# 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.

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### 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 ...
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 ...
160 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 "...
642 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 ...
439 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 ...
309 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 : $\min_x \frac{1}{2}\|Ax-b\|^2_2 + \lambda\|x\|_1$ ...
944 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: ...
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 ...
84 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 ...
355 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 ...
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### 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 ...
929 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: ...
81 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 ...
425 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 ...
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### 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 ...
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### 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 ...
147 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 ...