How to perform advanced statistical modeling in Spark?

Step 1: Understand Your Data
Before you begin modeling, you must know what data you are working with. Load your data into Spark using DataFrames, which are distributed table-like structures. Inspect your data, check for missing values, and understand the basic statistics of each column.

Step 2: Preprocess Your Data
Data rarely comes ready for analysis. You may need to clean it by handling missing values, encoding categorical variables, scaling numerical features, and potentially creating new features that may better capture the patterns in your data.

Step 3: Choose a Statistical Model
Spark’s MLlib library offers a variety of statistical models ranging from linear regression to clustering and classification algorithms. Select a model that fits your data type and analysis goals. For instance, if you're predicting a value, you might choose linear regression. If you're categorizing data points, you could use a classification model.

Step 4: Split Your Data
To properly evaluate your model, split your data into a training set and a test set. A common split ratio is 70% for training and 30% for testing. This will help you assess how well your model will perform on unseen data.

Step 5: Train Your Model
Using the training data, train your model in Spark by calling the appropriate training method. For example, if you're using linear regression, you would call 'fit' on a LinearRegression instance, passing in your training DataFrame.

Step 6: Evaluate Your Model
After training, use the test dataset to evaluate your model's performance. Spark provides evaluation metrics such as Mean Squared Error for regression models or accuracy for classification models. Use these metrics to understand how well your model is performing.

Step 7: Tune Model Hyperparameters
Most models have hyperparameters that you can tune for better performance. Use Spark's MLlib tools like CrossValidator and ParamGridBuilder to try different combinations of hyperparameters systematically and find the best model.

Step 8: Deploy Your Model
Once you are satisfied with the model’s performance, you can deploy it into a production environment where it can make predictions on new data. Spark allows you to save your trained models for later use, which is helpful for deployment.

Remember, advanced statistical modeling requires iterative refinement and a deep understanding of the problem you're trying to solve. Always test different approaches and optimally tune your models for the best results.