A data science team is developing a classification model to predict customer churn based on several continuous features. A preliminary analysis, which included a Bartlett's test, reveals strong evidence that the covariance matrices of the 'churn' and 'no churn' classes are statistically different. The team is deciding between Linear Discriminant Analysis (LDA) and Quadratic Discriminant Analysis (QDA) for the final model.
Given this finding, which of the following statements provides the most accurate guidance for model selection?
QDA should be preferred because it models each class using its own distinct covariance matrix, making it suitable for data where classes do not share a common covariance structure.
Either model can be used interchangeably, provided the features are first transformed using Principal Component Analysis (PCA) to ensure the covariance matrices are equalized.
LDA should be preferred because it is less prone to overfitting than QDA, and its robustness will provide a more generalized model even when the covariance assumption is violated.
QDA should be selected because it is a non-parametric method that can adapt to the differing class variances without making distributional assumptions.
The correct answer is that QDA should be preferred. The primary difference between Linear Discriminant Analysis (LDA) and Quadratic Discriminant Analysis (QDA) lies in their assumptions about the covariance matrices of the classes. LDA assumes that all classes share a common covariance matrix, which results in a linear decision boundary. In contrast, QDA does not make this assumption and estimates a separate covariance matrix for each class. This allows QDA to model a more flexible, quadratic decision boundary. Since the preliminary analysis indicates the class covariance matrices are different, the fundamental assumption of LDA is violated. Therefore, QDA, which is designed for this exact situation, is the more appropriate and potentially more accurate model.
The other options are incorrect. Preferring LDA for being less prone to overfitting is a misapplication of the bias-variance trade-off in this context; using a model whose core assumption is violated will likely lead to high bias, making it a poor choice despite its lower variance. QDA is a parametric model that assumes the data in each class is Gaussian; it is not non-parametric. Finally, using PCA does not 'equalize' covariance matrices between classes to satisfy LDA's assumption; PCA is an unsupervised dimensionality-reduction technique.
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Why does QDA handle differing class covariance matrices better than LDA?
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What is Bartlett's test and how does it inform model selection here?
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What are the risks of using LDA when its covariance assumption is violated?