A matrix (plural matrices) is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. The individual items in a matrix are called its elements or entries.

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interpreting PERMANOVA (adonis function) output?

I am trying to look at expression of some genes and relate the dist matrix (Sm) to a number of different factors that I collected on the individuals (e.g., litter size, licking behavior, group housing ...
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10 views

How to explain the correlation between the mean of each element and it's corresponding PC1 coefficient in a data.frame?

I am doing some PCA analysis by R now,I have a data,which is a data.frame:a,ncol(a) =1000,nrow(a)=100,each row represent a sample,each col represent a feature,so when I use R do PCA analysis like ...
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7 views

Error in creation of JAGS model in R: non-conformable arguments [closed]

I am currently practicing creating JAGS models in R. I'm using this set of Exercises (http://bendixcarstensen.com/Bayes/Cph-2012/pracs.pdf, specifically pages 18-19). However, one of the practice ...
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1answer
14 views

Difference between recentred and scaled eigenvalues and the Tracy Widom distribution

I have been generating correlation matrices from independent normal data simulated using the MASS package. I do this k times and extract the eigenvalues of the matrices. I was interested in comparing ...
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2answers
32 views

Apply function generating random numbers to a matrix (R) [closed]

I have a function which basically creates a random number. Now I want to apply the function to a matrix for given conditions to replace the value in the matrix with the random number created by the ...
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16 views

What is the best measure for matrix similarity [closed]

What is the best measure for matrix similarity?
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15 views

How to generate a list of intercorrelating items in R language? [closed]

I could build a correlation matrix from microarray experiment total intensity values. However, I can`t visualize 365X365 data matrix and I need to generate a list of mutually correlated genes from ...
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1answer
50 views

Variance expressed in Quadratic Form

Given a vector $\pmb x$ of length $n$, $\pmb x=\{x_1,...,x_n\}$ the variance is proportional to $\pmb x^\top \pmb x - \frac{1}{n}{\left(\sum_{i=1}^n x_i\right)}^2$ I'm trying to determine $(i,j)$ ...
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23 views

In R: Gravity model; how to handle vectorized data from symmetrical matrix?

I have vectorized data from a symmetrical matrix with collaboration data. So the collaboration between country i and country j is the same as between country j and country i. I deleted the principal ...
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0answers
19 views

Is there any matrix operations to find conditional probabilty distribution?

Is there any matrix operations defined in Matlab. Octave, R or Python to work with Joint, Marginal, and Conditional probabilities?For example if I have a probability distribution table which looks ...
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11 views

mat.regress/set.cor [migrated]

I am having a problem with the function mat.regress in the psych package that I was hoping someone would be able to give guidance on. I have a correlation matrix that is [76,76] with the first ...
2
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1answer
58 views

Why take transpose of regressor variable in linear regression

I am stuck trying to understand the basic calculation of ordinary least squares. From wikipedia $$y = \beta X^T + \varepsilon$$ where $X$ is the independent variable, $Y$ is the dependent variable ...
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0answers
59 views

Generate Symmetric Positive Definite Matrix with a pre-specified Sparsity

I am trying to generate a correlation matrix $p\times p$ (symmetric p.s.d) with a pre-specified sparsity structure (specified by a graph on $p$ nodes). The nodes that are connected in the graph have ...
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1answer
56 views

Recommenderlab - Getting the user_id out the RealRatingMatrix containing UBCF recommendations

I'm trying to use recommenderlab (with RSTUDIO) to get recommendations.When I'm using UBCF I can't extract the user id out of the realRatingMatrix containing the predictions, although I can do it with ...
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27 views

Transition probability matrix negative values of an M/M/C in R

I am trying to calculate a transition probability matrix of an M/M/C in R. The information given is the following : An IT support help desk represents a queuing system with five assistants taking ...
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1answer
32 views

Fix dominant columns/rows in symmetric data matrix?

I have a symmetric data matrix $A$, giving co-occurrence of events. That is, $A_{ij}$ is the frequency of occurrence of $i,j$ together. The diagonal elements of $A$ are unknown/indeterminate. I am ...
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38 views

R - system is computationally singular - dealing with small numbers

I'm working with a ~200x200 Markovian transition matrix of non-zero probabilities. Forcibly, these probabilities are, for the large part, going to be very small. I am trying to find the inverse of my ...
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1answer
46 views

Correcting for spatial autocorrelation in dissimilarity datasets

I have a community assembly dataset with 299 species at 15 sites. Im interested in correcting for the effect of spatial autocorrelation on beta-diversity (or species turnover). Dataset here. There is ...
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1answer
17 views

Steady state Markov Chain

is it able to count the steady state of problem with recurrent subchain.. for example if there are A B C D things and they are all recurrent. do they have steady state?? and also.. how to count ...
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1answer
36 views

Dimension Reduction

I have a $N \times M$ matrix, the rank of matrix, $r$, is near to $min(M,N)$. I want to minimize the rank by removing some of the rows or columns to get $r << min(M,N).$ The goal is to achieve ...
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1answer
154 views

Minimizing numbers along diagonal

Please forgive my ignorance if this isn't the appropriate place to ask this question, I'm by no means an expert in statistics. I'll omit most of the esoteric linguistic details here, but I've run up ...
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1answer
23 views

Why is this matrix code not behaving? [closed]

I'm running this code: ...
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2answers
73 views

Is every correlation matrix positive semi-definite?

I am generating correlation matrix by some new algorithm. Generated matrix is non positive semi definite matrix. I'm getting few negative eigenvalues. Rest of eigenvalues are quite equal to ideal ...
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1answer
94 views

Robust estimates of the covariance matrix in the big data space

I am trying to compute the robust estimates of the covariance matrix (and also the mean) in the big data space. I am aware of FastMVE and FastMCD (Minimum Covariance Determinant and Minimum Volume ...
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30 views

Efficient calculation of selected diagonals (bands) of a covariance matrix?

I'm looking for an algorithm that can calculate a select few diagonals of a covariance matrix. Here's the problem: I have an $m\times n$ data matrix $X$ where $m$ is the number of features, which is ...
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1answer
40 views

Why do some parameters not appear in the matrix equation for an ANOVA model?

Here is the question I have been working on and this is the answer of it I realised $\beta_3$ is not in the $\beta$ matrix. I don't understand why. Can anyone please explain this?
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1answer
35 views

Expected value of least squares estimator $\hat{\beta}$

Given $\hat{\beta} = (X^{T}X)^{-1}(X^{T}Y)$, how do you derive the expected value? I found answers for finding the variance matrix but not the expected value. Thank you kindly.
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24 views

How to find the covariance matrix? [duplicate]

I have some trouble understanding the concept of a covariance matrix. For instance, I'm going over this question that says: assume that we have U1, U2 and U3 as independent zero-mean, unit-variance ...
3
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1answer
78 views

Variance of Beta IV

I'm trying to calculate the variance of the Instrumental Variables (IV) estimator $${\hat \beta _{IV}} = {\left( {{Z^T}X} \right)^{ - 1}}{Z^T}y = \beta + {\left( {{Z^T}X} \right)^{ - 1}}{Z^T}u$$ (or, ...
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1answer
69 views

Determinant of the covariance matrix in a normal distribution

Suppose a $p \times 1$ vector $x \sim N_p(\boldsymbol 0, \boldsymbol \Sigma_1)$. Now, There is another covariance matrix $\boldsymbol \Sigma_2$. We know that $|\boldsymbol \Sigma_2| < |\boldsymbol ...
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0answers
26 views

Parametrizing a matrix (and algorithm) by its orthogonal complement

Given a large orthonormal matrix $U$, say $p\times p-k$ (with $k$ much smaller than $p$), is there an effficient way to parametrize $U$ by any matrix orthogonal complement (any orthonormal matrix ...
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1answer
59 views

How to correlate categorical personality and music genre preference scores?

I'm currently a third year Biology student and I've annoyingly screwed myself over by not following the golden rule of stats, always know how to analyze your data prior to conducting the experiment. ...
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13 views

Comparison of two correlation matrix of same dimension in R [duplicate]

I have two correlation matrices(Pearson).For example, metrices of (3 gene X 3 gene) for cancer samples and normal samples,individually. I have got gene-gene correlation for both sample. Now I want to ...
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30 views

What does hat matrix mean? [duplicate]

$$H= X(X'X)^{-1}X'$$ I understand that if we multiply $Y$ matrix by $H$ matrix, then we will have $\hat Y$. That's why we call it $H$ matrix. Can someone please let me know what $h_{ii}$ ($i$-th ...
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19 views

G and R matrices in mixed model and model selection

I have data in which the plants were subjected to four conditions and measured weekly for a month. I would like to incorporate "plot" as a random factor into my linear mixed model using SPSS. I am ...
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1answer
13 views

Generating Regression For Unknown Beta in Matlab

My professor wants me to generate a regression problem based on the following: B is fixed unknown 100,100 matrix, X is random 100,100 matrix and y and noise are a random scalar for every output. He ...
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1answer
84 views

Diagonal elements of the inverted correlation matrix

Is it true that the diagonal elements of the inverted correlation matrix will always be larger than 1? Why?
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1answer
49 views

Standardized regression coefficients

I have a question regarding standardized regression coefficients and the correlation matrix. I have a two part problem that I am working on, and I need to show that the correlation matrix R is equal ...
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0answers
8 views

Convergence of sample concentration matrix

I'm interested in the Frobenius or $\infty$ norm convergence rate bound for the sample inverse convariance (concentration) matrix. That is, suppose: $$ Y \sim \mathcal{N}_p\left(0, \Sigma\right) $$ ...
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15 views

Derive covariance of coefficients in simple linear regression [duplicate]

i just need help showing my work to show that Cov(b0,b1)=-xσ^2(sxx) i know that Cov(b0,b1)=E(b0b1)−E(b0)E(b1)=E(b0b1)−β0β1 and i know that var(b0,b1)=σ^2*(X'X)^-1
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215 views

Relative weights in regression analysis in SPSS: Matrix-approach vs. factor and regression

I am trying to perfome a relative weight analysis as described by Johnson (2000). I have 13 predictors to a more general indicator. Initially, I started by: running a principal component analysis ...
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8 views

How does this condition for exist?

The sum of the three vectors is b = (X′X)-1X′[Ed + En + Es] = (X′X)-1X′Y. Now, Y is the last column of X, so the preceding sum is the vector of least squares coefficients in the regression of the last ...
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23 views

Can anyone prove this?

A simple model of consumer spending on three types of goods consists of the following three equations: EDi = α1 + α2 PDi + α3 PNDi + α4 PSi + α5 Yi + εDi EN Di = β1 + β2 PDi + β3 PNDi + β4 PSi + ...
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1answer
35 views

Standard errors of the MLEs

Can anybody tell me how to find numerical values for standard errors of the MLEs of Weibull distribution using the uncensored real data set on the breaking stress of carbon fibres (in Gba) reported by ...
0
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1answer
89 views

Stata equivalent of array [closed]

I've been trying to solve this problem reading different material but I just can't figure it out. It's pretty simple and takes about 5 seconds to do in languages that work with arrays, but I can't ...
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1answer
44 views

Extremely new to R: Support.CEs package - help with design matrix please!

I've only started using R one day ago, still so much to get my head around. I need to create a choice experiment, and I have been following the example of H.Aizaki I think I have created a successful ...
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1answer
35 views

Mantel Test data assumptions

Does the Mantel Test works with non-normal distributed samples? I couldn't find anything clear enough about it.
3
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1answer
123 views

Design of matrix of contrasts in R

I am doing some post-hoc comparisons (in lme4, but here I'll just present a simple linear model), and I am having a hard time making sure that I am building the right matrix of contrasts to test ...
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158 views

Inverse covariance matrix, off-diagonal entries

Let $\Sigma$ be a covariance matrix. According to the material in this link, If the elements of $\Sigma$ are all positive, most of the off-diagonal elements in $\Sigma^{-1}$ will be negative ...
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15 views

Completing a matrix whose entries depend on time

Imagine you have a matrix, where each row represents an individual and each column represents a specific time interval. The entries of the matrix represent events occurring for a given person at a ...