# Tagged Questions

Multivariate refers to analyses where there is >1 response / dependent variable of interest in the statistical analysis. This can be contrasted w/ *multivariable* analyses, which typically implies >1 predictor / independent variable.

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### Interpreting weights from Fisher linear discriminant analysis

I have data that I'm trying to classify into two different groups using Fisher linear discriminant analysis. This gives me a vector of weights $\vec w$, used in the equation $\vec w\cdot \vec x$ to ...
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### Dimension reduction issues in self-organizing maps (SOM)

Self organizing maps are claimed to be able to visualize/cluster high-dimensional data in a smaller dimensional space. I have some difficulties in understanding this statement. Consider a ...
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### How do choices of probabilities and covariance matrices constrain each other for a correlated multivariate Bernoulli random variable?

I have a correlated multivariate Bernoulli random variable $\textbf{X} = (X_1, ..., X_N)$, where the $X_i$ are Bernoulli random variables with parameters $p_i$ and $N \times N$ covariance matrix ...
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### Issues in gesture recognition

Q1 - Paper download link extracts autocorrelation as features for every pixel. That means if there are 200 frames of video, will there be 200*2 univariate AR models? This is an exhaustive process for ...
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### Factor Analysis: calculate maximum likelihood factor loadings from only the correlation (R) matrix and/or covariance (S) matrix?

Does anybody know how to calculate the maximum likelihood factor loadings from only the correlation (R) matrix and/or covariance (S) matrix in Factor Analysis "by hand" (i.e., by Excel)? Or, even ...
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### Citation for the weakness of sequential univariate regression?

I'm rebutting a paper in which the author has done linear regression in two steps: Regression against a single predictor Regression of the residuals from the first model against a second predictor ...
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### How to estimate Relative Risks in Multivariate Binary Logistic Regression Models, instead of Odds Ratios?

All software programs I have tried report only odds ratios (ORs) for binary logistic regression predictors (as exponential of the betas). I am interested to know how can I compute the relative risk ...
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### Proof for two-sample Hotelling $T^2$ statistic?

I've been reading "A primer of multivariate statistics" by Richard J. Harris, page 546, which shows how to derive the Hotelling $T^2$ statistic, after seeing this related but different question (I ...
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### Dimensionality reduction using self-organizing map

Self-organizing maps are claimed to be an approach for dimensionality reduction. However, I am kind of confused about this claim. Consider the following example, I have a data set with 200 data ...
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### Fitting multivariate, natural cubic spline

note: with no correct answers after a month, I have reposted to SO Background I have a model, $f$, where $Y=f(\textbf{X})$ $\textbf{X}$ is an $n \times m$ matrix of samples from $m$ parameters and ...
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### How to compare ratings of airlines on a Likert scale when different participants have rated different airlines?

I conducted a survey using a 5 point Likert scale. Firstly, I asked the respondent to select one airline out of six airlines given and then there were 20 statements regarding the services offered by ...
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### Does the multivariate Central Limit Theorem (CLT) hold when variables exhibit perfect contemporaneous dependence?

The title sums up my question, but for clarity consider the following simple example. Let $X_i \overset{iid}{\backsim} \mathcal{N}(0, 1)$, $i = 1, ..., n$. Define: S_n = \frac{1}{n} ...
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### Exploring a scatter-plot matrix for many variables

I am analyzing a dataset with many parameters (say, 50-200) and I am interested in looking at relations between variables (e.g. in terms of 2-variable scatter plots or 2d histograms). However, for ...
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### Is PCA the same as CCA for the same random vector?

Reading Wikipedia about canonical correlation analysis (CCA) for two random vectors $X$ and $Y$, I was wondering if PCA is the same as CCA with $X$ and $Y$ are the same? Thanks and regards!
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### What statistical test should I use?

I have 10 different biological features (for example: normal, disease 1 , disease 2, ..., disease 9). Tissue samples from various patients were imaged and 60 imaging parameters were measured. A ...
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### Smart way to search through a very large parameter space

I have a system whose performance is based on a rather large parameter set (200 parameters, lets say, of which each can take a very wide range of values). There are tests to evaluate the performance ...
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### Linear Equation System with Random Coefficients

I want to find a 1-$\alpha$ confident region for a value $\left(\Gamma_1,\Gamma_2\right)$. (Which are not random variables) I can obtain diferent $m_i$ and $b_i$ that satisfy ...
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### Estimation of covariance and mixing parameter by a bivariate normal-lognormal model

I have to create a model which is a mixture of a normal and log-normal distribution. To create it, I need to estimate the 2 covariance matrixes and the mixing parameter (total=7 parameters) by ...
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### When data has a gaussian distribution, how many samples will characterise it?

Gaussian data distributed in a single dimension requires two parameters to characterise it (mean, variance), and rumour has it that around 30 randomly-selected samples is usually sufficient to ...
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### 68% Confidence level in multinormal distributions

I wanted to create some contour plot to give confidence level say at 68% and 95% of some 2-dim multivariate normal distribution. (later I will have to go to 3-dim). I was wondering whether there was ...
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### Number of dependent variables greater than # IV's in multivariate hypothesis test

I have a multivariate regression model $\mathbf{Y}$ = $\mathbf{XB}$ + $\mathbf{E}$ where $\mathbf{Y}$ is $n \times m$. In my case $\mathbf{n < m}$, the number of columns in $\mathbf{Y}$ is ...
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### Finding latent variables in 7 dichotomous variables

I have read other posts on conducting Factor analysis (FA) with dichotomous variables and although it appears clear that FA done in the default way is not appropriate, I am still unclear about a few ...
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### Modeling multivariate density with semiparametric methods

I am trying to model (using R) the density of multivariate data conditioned on a few known parameters so I can simulate sampling from new sets of parameters. I have about 100,000 data points that ...
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### One-sample multivariate test for equal variances with known means

I have a $N$ $M$-dimensional observations $(x_1,\ldots,x_N)$. Given the $M$-dimensional vector $\mu$ and the $M\times M$ covariance matrix $\Sigma$, I would like to test whether it is likely or not ...
Consider two multidimensional random vectors $x$ and $z$ having Gaussian distributions $P(x)=N(x\mid\mu_x,\Sigma_x)$ and $P(z)=N(z\mid\mu_z,\Sigma_z)$, respectively, together with their sum $y=x+z$. ...