9 🚀 Advanced Modeling Techniques
This chapter covers advanced modeling techniques taught by Prof. Sophie Dabo-Niang during the intensive session. These methods extend beyond basic statistical analysis to include sophisticated machine learning and modeling approaches.
9.1 Learning Objectives
By the end of this chapter, you will be able to:
- Understand and apply factor analysis techniques
- Perform cluster analysis for data segmentation
- Implement discrimination and classification methods
- Use binomial and multinomial logistic regression
- Apply kernel methods for non-linear relationships
- Work with general additive models
- Explore other supervised learning models
9.2 Course Structure
This part of the course consists of 5 hours of intensive sessions held during the week of November 17th. The sessions are designed to provide hands-on experience with advanced modeling techniques that build upon the foundations covered in Part 1.
9.3 Factor Analysis
Factor analysis is a statistical method used to identify underlying latent factors that explain the correlations among observed variables.
9.4 Cluster Analysis
Cluster analysis groups similar observations together based on their characteristics, without prior knowledge of group membership.
9.5 Discrimination & Classification
These methods aim to classify observations into predefined categories based on their characteristics.
9.6 Logistic Regression
Logistic regression models the probability of categorical outcomes.
9.7 Kernel Methods
Kernel methods extend linear algorithms to handle non-linear relationships by mapping data to higher-dimensional spaces.
9.8 General Additive Models (GAMs)
GAMs extend linear models by allowing non-linear relationships between predictors and the response variable.
9.9 Other Supervised Models
Additional supervised learning techniques for classification and regression.
9.10 Practical Implementation
All methods will be implemented using R with appropriate packages:
# Load required packages for advanced modeling
library(factoextra) # Factor analysis
library(cluster) # Cluster analysis
library(MASS) # LDA, QDA
library(e1071) # SVM
library(mgcv) # GAMs
library(randomForest) # Random Forest
library(gbm) # Gradient Boosting
library(nnet) # Neural Networks
library(caret) # Model training and validation9.11 Assessment and Evaluation
9.11.1 Model Evaluation Metrics
- Classification: Accuracy, Precision, Recall, F1-score
- Regression: RMSE, MAE, R-squared
- Clustering: Silhouette score, Within-cluster sum of squares
- Cross-validation: Ensuring model generalizability
9.11.2 Best Practices
- Data Preprocessing: Handle missing values and outliers
- Feature Selection: Choose relevant predictors
- Model Validation: Use cross-validation techniques
- Hyperparameter Tuning: Optimize model parameters
- Model Comparison: Compare different approaches
- Interpretation: Understand and communicate results
9.12 Intensive Session Schedule
The intensive session will cover:
Day 1: Factor Analysis and Cluster Analysis - Morning: Theory and concepts - Afternoon: Hands-on implementation
Day 2: Classification and Logistic Regression - Morning: Discrimination methods - Afternoon: Logistic regression applications
Day 3: Advanced Methods - Morning: Kernel methods and GAMs - Afternoon: Ensemble methods and model comparison
9.13 Prerequisites
Students should be familiar with: - Basic statistical concepts from Part 1 - R programming fundamentals - Linear regression concepts - Hypothesis testing
9.14 Resources
- Course slides and materials will be provided during the intensive session
- Additional resources available in the course drive
- R documentation for specific packages
- Practice datasets for hands-on exercises