Questions tagged [singular]

A matrix is singular when its determinant is 0; for such matrices, the inverse is not defined.

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Linear dependency among columns and rows

Singular matrix is defined as square matrix with the determinant of zero. The determinant of zero occurs when matrix columns are linearly dependent (i.e. one of the columns can be defined as a linear ...
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“System is computationally singular” error in igraph

I'm using igraph to build some indicators about the railway network. I have a graph with 9,000 nodes. I want to calculate the distance resistance using ...
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1answer
55 views

Singular Matrix and Linear Dependency

Singular matrix is defined as a square matrix with determinant of zero. I am aware that linear dependency among columns or rows leads to determinant being equal to zero (e.g. one column is a linear ...
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104 views

Problematic data for regression model

This is a follow-up question to Which model for my data? (testing the differences in slope for three groups). The solution from there works (big thanks to Heteroskedastic Jim!), but I have a problem ...
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How to prove that this joint distribution is Gaussian without using probability densities?

Question: I am wondering if there was a way to prove this result without using probability densities: If $\bf x \sim \mathcal N (m, P)$ and $\bf y \;|\; x \sim \mathcal N (Hx, R)$, then $$\begin{...
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141 views

Are Kalman Filter recursions valid when the state noise has a singular covariance matrix?

Consider a Linear Gaussian State-Space Model where the states are denoted by $X_t$ and observations are denoted by $Y_t$: \begin{align} X_t &= A X_{t-1} + \epsilon_t, &&\epsilon_t \sim \...
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1answer
61 views

Linear Mixed Model equation (as of lme4 package)

I am trying to derive the equations of a linear mixed model as specified in the documentation of the lme4 package: "Fitting Linear Mixed-Effects Models using lme4" jstatsoft.org/article/view/v067i01 ...
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Problems with singularity and a cross-level interaction

I have the following data structure: 200 Participants each saw 32 visual stimuli. These stimuli were manipulated on two properties (level-1 predictors). The participants came from two different ...
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136 views

Singular Spectrum Analysis Explanation

I need you to help me understand the Singular Spectrum Analysis algorithm. I already read a lot of articles about the subject but they never answered my questions like what is the mathematical reason ...
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lme4 mixed model unbalanced error factors + singular fit

I am studying the effects of 5 treatments (CT,CCM,CCI,F, S) on grape yield. My experimental design consists in: 5 treatments and 2 farms (SG, MT) which I use as block. I created an additional ...
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84 views

Can I remove random effect from my model?

I have some data which I am getting a singular fit error and I would like to work out the reason so I can decide whether I can remove the random factor from the model. I have 835 data points with a ...
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722 views

Singular fit error caused by random factor

I'm trying to fit a generalised mixed model for some embryo data and I am getting the error for singular fit. my model is ...
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61 views

R BEKK GARCH H is singular

So I havbe used several BEKK GARCH packages, but I keep getting the same error message: "H is singular". I have taken the Log returns, and also tried to use the scaled log returns (x100). Anyone knows ...
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lme4 lmer() multilevel model: why do I have singular fit and a -1 correlation between random effects slope and intercept?

I'm running a varying intercepts varying slopes multilevel model with the lme4::lmer() function with no group level predictors and only one predictor: FilingFee to predict evictionfilingrate. I ...
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Singular fit with simplest random structure in lmer (lme4), is a Bayesian approach the only option?

I'm running a mixed model with the lmer function from the lme4 package in R and ran into some issues with singular fits. I get the warning message 'singular fit', ...
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singular fit in lmer, despite no high correlations of random effects

I ran a mixed effects model a few weeks ago, it all went fine, no errors. Here is the model: ...
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152 views

Mixed Model Repeated Measures for Before & After Comparison

I'm trying to assess the effectiveness of a program by comparing employee performance before the program vs. after the program. I have 4 years (2 years before vs. 2 years after) of individual-level ...
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596 views

lme4 singular fit non randomized design

I am analyzing a dataset with lme4. I am investigating the effects on vine yield of 5 different "Treat". We are working on-farm and we were not offered the possibility of a randomized design. So we ...
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Approach to automatically determining the source of data matrix singularity?

When you're using R built-in glm functions (and in other languages I assume), the software has a built-in ability to automatically eliminate redundant or inestimable parameters. For example, when ...
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Mixed effect model covariance prior

How should I choose the covariance prior for my bglmer model? This is a model which has the singularity problem. ...
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30k views

Dealing with singular fit in mixed models

Let's say we have a model ...
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1answer
1k views

Matrices: system that is “computationally singular” versus “exactly singular” [closed]

I would like to know the mathematical concepts behind singular matrices. Matrices that do not have inverses in R throw one of two errors. I have provided some examples of both errors below: Error in ...
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Multiple regression - singularity issues [duplicate]

I am trying to fit multivariate regression models to my data; however, I get singularity warnings. Please find a part of my data below: ...
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Why financial time series have perfect multicollinearity?

I have daily financial time series of stock returns (35 stocks) which I took the natural logarithm and subtracted the risk-free rate. However, I get the issue non-invertibility of the covariance ...
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1answer
200 views

Why may a matrix be singular or ill-conditioned with standard learning algorithm for linear classification?

In the learning algorithm for linear classification by least square method, which find a weight vector $\hat w\in R^d$ and bias $\hat b\in R$ for a linear scoring function $f(x) = \hat w ^T x +\hat b$ ...
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264 views

Prior for covariance matrices in Gaussian Mixtures Model

I am looking to choose a prior that helps me avoid singularities (as mentioned in this answer) in the covariance matrices of a GMM model. The Jeffrey prior (or a simple improper prior) would be very ...
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1answer
239 views

Prove $A(A+B)^{-1}B=B(A+B)^{-1}A$

I have this equality, $A(A+B)^{-1}B=B(A+B)^{-1}A$ and the question specifically only states that $A+B$ is nonsingular. I have looked at this many ways but the only I can see it working is if $A+B$ ...
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differences in forecast and reconstruction in SSA, in R

I was playing around with the Rssa when I discovered this: Firstly: I created to sequences: library Rssa x<-1:100 x1<-1:80 then the corresponding function:...
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304 views

Boundaries on correlation coefficient given five other correlations

Is there a general formula for the boundaries of a correlation coefficient given a set of other correlation coefficients? I have seen the formula for three random variables where two correlations are ...
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1answer
491 views

Stepwise quantile regression: What's the reason behind these strange results?

So I am attempting to build a model using quantile regression & am using stepwise regression for initial data exploration. I'm well aware that stepwise methods are widely frowned upon & am ...
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70 views

Consequence of singular weight matrices in neural networks

I want to know the effects of weight matrices being singular when using neural networks. Is there any supported literature? For non-square weights matrices, I am concerned about lower rank matrices. ...
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15 views

p-values close to eps [duplicate]

After fitting a linear mixed effect model with lme, I run a posthoc analysis with glht and get the following results: ...
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1answer
51 views

Under-constrained models and invertibility of covariance matrix

In Goodfellow et al.'s Deep Learning, the authors write on page 232: [$\mathbf{X^\top X}$] can be singular whenever the data-generating distribution truly has no variance in some direction, or when ...
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180 views

How can I figure out the singularity problem in estimating the indicator variable coefficient in time series model ?

I want to capture the role of the sign of the previous return in my time series model(AR(1) and QAR(1)) in R both with quantile and OLS regression , but I face error. Here is the code: ...
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Singular Fisher Information matrix, why is it a problem

I need to perform some research on the consequence of a singular Fisher Information matrix in statistical inference. I am confused what kind of problems a singular Fisher Information matrix creates. ...
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1answer
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Uniqueness for OLS linear regression

I'm implementing OLS linear regression without using the built-in functions in Matlab with normal equation: I know this is probably very basic, but I want to double check, the input X yields a unique ...
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1answer
3k views

Understanding degenerate multivariate normal distribution

MVN is degenerate when the covariance matrix $\Sigma$ is singular. I am trying to understand mainly conceptual (but also theoretical) implications of this. The Wikipedia article is quite terse. It ...
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536 views

Singular matrix but it's full rank

I'm using matlab to fit a logit GLM to a data (detection problem). I have a Nx5 matrix of independent variables and a binary (i.e 0-1) column vector of responses. When I try to fit the GLM model with <...
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188 views

Choice of window length in Singular Spectrum Analysis

Thanks in advance for your answers, I'm trying to decompose a stock price using the Rssa package provided in R, after millions of trials, I tried to change the window Length and the eigentriples, the ...
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154 views

Where does problems analytically arise in logistic regression on singular data matrix?

If you do linear regression without regularization on close-to-singular data matrix $X$ (or it does not have enough data), the problem arises even in closed-form solution $w = (X^TX)^{-1}X^Ty$ when ...
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2answers
7k views

How do I avoid computationally singular matrices in R?

I'm fitting a logistic regression model (with R's caret package) to data here. I aim to predict whether Hillary or Trump will ...
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1answer
2k views

Why is within class scatter matrix in LDA singular? [closed]

I read that when number of data points are much less than the dimension of data, the within class scatter matrix in singular? Can someone explain why this is the case? For example, while using LDA for ...
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2answers
652 views

Sampling from matrix-variate normal distribution with singular covariances? [duplicate]

The matrix-variate normal distribution can be sampled indirectly by utilizing the Cholesky decomposition of two positive definite covariance matrices. However, if one or both of the covariance ...
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1answer
98 views

Limit of Bernoulli R.V.s is a singular distribution

Working through an exercise in Probability (the question can be found in Lamperti). Let $X_1,\dots$ be independent Bernoulli random variables with $\mathbb{P}(X_i=1) = p$ and $\mathbb{P}(X_i=0)=1-p$. ...
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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.
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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 ...
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221 views

Bayesian regression with singular $(X'X)$ - Is the posterior well-defined?

SE community, I hope to get some insights into the following problem. Given a simple linear regression model $$Y=X\beta+\epsilon\text{ , where } Y\in\mathbb{R}^T,X\in\mathbb{R}^{T \times N}.$$ Under a ...
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453 views

Multinomial logistic regression on categorical data results in singular matrix

I have a categorical dataset from a biological sampling study consisting of six variables, see http://pastebin.com/ncLzw0Mt for the actual dataset. ...
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1answer
144 views

estimators with singular covariance matrix

Suppose I have 2 vectors of random variables $\boldsymbol\theta_1 \in \mathbb{R^n}$ and $\boldsymbol\theta_2 \in \mathbb{R^m}$ with asymptotic covariance $\Sigma_1$ and $\Sigma_2$ respectively. I want ...
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547 views

Identical observations in linear regression

I want to do a linear regression $Y = X\beta + e$, but some of the observations (rows in $X$) are identical (about 30 000 out of 50 000 remain after deleting all duplicates), so when I try to ...