning models to the data to get a sense of which models had the most predictive power. Critically, we performed a series of rounds where we tuned model hyperparameters iteratively to minimize our prediction error. After identifying the most successful models, we ensembled different model combinations together to further improve our predictions.
Finally, with a set of sale price predictions, we submitted the values to Kaggle to see how well we fared against the competition.
Data and Feature Engineering
The data for this project came from a Kaggle competition, pre-split evenly into a training set and test set with 1460 observations and 79 features.
We first explored our target variable, Sale Price. In order to meet a key requirement of regressive models, we applied a logarithmic transform to this variable. This gave us a more normal distribution from which we could train our model.
The 79 features were a mix of 28 continuous and 51 categorical variables. 34 features contained missing values, and our team used a variety of techniques to handle this, including dropping variables outright that had 99%+ missingness (e.g. Utilities) and the application of imputation methods on features we deemed critical for our analysis (e.g. Lot Frontage).
We generated the following criteria to transform features:
- In order to meet the assumption of linear relationship between the target and predictors, we logged square footage variables.
- Variables that naturally had a hierarchical nature to them were encoded as ordinal variables. We chose to do this, rather than transform them into a set of dummy variable (i.e. one-hot encoding), in order to both reduce the total number of predictors in our model as well as keep important information about the continuous nature of the variable.
- Finally we collapsed naturally categorical variables into smaller and more meaningful categories and transformed them into dummy variables.
We established a correlation plot to identify features that were highly correlated with one another. Based on this analysis, we removed a few additional features, allowing us to address multicollinearity.
With a clean dataset, we were ready to begin modeling our data.
The four models we combined in each of our meta-models were Ridge Regression, Lasso Regression, Random Forest Regression and Gradient Boosting Regression. We optimized each of our base models by performing a grid search and 5-fold cross validation to find the optimal hyperparameters that yielded the best prediction. Next, we ensembled (or “stacked”) different models into meta-models. In the first meta-model, we ensembled the models by averaging their predictions. In the second meta-model, we stacked the four models and used multiple linear regression to make our final prediction. For a more detailed model-by-model breakdown, see directly below.
The first model that we used was Ridge Regression. Ridge Regression minimizes the sum of the RSS and the l2 penalty, which is the sum of squared coefficient estimates. By finding the value for lambda that minimizes this sum, the model aims to shrink the group of coefficients in our model, which prevents the model from overfitting and allows for more robust predictions. After tuning the model, we found that the optimal value for alpha(lambda) was 9.48 which resulted in an RMSE of 0.1207. Although Ridge Regression is able to shrink coefficients such that they asymptotically approach zero, it cannot set coefficients exactly to zero like the next model.
The second model that we used was Lasso Regression. Lasso Regression is similar to Ridge Regression because they both strive to minimize the sum of the RSS and a shrinkage penalty. The difference between the two models is that the Lasso Regression model uses a different shrinkage penalty. Lasso Regression uses the l1 penalty, whereas Ridge Regression uses the l2 penalty mentioned above. After tuning our model, we found our alpha(lambda) to be 0.00048413 and the model’s RMSE to be 0.1195. A key assumption in Lasso and Ridge Regression is that the target data is linear. We chose to incorporate the next two models into our meta-models because they do not make this assumption.
The third model that we used was Random Forest Regression. A Random Forest model builds different decision trees on bootstrapped data from the training set. The decision trees are different because each tree can only consider a random subset of the total number of predictors at each split. Thus, only predictors in that subset have the opportunity to be the splitting factor. This characteristic of the Random Forest model creates decision trees that are not correlated and reduces the variance of the model. After tuning our hyperparameters, our model yielded an RMSE of 0.1239. Like the Random Forest model, our last model is based on the premise of combining many weak learners into a single model that is a strong learner.
The fourth model that we used was Gradient Boosting Regression. Gradient Boosting Regression makes an initial prediction; then the algorithm improves on that prediction by adding an estimator term to the initial prediction. Next, it optimizes the model by fitting the estimator term to the residual using gradient descent. Our optimized Gradient Boosting model had an RMSE of 0.1301. After optimizing each of the individual models, we used them to create two different meta-models.
The first meta-model averaged the predictions of the four base models. We weighted each of our predictions equally. If we were to continue to develop this meta-model, we would perform a grid-search using cross validation to find the weights that yielded the optimal result via a weighted average of the predictions. This meta-model yielded an RMSE of 0.12582 when submitted to Kaggle.
The second meta-model stacked the base models. We took the predictions of each of our individual models and created a four-dimensional matrix. We then performed multiple linear regression to yield our final prediction. When we submitted this model to Kaggle, we yielded an RMSE of 0.1267.
Our team used this opportunity to simulate a real-life data science project. It was a great opportunity to learn from one another and collaborate to productionalize machine learning algorithms.
In order to effectively predict residential home prices, it's important to examine external factors as well. This includes supply and demand indicators such as construction pipeline, net absorption, days on market. Furthermore, when predicting something like home prices, it’s important to take into account the local economy. This would include investigating job growth, income levels, and family-mix in the local area.
However, given limited resources (a relatively small dataset) we made do with what we had. The project was fantastic practice in tweaking models to maximize predictive power and minimize model overfitting. These skills will surely prove useful as we go on to future projects in the data science field.