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.
69
questions
3
votes
2
answers
164
views
Test for multicollinearity with binary and continuous independent variables
I have a question concerning multicollinearity: I have several independent variables. Some are binary and some continuous. The dependent variable is binary. Can I use the Pearson correlations to test ...
- 31
2
votes
1
answer
69
views
Can you specify correlated coefficients in Stan models?
Closest question I could find to mine was this one, which doesn't cover it.
Is it possible to specify a correlation between two parameters in a Stan model? Consider a linear regression specified by:
$$...
1
vote
1
answer
82
views
How to analyze uncorrelated data?
Sometimes we encounter data that is uncorrelated. Specifically, from the correlation matrix we observe that the target variable shows low or no correlation with any of the features.
To provide context,...
1
vote
1
answer
18
views
Efficient construction of correlation matrix—serial correlation
Given $\rho$, is there a way to efficiently construct this matrix (i.e., as a product of matrices, rather than using a for loop)?
$$
\Sigma =
\begin{pmatrix}
1 & \rho & \rho^2 &\cdots &...
0
votes
0
answers
26
views
Sample covariance of t distribution and degree of freedom
If $X$ is a P by N size matrix, $X_{ij} \sim N(0,\sigma_i^2)$ if I standardize this X matrix with sample mean and sample variance (assuming I don't have access to the population mean and variance) I ...
- 21
0
votes
1
answer
77
views
Sample correlation matrix: $\hat{\mathbf{R}} = - \sum_{i=1}^{N}\sum_{j=1}^{N} \mathbf{x}_i \mathbf{x}_j^\top$?
Suppose we have the set $\{\mathbf{x}_i\}_{i=1}^{N}$, where $N$ is the size of the data set and $\mathbf{x}_i \in \mathbb{R}^m$ is the $i$th $m$-sized regressor.
The question is simple: how to compute ...
- 131
4
votes
3
answers
273
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 ...
- 322
1
vote
0
answers
128
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 ...
- 11
2
votes
1
answer
152
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
27
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 ...
- 41
1
vote
1
answer
174
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 ...
- 319
6
votes
1
answer
706
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
192
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 ...
- 111
5
votes
0
answers
160
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 $...
- 441
1
vote
1
answer
72
views
Correlation bounds in terms of spectral radius
My application requires that the following is true for random variables $X$, $Y$ in $\mathbb{R}^d$ with $E[X]=0, E[Y]=0$ and spectral radius $\rho$
$$\rho(E[XX]^{-1}E[XY]E[YY]^{-1}E[YX])<0.5$$
Can ...
- 6,307