Questions tagged [correlation-matrix]

A $k\times k$ matrix of correlations between all pairs of $k$ random variables. All its diagonal elements are equal to one.

Filter by
Sorted by
Tagged with
1 vote
0 answers
35 views

Looking at how covariance/correlation between variables differs in two groups?

I have a few hundred variables representing different biomarkers. These variables have been measured in both cases and controls. The underlying units of measurement are not important, so I have ...
  • 340
1 vote
0 answers
19 views

How can I compare one full PCA model to two smaller ones?

I have nearly 30 variables going in to a large PCA, but the variables really fall into two conceptual categories. I want to test whether leaving all the variables to correlate freely with one another ...
0 votes
0 answers
31 views

How do we interprete the significance of the phi-k correlation coefficients in python?

I recently found out of phi-k correlation. All relevant libraries can be imported as: import phik, ...
2 votes
1 answer
67 views

Generate two random correlation matrices which share equal correlations

My setting is, I want to simulate a data set in two conditions, e.g. control and disease. I want them to share mostly the same correlations except some should be different to simulate a "signal&...
  • 21
0 votes
0 answers
22 views

How to pick a subset of the rows of a matrix data sample so that the resulting correlation matrix of the curated data approaches the identity matrix?

If I have a data sample in the form of a matrix $X$ of dimensions $n \times m$, is there a standard procedure to optimally pick $n'$ rows ($n'$ fixed) of the matrix $X$ so that $C_{X'}$, the ...
0 votes
0 answers
18 views

Generate dataset that adhere to a given correlation matrix [duplicate]

I'm newbie in statistics and this question might be naive so kindly excuse me in advance. I have a correlation matrix of 40 features and I want to generate a dataset of hundreds of observations that ...
  • 101
1 vote
1 answer
104 views

What is the null and alternative hypothesis of a chi square test whether a single matrix is an identity matrix?

Say I had a correlation matrix: $$ M = \begin{bmatrix} 0.8 & 0.1 & 0.1\\ 0.3 & 0.7 & 0.1 \\ -0.1 & -0.2 & 0.9 \end{bmatrix} $$ I want to show that it is approximately an ...
6 votes
1 answer
460 views

Independent copula vs Student-$t$ copula with zero correlation matrix?

Suppose I have the random variables $X_1, \dots, X_n$ with the marginal distributions are not normal (in fact, unknown marginal distribution). Will there be any difference between the assumption $X_1, ...
1 vote
1 answer
83 views

When to use Simple Linear Regression over Multiple Linear Regression

I am fairly new to the world of statistics and approaching it as I learn more about machine learning. I have a fairly firm grasp on regression analysis so far but not necessarily on nuances and best ...
4 votes
0 answers
70 views

Difference between a multivariate normal regression and multiple regressions with shared random effect

Let's $Y_1$, $Y_2$ be two random variables representing two outcomes and $X$ a covariate. I want two regress $Y=(Y_1,Y_2)$ on X, but by taking into account the potential correlation between $Y_1$ and $...
  • 401
-1 votes
1 answer
53 views

What came first, the covariance or the correlation matrix?

Covariance can be calculated from correlation and correlation can be calculated from covariance. Is it sufficient to refer to them as only transformations of one another? Is one considered more of a ...
  • 3,343
0 votes
1 answer
433 views

How can one derive the original data from the correlation- or covariance matrix of that data?

How can one derive the original data from the correlation- or covariance matrix of that data? I know the way a new, reduced dataset can be calculated from the correlationmatrix and it’s eigenvectors ...
3 votes
1 answer
3k views

Clustering data based on correlation

I have a dataset where each row represents a sample and each sample is described by its chemical composition. You can see the 10 first rows of the dataset in figure 1. Figure 1 - Each row represent a ...
  • 209
4 votes
1 answer
201 views

Bounds for common correlation of uncorrelated random variables with another random variable

Suppose we have a random variable $y$ and a collection $(x_1,\dots,x_n)$ of $n$ random variables that are all uncorrelated: $\operatorname{corr}(x_i,x_j) = 0$ $\forall i \ne j$ and that all have the ...
  • 223
0 votes
1 answer
32 views

Correlation matrix: decline in correlation

I performed a correlation matrix with Python. The following variables were included total_equity,net_income,...
  • 11
1 vote
0 answers
71 views

Calculate unbiased standard errors for a regression from latent factor correlations

I have a SEM where various latent variables are correlated with each other. I want to use a subset of these correlations to run a regression. This can be done easily enough to find point estimates, ...
0 votes
1 answer
845 views

How to determine mse of estimate from correlation matrix of estimate error?

I have a model of an information transmission system Y = XH + N, where X is a diagonal matrix with the transmitted "symbols" (known), H is a column vector which distorts the transmitted symbols and N ...
1 vote
1 answer
3k views

Eigenvectors for correlation and covariance matrix PCA

I know the generally reasons of using correlation matrix vs a covariance matrix when doing PCA (and visa versa) however when thinking about the eigenvectors (principal components of the data) of each ...
  • 129
1 vote
0 answers
177 views

Change in eigenvalues due to perturbation to a correlation matrix

Let $A$ be a $m \times n$ matrix defined as $ A = \Big[\frac{a_1}{\|a_1\|} \cdots \frac{a_n}{\|a_n\|}\Big]$ and $a_k \in \mathbb{R}^{m\times 1}$ where $k \in [1,\dots,n]$. Now, we define a ...
  • 11
1 vote
1 answer
197 views

How to simulate random correlation matrix containing off diagonal structures

I want to simulate a correlation matrix which has some off-diagonal structures and also should have some hierarchical structures. For simulating correlation matrices which contain hierarchical ...
  • 205
0 votes
0 answers
115 views

Simulate correlation matrix using a given structure [duplicate]

I want to generate correlation matrix such that it follows the below structure $$\Sigma = B \Lambda B^T $$ where $\Lambda$ is a diagonal matrix containing positive elements, $\Sigma \in R^{n \times n}...
  • 205
5 votes
0 answers
493 views

How do I simulate a random valid correlation matrix of ordinal variables given a list of marginal probabilities?

I am trying to use R to simulate random variations in a real dataset with a known number of categorical and continuous predictor variables, as well as known marginal probabilities for each ordinal/...
  • 51
16 votes
4 answers
4k views

Is it possible that 3 vectors have all negative pairwise correlations?

Given three vectors $a$, $b$, and $c$, is it possible that correlations between $a$ and $b$, $a$ and $c$, and $b$ and $c$ are all negative? I.e. is this possible? \begin{align} \text{corr}(a,b) < ...
  • 261
3 votes
0 answers
3k views

What is the best way to Show a Correlation Matrix as a Cluster/Network Graph in Python? [closed]

I'm struggling because while I want to show the interrelationship of correlation between my fields, I realize that trying to plot nodes in terms of distance away from each other based on correlation ...
2 votes
0 answers
391 views

Method to generate random correlation matrices with specified structure.

Within the social sciences there is a popular technique called Factor Analysis and I am interested in generating random correlation matrices that uniformly sample all the space parameterized by one ...
  • 763
1 vote
1 answer
1k views

Help needed with intuition of eigenvalue spectrum of correlation matrix

I wish to get a better understanding of the meaning of the eigenvalues of a correlation matrix I am studying. I have a correlation matrix of noise levels for 10 cells in a wireless network over time....
  • 579
1 vote
0 answers
54 views

How to generate a set of random variables with specific correlations and correlational distributions

I apologize if this question is a bit confusing. Suppose we get to generate an $n \times n$ matrix, $M$, whose values are all between 0 and 1. How can we generate a set of $n$ random variables, $\{...
11 votes
1 answer
8k views

Do the Determinants of Covariance and Correlation Matrices and/or Their Inverses Have Useful Interpretations?

While learning to calculate covariance and correlation matrices and their inverses in VB and T-SQL a few years ago, I learned that the various entries have interesting properties that can make them ...
1 vote
2 answers
488 views

Cluster analysis using the posterior distribution of a Bayesian correlation matrix

Background and Problem I recently ran a Bayesian multivariate epidemiological meta-analysis on prevalence estimates for several disorders. This analysis included a probit-based model to deal with the ...
  • 412
5 votes
2 answers
8k views

Does using a covariance matrix of scaled and centered variables compare with using a correlation matrix?

I have some data with features which have different units of measurements. Here, by data, I'm trying to say that the row represents the observations and column the features. There are correlations ...
2 votes
1 answer
116 views

Correlation matrix for biostatistics [closed]

I want to convert the expression of the genes from an array to a gene correlation matrix, to know the correlation of each gene with the other genes. I have 6 samples, 3 controls and 3 test, is it ...
  • 31
2 votes
0 answers
369 views

correlation matrix test: is this code correct or is it missing a multiple comparisons correction?

I have $m$ variables $x_1,\dots,x_m$, measured in $N$ independent tests $\{x_{i1},\dots,x_{im}\}_{i=1}^N$, leading to the design matrix $X$. I noted that the demo function ...
  • 16.7k
2 votes
0 answers
141 views

Check whether a sample correlation matrix is valid [duplicate]

Is it possible to have the following sample correlation matrix for $x$, $y$, $z$? $\begin{pmatrix} 1 & 0.8 & 0.2 \\ 0.8 & 1 & 0.7\\ 0.2 & 0.7 & 1\end{pmatrix}$ Where a 3 by 3 ...
  • 175
3 votes
1 answer
1k views

Reporting Fisher-transformed Pearson's correlations when the magnitude of difference is relevant

My field regularly demonstrates a certain type of result with pairwise Pearson's correlation matrices between predicted and measured data. As soon as such correlations become high, Fisher-transforming ...
13 votes
3 answers
4k views

Is there a serious problem with dropping observations with missing values when computing correlation matrix?

I have this huge data set with like 2500 variables and like 142 observations. I want to run a correlation between Variable X and the rest of the variables. But for many columns, there are entries ...
2 votes
0 answers
634 views

How to compare diagonal elements of precision matrix (the inverted correlation matrix)?

Let $$C=\begin{pmatrix}C_{11} & C_{12}\\ C_{21} & C_{22}\end{pmatrix}$$ be a $p\times p$ correlation matrix with positive entries, where $C_{11}$ is a $q\times q$ matrix. Define $D=C^{-1}=(d_{...
  • 21
6 votes
1 answer
165 views

How to randomly generate a positive semidefinite matrix subject to Loewner constraint?

For real, symmetric, positive semidefinite matrices $A$ and $B$, let $\leq_L$ denote the Loewner partial order: $A \leq_L B$ iff $B-A$ is positive semidefinite. Suppose $A$ and $B$ are fixed PSD ...
21 votes
6 answers
7k views

Completing a 3x3 correlation matrix: two coefficients of the three given

I was asked this question in an interview. Lets say we have a correlation matrix of the form \begin{bmatrix}1&0.6&0.8\\0.6&1&\gamma\\0.8&\gamma&1\end{bmatrix} I was asked to ...
  • 333
5 votes
2 answers
1k views

With an R function that expects a covariance matrix, can I give it a correlation matrix?

The R function mvrnorm from the MASS package generates random numbers from a multivariate normal distribution. It expects a ...
  • 145
2 votes
1 answer
289 views

Is there a way to reconstitute the unit of measurement in PCA?

I have a data set composed of changes in financial asset prices. Because they are on different levels, e.g., one asset is trading in the 100s, the other in the 5s, the change their prices have vastly ...
  • 205
3 votes
1 answer
828 views

Exact meaning of correlation coefficient

What is the exact meaning of the entries of a correlation coefficients matrix? I have spent time researching this, but could find only approximate interpretations which give me no good understanding ...
  • 133
3 votes
1 answer
2k views

How the Correlation Matrix is built for PCA in Weka?

Just to give a context, I want to use PCA (Principal Component Analysis) to identify which attributes are similar to others, so I can use just one (or a subset) of them. The correlation matrix of n ...
  • 41
2 votes
1 answer
879 views

Covariance Matrix and Correlation Matrix - Singularity

If a covariance matrix is non-singular, does this implies that correlation matrix is also non-singular. My guess is it depends on mean vector in $K_{X} = R_{X} - m_X.{m_X}^H$ Not sure though.
1 vote
0 answers
205 views

Correlation Matrix from given R output of Factor Analysis

I carried out a factor analysis of 5 variables using a single factor. How do I estimate the correlation matrix assuming the one factor model holds? The R output is:
4 votes
1 answer
2k views

Does it make sense to use PCA when the determinant of the correlation matrix is (almost) zero?

I'm running a PCA over a data set of $N \times p$ size ($N\approx 1000$ being the number of measurements and $p\approx 200$ being the number of dimensions/predictors). I expect many of the predictors ...
4 votes
1 answer
2k views

Off-diagonal elements of a correlation matrix after removing the first principal component

I have some data with more variables than observations, that I'd like to subject to a principal components analysis. For didactic reasons (to give an intuition for factor retention criteria under ...
  • 732
13 votes
3 answers
12k views

Is every correlation matrix positive definite?

I'm talking here about matrices of Pearson correlations. I've often heard it said that all correlation matrices must be positive semidefinite. My understanding is that positive definite matrices must ...
2 votes
1 answer
2k views

Fisher z-transformation and normality

I have 100 50x50 correlation matrices, which I have all Fisher z-transformed. I understood that this results in the all the entries of one matrix being approximately normally distributed. Questions ...
  • 1,411
6 votes
1 answer
5k views

Matrix multiplication to find correlation matrix

In this book on matrix factorizations, the author states the following, which I don't find to be true empirically. Is it true and under what conditions? ADD: Trying to recreate the answer in R, what ...
  • 7,950
14 votes
2 answers
6k views

Does a correlation matrix of two variables always have the same eigenvectors?

I perform Principal Component Analysis using two variables that are standardized. This is done by applying a SVD on the correlation matrix of the concerned variates. However, the SVD gives me the same ...
  • 391