Prediction ideas
Background
The chapter provides a comprehensive guide to prediction modeling for cholesterol levels, focusing on the challenges and solutions involved in building robust prediction models. It begins by addressing the issue of collinearity among predictors and progresses to cover the intricacies of modeling both continuous and binary outcomes. Special attention is given to diagnosing and preventing model overfitting through various techniques such as data splitting and cross-validation. Advanced topics in model validation like bootstrapping are also explored. The overarching theme is to equip data analysts with the tools and methods needed to build, assess, and improve predictive models while addressing common challenges like collinearity and overfitting.
As we’ve journeyed through the previous chapters, we’ve gained a comprehensive understanding of various research questions, particularly distinguishing between causal and predictive inquiries. While the prior chapter delved into the intricacies of causal questions and the challenges they present, this chapter shifts the spotlight to the realm of prediction. Predictive questions have their own set of complexities and methodologies, distinct from those of causal inquiries. Here, we’ll explore the art and science of making accurate predictions, understanding the factors that influence them, and the tools and techniques best suited for predictive analysis.
Furthermore, this chapter serves as a precursor to our upcoming exploration of machine learning. While prediction provides the foundation, machine learning offers advanced tools and algorithms to refine and enhance our predictive capabilities. By building on the foundational knowledge from the preceding chapters and setting the stage for the machine learning chapter, we aim to provide a holistic view of how prediction and machine learning intertwine in the broader landscape of research inquiry.
Datasets:
All of the datasets used in this tutorial can be accessed from this GitHub repository folder
Overview of tutorials
Identify collinear predictors
This tutorial focuses on identifying collinear predictors in a dataset related to cholesterol levels from the NHANES 2015 collection. The tutorial guides you through summarizing its structure, and applying methods for variable clustering to detect collinear predictors. The tutorial is practical for data analysts aiming to improve model accuracy by identifying and addressing redundant variables.
Explore relationships for continuous outcome variable
This comprehensive tutorial walks you through the process of analyzing a dataset on cholesterol levels, focusing on exploring relationships for a continuous outcome variable. It starts by generating a correlation plot. Multiple methods for examining descriptive associations are provided, including stratification by key predictors. The tutorial also covers linear regression modeling, diagnosing data issues like outliers and leverage, and refitting the model after cleaning the data. Additionally, the tutorial delves into more complex modeling techniques like polynomial regression and multiple covariates, and addresses issues of collinearity using Variance Inflation Factors (VIF).
Explore relationships for binary outcome variable
A binary outcome variable is created to classify cholesterol levels as ‘healthy’ or ‘unhealthy’. This transformed variable is then modeled using logistic regression. Various predictors including demographic variables, vital statistics, and other health parameters are considered in the model. The performance of the model is evaluated using Variance Inflation Factor (VIF) for multicollinearity and Area Under the Curve (AUC) for classification accuracy. Two models are fitted, and their respective AUCs are calculated to assess the predictive power.
Overfitting and performance
The tutorial focus is on addressing overfitting and assessing model performance. A linear regression model is fitted using a comprehensive set of predictors. Various statistical metrics such as the design matrix dimensions, Sum of Squares for Error (SSE), Total Sum of Squares (SST), R-squared (R2), Root Mean Square Error (RMSE), and Adjusted R2 are calculated to evaluate the model’s predictive power and fit. Functions are also created to streamline the calculation of these metrics, allowing for more dynamic and customizable performance assessment. One such function, perform, encapsulates the entire process, outputting key performance indicators including R2, adjusted R2, and RMSE, and it can be applied to new data sets for validation.
Data spliting
The tutorial focuses on splitting data into training and testing sets to prevent model overfitting. We allocate approximately 70% of the data to the training set and the remaining 30% to the test set. The linear regression model is then fitted using the training data. Performance metrics are extracted using the previously defined perform function, which is applied not only to the training and test sets but also to the entire dataset for comprehensive performance evaluation. This data splitting approach allows for more robust model validation by assessing how well the model generalizes to unseen data.
Cross-vaildation
The tutorial outlines the process of implementing k-fold cross-validation to validate a linear regression model’s performance, aiming to predict cholesterol levels. The dataset is divided into 5 folds, by turn used as training (to fit the model), and test sets (used for prediction and performance evaluation). Performance metrics such as R-squared are calculated for each fold. The process can also be automated , which helps in fitting the model across all folds and summarizing the results, including calculating the mean and standard deviation of the R-squared values to understand the model’s consistency and reliability.
Bootstrap
The tutorial outlines methods for implementing various bootstrapping techniques in statistical analysis. It demonstrates resampling methods using vectors and matrices. The idea of bootstrapping is emphasized as a useful technique for estimating the standard deviation (SD) of a statistic (e.g., mean), when the distribution of the data is unknown. This SD is then used to calculate confidence intervals. Different variations of bootstrap methods, such as “boot,” “boot632,” and “Optimism corrected bootstrap,” are demonstrated for linear regression and logistic regression models. They are used to obtain performance metrics like R-squared for regression models and the Receiver Operating Characteristic (ROC) curve for classification models. The tutorial also includes an example of calculating the Brier Score. The examples aim to offer various strategies for model evaluation, from the basics of resampling a vector to applying complex methods like ‘Optimism corrected bootstrap’ on real-world data.
Optional Content:
You’ll find that some sections conclude with an optional video walkthrough that demonstrates the code. Keep in mind that the content might have been updated since these videos were recorded. Watching these videos is optional.
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