Linear Discriminant Analysis

Linear discriminant analysis finds linear combinations of predictors that best separate known groups, assuming a common covariance matrix, and uses them to classify cases.

선형판별분석은 공통 공분산행렬을 가정하고 이미 알려진 집단을 가장 잘 구분하는 예측변수의 선형결합을 찾아 사례를 분류하는 기법입니다.

Which of my measured variables best separate the three customer segments, and how accurately can they classify new customers?

측정한 변수들 중 어떤 것이 세 고객 세그먼트를 가장 잘 구분하고, 새 고객을 얼마나 정확히 분류할 수 있나요?

Linear discriminant analysis builds discriminant functions that maximize between-group variance relative to pooled within-group variance and classifies each case into the group with the highest posterior probability. Wilks' lambda tests whether group centroids differ, and cross-validated accuracy estimates how well the rule classifies new cases.

When to use Linear Discriminant Analysis

• The outcome is a categorical group label and predictors are continuous.
• Group covariance matrices are roughly equal.
• You want both a classification rule and an interpretable description of group separation.

When to use something else

• Group covariance matrices clearly differ; use quadratic discriminant analysis instead.
• Predictors are mostly categorical or strongly non-normal; use multinomial logistic regression instead.

Assumptions and requirements

• Multivariate normality of predictors within each group.
• Equal covariance matrices across groups (Box's M).
• More cases in each group than predictors.
• No perfect multicollinearity among predictors.

What the analysis reports

• Wilks' lambda with Bartlett chi-square test
• Eigenvalues and canonical correlations of discriminant functions
• Structure (discriminant) loadings
• Cross-validated and resubstitution accuracy
• Confusion matrix

How to report it

A linear discriminant analysis with [p] predictors and [g] groups (N = [n]) was significant, Wilks' Λ = [value], χ²([df]) = [value], p = [value]; cross-validated classification accuracy was [value]%.

Related methods

• Quadratic Discriminant Analysis
• Multinomial Logistic Regression
• MANOVA

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