Questions tagged [condition-number]

The condition number (also known as condition index) is a diagnostic tool for collinearity in regression models. A regression model has as many condition numbers as it has independent variables. Each is defined as the square root of the ratio of the largest eigenvalue to the eigenvalue for the respective variable. Condition numbers over 30 are considered to be signs of problematic collinearity.

Filter by
Sorted by
Tagged with
0
votes
0answers
8 views

How to measure changes in condition indices over time

I am trying to understand how adding data, one observation at a time, affects the condition indices of a model. A similar question is how adding individual observations affects the principal ...
0
votes
0answers
15 views

QR decomposition used for estimating condition numbers

I have read that the QR decomposition is often used to estimate the condition number of a matrix but I don't understand... what is the benefit of using the QR decomposition for this? Is it purely ...
0
votes
1answer
125 views

Kappa condition number in R

I have read that the kappa function in R does not always explicitly calculate the condition number of a matrix, but rather, estimates the 2 norm of a matrix or a QR ...
2
votes
1answer
72 views

How are the condition numbers of a design matrix and its correlation matrix related?

Given a design matrix $X$ for a linear regression model, what is the relationship between the condition number of $X$ and its correlation matrix $R$? I would be interested in the case of a centered ...
0
votes
0answers
14 views

OLS Multicolleniarity

I have a pretty simple task to estimate ols multiple regression. I need a measure of multicolleniarity. Is condition number a good measure and what criteria exists fot its value?
2
votes
1answer
793 views

Why does matrix condition number change drastically when a constant is added?

If I create a regression model design matrix with 3 uncorrelated variables, I get a small condition number as expected. MWE: ...
4
votes
0answers
390 views

Choosing the basis functions in a linear regression

I have two random variables $X$ and $Y$ and I'm trying to model $\mathbb{E}[Y|X]$. To this end, I'd like to pick a collection of functions $f_1, f_2 \dots f_n : \mathbb{R} \to \mathbb{R}$ and then ...
2
votes
2answers
1k views

Deep Learning: Condition Number and Poor Conditioning

I am reading the following section of the book Deep Learning. Can you provide an intuitive explanation of the above section? I don't quite understand the statement "When this number is large, matrix ...
4
votes
0answers
293 views

Proximal Gradient Descent and Proximal Coordinate descent for Lasso Problem

Why is proximal coordinate descent much less affected by bad conditioning than proximal gradient descent? For example, we can consider this problem : $\min_x \frac{1}{2}\|Ax-b\|^2_2 + \lambda\|x\|_1$ ...
1
vote
0answers
79 views

Is condition number important when fitting splines?

I am fitting data using p-splines. The authors of p-splines, Eilers and Marx, remark that there is no technical requirement to have a small number of knots and in fact you can have many more knots ...
2
votes
2answers
2k views

Multicolinearity and Condition number of logistic regresison

It seems to be common to take a "high" condition number as a sign for multicolinearity in regression analysis. For linear models I'm totally convinced that this is a good idea, but is there any ...
5
votes
0answers
5k views

Cause of a high condition number in a python statsmodels regression?

I'm pretty new to regression analysis, and I'm using python's statsmodels to look at the relationship between GDP/health/social services spending and health outcomes (DALYs) across the OECD. Just to ...
1
vote
1answer
878 views

Condition number calculation in R

If I understood correctly, the condition number should be a product of Frobenious norms of a matrix and its inverse. In R if I do the following: ...
0
votes
1answer
141 views

Wrong choice of covariance function?

I am applying Gaussian process regression (GPR) model on some data assuming covSEiso (a.k.a. RBF) covariance function. I made sure there are no identical data points (but there are similar data ...
4
votes
1answer
596 views

When is it appropriate to override the default reciprocal condition number tolerance for solve() in R?

I am estimating a GMM IV model, where I'm creating a weighting matrix by taking the inverse of Z'Z, where Z is a matrix of instruments. For certain combinations of instruments, when I try to compute ...
2
votes
0answers
337 views

Should the intercept be included when you check the condition index?

Many sources state that a condition index >30 constitutes a multicollinearity problem. When I've tried to implement this check in practice, I've realized that the condition index (and VIFs) change ...
0
votes
0answers
40 views

Problems with ill-conditioned matrix for Dantzig Selector

I'm using the Dantzig Selector on high dimensional data and my matrix is ill conditioned (condition number on the order of magnitude of 10^17). I know there are ways to improve the conditioning, ...
1
vote
0answers
389 views

How to interpret differences in VIF and condition number?

In my present data, the Variance Inflation Factors suggest lack of substential multicolliniearity (<1,7). However, the condition number of 28 is almost at the critical value of 30. How do I ...
8
votes
2answers
8k views

How do you interpret the condition number of a correlation matrix

I have two correlation matrices, one with a condition number of 9 and the other with a condition number of 70. From what i have read, it will appear that the first matrix is better conditioned than ...
5
votes
1answer
151 views

Automatically fixing ill-conditioning or collinearity

I'm backtesting a regression model, which entails running it on a bunch of bootstrap samples of a "rewound" version of our data set. Unfortunately, in some of these resamplings, I end up getting some "...
1
vote
0answers
738 views

Propogation of error in a matrix inversion

I'm trying to find the deterministic error bounds for some parameters calculated through distance geometry. The equation can be simplified to the following form: $ \left[\begin{matrix} x_1 \\ x_2 \\ ...
0
votes
2answers
824 views

Condition number of data matrix and stability of OLS estimates

I have a multivariate regression model $Y=X\beta ' + \epsilon$. The variables in the $X$ matrix have very different scales and hence the condition number of $X'X$ is huge (order of trillions). I ...