Linked Questions

28
votes
4answers
23k views

What is the relationship between regression and linear discriminant analysis (LDA)?

Is there a relationship between regression and linear discriminant analysis (LDA)? What are their similarities and differences? Does it make any difference if there are two classes or more than two ...
21
votes
2answers
7k views

How does linear discriminant analysis reduce the dimensions?

There are words from "The Elements of Statistical Learning" on page 91: The K centroids in p-dimensional input space span at most K-1 dimensional subspace, and if p is much larger than K, this ...
14
votes
1answer
13k views

Algebra of LDA. Fisher discrimination power of a variable and Linear Discriminant Analysis

Apparently, the Fisher analysis aims at simultaneously maximising the between-class separation, while minimising the within-class dispersion. A useful measure of the discrimination power of a ...
11
votes
2answers
16k views

What is the null hypothesis of a MANOVA?

Background In order to analyze differences in some continuous variable between different groups (given by a categorical variable), one can perform a one-way ANOVA. If there are several explanatory (...
9
votes
2answers
30k views

Post-hoc tests for MANOVA: univariate ANOVAs or discriminant analysis?

I am using a MANOVA test to compare nine different dependent variables (from neuropsychological and neuropsychiatric assessment) between three groups. The output shows a significant influence from ...
11
votes
1answer
9k views

Bayesian and Fisher's approaches to linear discriminant analysis

I know 2 approaches to do LDA, the Bayesian approach and the Fisher's approach. Suppose we have the data $(x,y)$, where $x$ is the $p$-dimensional predictor and $y$ is the dependent variable of $K$ ...
4
votes
2answers
5k views

Assessing group differences on multiple outcomes

I have one independent variable with two levels: Gender (Male and Female), and dependent variables will be composed of three test scores: Impulsivity, Assertiveness, and Social Desirability. My ...
4
votes
1answer
7k views

How to follow up a factorial MANOVA with discriminant analysis?

This is a follow-up to to my previous question: How can MANOVA report a significant difference when none of the univariate ANOVAs reaches significance? I have two IVs with each having three levels ...
2
votes
1answer
8k views

How do I compare two groups by several dependent variables and get 1 p-value as a result?

Suppose I have two groups and several dependant variables. I would like to show statistically whether the two groups are different or not, based on the combination of these dependant variables. The ...
6
votes
2answers
1k views

Many dependent variables, few samples: is this an example of “large $p$, small $n$” problem?

"Large $p$, small $n$" typically refers to "many independent variables, few samples". In my case, I have $1$ independent variable, $300$ dependent variables, and $n < 20$ samples. Thus, my case ...
4
votes
1answer
1k views

How can MANOVA report a non-significant p-value while LDA results in perfect separation of two groups?

I am new to statistics and currently got a dataset which contains $80$ dependent variables and $1$ independent variable with $2$ groups. MANOVA reports a $p$-value of $> 0.6$ on this dataset. But ...
7
votes
1answer
1k views

What is “Descriptive Discriminant Analysis”?

I have found some references to "Descriptive Discriminant Analysis" or DDA. In particular, this paper recommends it as a follow-up to a significant MANOVA result. Briefly, it is described as "a ...
5
votes
1answer
447 views

Interpretation of the cluster criterion $\operatorname{tr}(S_W^{-1}S_B)$

There is a cluster criterion defined as: $$\mathcal{C} = \operatorname{tr}(S_W^{-1}S_B) = \sum_{i=1}^d \lambda_i,$$ where $\operatorname{tr}$ is the trace, $S_W$ is the pooled within-group scatter ...
1
vote
1answer
218 views

Using MANOVA for classification without separating training and test sets

In this study: Rosenblum, Sara, et al. "Handwriting as an objective tool for Parkinson’s disease diagnosis." Journal of neurology 260.9 (2013): 2357-2361 The researchers attempt to classify ...