Predicting Housing Sale prices via Kaggle Competition
The objective of this Kaggle competition was to accurately predict the sales prices of homes in Ames, Iowa, using a provided training dataset of 1400+ homes & 79 features. This exercise allowed both experimentation/exploration for different strategies of feature engineering & advanced modeling.
To familiarize with the problem, some initial research was done on the town of Ames. As a college town, home to Iowa State University, everything (including real estate) can be tied to the academic calendar. The location of airports & railroads were also noted, as well as which neighborhoods are rural vs. mobile homes vs. dense urban. Another interesting discovery was the Asbestos Disclosure Law, requiring sellers to notify buyers if the material is in or on their homes (such as roof shingles), which may have a direct impact on home’s price.
To familiarize ourselves with the dataset’s features, features were divided into Categorical & Quantitative categories, where some could be considered both. A function was written to visualize each through either box plots (abc) or scatter plots (123) to gain quick insights such as NA / 0-values, value/count distribution, evidence of relationship with the target, or obvious outliers.
To dig-in a little deeper, two functions,
quantdf(), were scripted to create a dataframe of summary details for both types of features:
The CATDF dataframe includes number of unique factors, the total set of factors, the mode, the mode percentage & the number of NAs. It also ran a simple linear regression with only the feature & sales price, and returned the score when the feature was converted into dummy variables, into a binary one (mode) vs. rest variable, or a quantitative variable (eg Poor = 1 while Excellent = 5). It would also suggest an action item for the specific feature depending on results.
The QUANTDF dataframe includes range of values, the mean, the number of outliers, NA & 0-values, the pearson correlation with saleprice and a quick linear regression score. This also flags any high correlation with other variables, to alert of potential multicollinearity issues. This proved particularly useful when comparing the TEST vs. TRAIN datasets - for example patios sizes were overall larger in the TEST set, which may affect the overall modeling performance if that particular feature were utilized.
Feature Engineering & Selection
The second step was to add, remove, create & manipulate additional features that could provide value to our modeling process.
We attempted to create multiple versions of our dataset, to see which “version” of our feature engineering proved most beneficial when modeling.
Here are our dataset configurations, created to compare model performance:
only quantitative features were used
quantitative features + converted ordinal categorical (1-5 for Poor-Excellent)
using all original features but dummified all categorical
using some new features & converted categorical based on CATDF suggested actions
all feature engineering (+ a few extra), intelligent ordinality, usually our best
Missingness was handled differently depending on our dataset configurations (see below). Particularly in the MATCAT dataset, significant time and energy was spent meticulously choosing appropriate missing values within the dataset, with the general assumption made that if a home contained a null value related to area-size, that the home did not include that area on its lot (i.e. if the Pool Square Footage was null, we assumed the property did not contain a pool). Some of the earlier versions of our models, such as our initial simple linear regression model makes use of mean imputation for numeric columns (after outlier removal), and mode imputation for categorical values prior to dummification.
Upon analyzing the dataset, it was clear that several features needed to be combined prior to modeling. The dataset contained square-footage values for multiple different types of porches and decks (screened-in, 3Season, OpenPorch, and PoolDeck) which combined neatly to become a Porch square-footage variable. The individual features were then removed from the dataset.
Other features were converted from square-footage units to binary categories, denoting whether the home contained that item, feature, or room or not.
The function written to create the MATCAT dataset allows the user to apply scaler transformations, and boxcox transformations for largely skewed features. These transformations generally improved the models’ accuracy, especially in the linear models.
Additionally, the MATCAT dataset makes use of intelligent ordinality while handling NA values for categorical features being converted to numeric. We found that in certain cases, having a poor-quality room was more detrimental to a home’s saleprice than a home not possessing that room or item at all. For instance, in our dataset, homes without a basement have a higher average saleprice than homes that have basement of the lowest quality. In cases such as this one, NA values were given the numerical value closest-matching the average saleprice of homes with NA for that category.
Other feature selection strategies used were:
- Starting with all of the features, running a while-loop VIF analysis to remove anything > 5
- Starting with single feature, adding new features iff it contributes to a better AIC/BIC score
- Converting selected features to PCA and modeling with new vectors
- Using Ridge/Lasso to remove features through penalization
- Using RandomForest Importance listing to use top subset for decision tree splits
Models & Tuning
Linear Modeling - Ridge, Lasso & ElasticNet were used, GridSearchCV optimized for alpha and l1_ratio. Since many significant features have a clear linear relationship with the target variable, these model gave a higher score than the non-linear models.
Non-Linear Modeling - Random Forest (RF), Gradient Boosting (GBR) and XGBoost were used, GridSearchCV optimized for MaxFeatures for RF, as well as MaxDepth & SubSample for GBR. The performance was not improved using our optimized dataset, since the optimized dataset was optimized for linear regression only. In addition, it was difficult to balance over-fitting when using the GBR model.
Model Stacking - H20.ai is an open-source AutoML platform, and when it was asked to predict saleprice, based on our MATCAT dataset, the AutoRegressor utilized various models (RF, GLM, XGBoost, GBM, Deep Neural Nets, Stacked Ensembles, etc) that ultimately lead to our best Kaggle Score. While it is more difficult to interpret this model’s findings compared to traditional machine learning techniques, the AutoML model neutralizes any major disadvantages any specific model may have while taking the best of each family.
In addition to our standard collaboration tools (github, slack, google slides) - we also utilized Trello organize our thoughts on the different features & Google Python CoLab to work on the same Juptyer notebook file. This allowed us to work together virtually anywhere & at anytime.