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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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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26 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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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
10 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
41 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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36 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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4 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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11 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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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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11 views

Fisher information and asymptotic covariance matrix [duplicate]

I am reading the Categorical Data analysis by Dr. AGRESTI. Here, it explains "The liklihood function of for the GLM also detemines the asymptotic covariance matrix of the ML estimator Beta_hat. This ...
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1answer
26 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 ...
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1answer
45 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
32 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
22 views

Mantel Test data assumptions

Does the Mantel Test works with non-normal distributed samples? I couldn't find anything clear enough about it.
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73 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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66 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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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 ...
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1answer
27 views

Order of Matrix Operations in Mahalanobis Calculations

I'm teaching myself to translate equations to code after many years of letting my math skills atrophy, and am trying to do it on my own as much as possible. I've run into a couple of difficult ...
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67 views

Restriction matrix for a VAR

In New Introduction to Multiple Time Series Analysis by Luetkepohl (2005), section 5.2.1, it says that one can specify linear restraints for a VAR, $Y = \beta X + U$, in the form $$ ...
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371 views

Does every semi-positive definite matrix correspond to a covariance matrix?

It is well-known that a covariance matrix must be semi-positive definite, however, is the converse true? That is, does every semi-positive definite matrix correspond to a covariance matrix?
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57 views

What does Determinant of Covariance Matrix give?

I am representing my 3d data in covariance matrix. I just want to know what the determinant of a covariance matrix gives. If the determinant is positive, zero, negative, high positive, high negative, ...
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11 views

How to calculate the correlation between a variable and a matrix of variables

I'm trying to improve a factory quality control. I have some variables from the melting process (something like ten control variables) that changes trough time (a matrix of the values of those ...
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45 views

How to calculate the correlation between a variable and a matrix of variables

I'm trying to improve a factory quality control. I have some variables from the melting process (something like ten control variables) that changes trough time (a matrix of the values of those ...
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2answers
56 views

Finding independent “clusters” in a matrix

I've called my question "clustering" but I am not sure if that's the right term. Imagine my matrix looks like this: ...
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Calculation the Expectation of an Inverse Wishart matrix

I have $\boldsymbol{A} = \boldsymbol{G}^H \boldsymbol{G}$ is a Wishart matrix, i.e, $\boldsymbol{G}^H \boldsymbol{G} \sim \mathcal{W}_K (M, \boldsymbol{\Lambda})$ with $\boldsymbol{\Lambda} = ...
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Is it a Wishart matrix?

We know that an $m \times m$ random matrix $\boldsymbol{A} = \boldsymbol{H} \boldsymbol{H}^H$ is a (central) real/complex Wishart matrix with $n$ degrees of freedom and covariance matrix ...
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1answer
49 views

Different results for Singular Value Decomposition (SVD) using different tools

I am currently implementing Latent Semantic Analysis in Java using the EJML library for the preliminary Singular Value Decomposition (SVD). I am testing my code against the original term frequency ...
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51 views

Problem constructing model matrix to generate predicted values to plot Bayesian glmmBUGS output

My goal is to plot the predicted values generated from a Bayesian model using glmmBUGS run through R. I believe my problem stems from a lack of understanding in 1) how to properly construct a model ...
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20 views

Effective ways to display confusion matrices from different predictors in an academic publication?

I want to display the results of two different predictors' performance on a dataset. I have a confusion matrix for each of the predictors' results on the test cases. I want to present these confusion ...
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53 views

Matrix completion approaches for healthcare big data

I am working on a prediction problem that leverage sparse clinical datasets. Missing data rate is in the range of 80%. 1- I am wondering if there is any example of application of matrix completion ...
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36 views

Cholesky decomposition and confidence ellipsoid

I'm trying to construct an error ellipsoid from a covariance matrix (which exists for a 3D point) and then sample consistent xyz points in this region. (This question succeeds this one.) What I'm ...
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1answer
61 views

Is the information matrix equality valid for the Poisson distribution?

As far as I know it should, since the support of the Poisson is independent of its lambda parameter. The negative of the expected Hessian equals $\frac{n}{\hat{\lambda}}$, where $\hat{\lambda}$ is ...
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45 views

Build corpus with phrases

I have my documents as: doc1 = beautifull, very good, very bad, you are great doc2 = very bad, good restaurent, nice place to visit I want to make my corpus ...
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107 views

Difference in values of tf-idf matrix using scikit-learn and hand calculation

I am playing with scikit-learn to find the tf-idf values. I have a set of documents like: ...
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1answer
70 views

Difference in tf-idf values in R

I am playing around in R to find the tf-idf values. I have a set of documents like: ...
3
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1answer
171 views

Generating a correlated data matrix where both observations and variables are correlated

I am trying to generate a simulated data matrix that is correlated by both observation and variable directions. So far I know how to do this for variable x variable. ...
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Matrix rank and amount of regressors

A question states: $X$ is the vector of regressors stacked for 30 observations and $Rank(X)=5$. There are no lags of $y_t$ in the set $X_t$. Using the Durbin-Watson statistic, test the null hypothesis ...
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48 views

Which contingency method to use with a 3x3 table yet still account for expected or discrete choice?

Im not sure what test to conduct when I have 3x3 matrix of data and still account for availability. So, in a simple chi square you have an observed observation and then you are often able to ...
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110 views

LDA - Why differents formulas to calculate covariance and pooled covariance matrix

Reading materials from differents sites some questions have risen about covariance and the pooled covariance matrix calculation to implement LDA: Definitions Ci - covariance matrix of group i (C1 and ...
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79 views

Can you use the chi-squared test with tables of real numbers?

Consider a $N \times 2$ matrix (MATLAB notation): M = [1.2, 3; 1.4, 2; 1.8, 1; 2.0, 2]; That is a $4 \times 2$ matrix where the first column ...
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1answer
41 views

can matrix completion work in the presence of many missing values?

I have a matrix with about 550k elements (2500 x 220) with 100k values known and the rest are unknown. Would it make sense to use matrix completion in this case, or are there too many values which ...
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44 views

Is there a way to perform SVD in a sequential manner?

My neurology experiment has a spike detector outputting 40 sample long spike waveforms. I'm using a dictionary method for sorting the spikes in real time. To ...
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2answers
31 views

OLS Coefficient estimator; Transformation from Matrix to sum of matrices form

I do not understand why the following equality holds (taken from Cameron & Trivedi 2005: Microeconomtrics): ...
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1answer
124 views

Removing structure with a known functional form from the covariance matrix

I have a set of timeseries data $X^B = \begin{bmatrix} {X^B_1},{X^B_2},\dots, X^B_n \end{bmatrix}$ consisting of observations recorded at different spatial locations. There is crosstalk between the ...
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104 views

PCA Using prcomp in R

I'm trying to do principal component analysis (PCA) in R using the prcomp function. My input is a large matrix of 1,188 observations (rows) and 15,462 features (cols). I input this to the function ...
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75 views

Item-based collaborative filtering – Can you add demographic information to initial user×item matrix?

I am building an item-based collaborative filter recommendation system. I have a matrix of users and items, which in this case, are products that were either bought or not (i.e., binary: ...
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2answers
154 views

Why is the Pearson correlation 1 when only two data values are available?

I am trying to obtain a Pearson correlation between 6 different variables (represented by columns in the matrix below) with two datapoints each (rows). This is the matrix: ...