Multivariate analysis is used when there is more than one variable of interest in the statistical analysis.
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2answers
1k views
Is it possible to have a pair of Gaussian random variables for which the joint distribution is not Gaussian?
Somebody asked me this question in a job interview and I replied that their joint distribution is always Gaussian. I thought that I can always write a bivariate Normal with their means and variance ...
1
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0answers
242 views
Multivariate time series simulation in RapidMiner? [closed]
I'm actually "Getting started" with RapidMiner (RM).
I'm an R expert but totally newbie to RM. The problem involved is analysing and forecasting the dispersion of multivariate timeseries (in finance). ...
5
votes
1answer
274 views
Confidence interval about a multivariate normal probability
From a given sample $x_i \underset{\mathrm{iid}}{\sim} {\cal N}(\mu, \sigma^2)$ it is possible to get a confidence interval about the probability $\Pr(x_i \geq a)$ for any number $a$, by "inverting" ...
1
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0answers
312 views
Construction of Dirichlet distribution with Gamma distribution
Let $X_1,\dots,X_{k+1}$ be mutually independent random variables, each having a gamma distribution with parameters $\alpha_i,i=1,2,\dots,k+1$ show that ...
0
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1answer
86 views
Methods of “Two-Way” Multidimensional Scaling (MDS)?
I just want to ask about the MDS. Below is the subcategory of the Multidimensional Scaling topic.
Multidimensional Scaling
Metric and Non-Metric Models
Methods of "Two-Way" Multidimensional Scaling ...
0
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1answer
38 views
Show that all the characteristic roots of a dispersion matrix of a random variable are non-negative
Show that all the characteristic roots of a dispersion matrix of a random variable are non-negative.
$$\begin{vmatrix} \sigma_{11}-\lambda & \sigma_{12} & \cdots & \sigma_{1p}\\ ...
2
votes
1answer
192 views
What analysis to use with two groups, a pre- and post-test, and three outcomes?
I am doing a pre- and post-test intervention. I have two groups, each doing a different intervention. I will test the success of the interventions using three outcome measures.
In another way to ...
2
votes
2answers
173 views
How do I evaluate relationships between 500 binary attributes and corresponding continuous score?
I'm going to preface this all by saying that I'm pretty pedestrian when it comes to large statistical analysis.
I have approximately 11K discrete events and a corresponding score. I also have ...
21
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2answers
348 views
What is the relationship between independent component analysis and factor analysis?
I am new to Independent Component Analysis (ICA) and have just a rudimentary understanding of the the method. It seems to me that ICA is similar to Factor Analysis (FA) with one exception: ICA assumes ...
9
votes
2answers
223 views
Computationally efficient estimation of multivariate mode
Short version: What's the most computationally efficient method of estimating the mode of a multidimensional data set, sampled from a continuous distribution?
Long version: I've got a data set that I ...
3
votes
2answers
170 views
Modelling dependency between random variables
Assume we have 2 random variables $(X,Y)$ with same distribution $G(.)$. Suppose we are interested in a joint probability of these r.v.'s without any information about dependence or correlation ...
1
vote
2answers
121 views
How to cluster multidimensional (parametric) distributions?
It seems to me that it is possible to cluster unidimensional distribution in the space of their parameters, for example, we can try to find similar normal distributions in the space of $(\mu,\sigma)$ ...
11
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0answers
297 views
SVD of correlated matrix should be additive but doesn't appear to be
I'm just trying to replicate a claim made in the following paper, Finding Correlated Biclusters from Gene Expression Data, which is:
Proposition 4. If $X_{IJ}=R_{I}C^{T}_{J}$. then we have:
...
1
vote
1answer
166 views
Joint distribution of dependent exponential variables
I am trying to model a joint probability constraint of a union of correlated / uncorrelated exponential functions.
Formally, assume we have random variables $A_i \sim exp(\theta_i), \forall i \in ...
1
vote
1answer
100 views
Draw balls from a set of color balls: the probability of drawing a color seen before?
Recently I am studying a probability problem related to the multivariate hypergeometric distribution. The problem is stated as:
Given well-mixed $n$ balls of $m$ colors, and assume that $n_i$ is ...
9
votes
1answer
204 views
Is there a generalization of Pillai trace and the Hotelling-Lawley trace?
In the setting of multivariate multiple regression (vector regressor and regressand), the four major tests for the general hypothesis (Wilk's Lambda, Pillai-Bartlett, Hotelling-Lawley, and Roy's ...
5
votes
2answers
68 views
Supervised classifier for events with missing data
I'm working on an experiment in which we try to sort events into three categories based on roughly 20 inputs using a feed-forward neural network (trained via backpropagation). Unfortunately, many ...
2
votes
0answers
59 views
Effect of duration of treatment on the outcome at different time points
I am interested in knowing if the duration of treatment has an effect on treatment with two different drugs. We have used two different drugs to treat cerebral ischemia (brain damage) and continued ...
5
votes
1answer
75 views
Designing a Simple (a.k.a 'bad') Ranking value from several values of unknown distribution
I am but a humble developer, so please forgive if I butcher terminology of confuse concepts.
I am looking at designing a simple ranking of Average Internet Audience Rank based upon a bloggers ...
1
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0answers
37 views
How can I estimate a “rank” dependent variable in a multivariate dataset?
I have a dataset where $x_{1}$, $x_{2}$, ..., $x_{k}$ are of mixed type and $y$ is a ranking from $1$ to $n$ where $n$ is the number of observations in the dataset. I'd like to predict $y$ based on ...
0
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0answers
32 views
multiple variables taken several times [closed]
I need to analyse the correlation between glucose and creatinine and urea (ie.) measures everyday during a week. I need to know which of the others impact on glucose levels.
Thank you
7
votes
4answers
193 views
p-value as a distance?
Can p-values between multiple pair-wise tests be considered as a similarity/distance measure and multidimensional scaling be applied over a pair-wise matrix of p-values to reduce the dimensionality? ...
0
votes
1answer
153 views
Which statistical test should I use when there are multiple latent predictors and multiple latent outcomes?
I am doing my research on Personality (the big five factors) and if personality can predict commitment to an organization. However, commitment is composed of three dimensions.
What is the best ...
2
votes
1answer
367 views
Nonlinear principal component analysis MATLAB code
I'm working on multivariate process monitoring using NLPCA method.
I need MATLAB code to implement this method.
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0answers
82 views
Can I use multi-response permutation procedure test on the entire likert scale score dataset?
I have a dataset from a 7-point likert scale scores of 30 questions asked to 145 individuals. I would like to know if I can use MRPP on the entire dataset to test for difference between different ...
4
votes
1answer
136 views
Testing whether there is a difference between two groups who were asked the same set of questions
I asked two groups of individuals (80 males and 10 females) fill out a questionnaire asking them their attitude towards a series of political variables. Every individual had to answered a set of 16 ...
3
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0answers
122 views
Clustering & Time Series
I have a multivariate dataset that changes over time. I have extracted (and normalised) some features and used k-means to generate clusters over the entire span of the dataset.
Now I want to see ...
4
votes
2answers
448 views
Generation of random numbers from the multivariate normal distribution in spherical coordinates
Can any one point me to a research article or post the actual algorithm to generate random numbers from the multivariate normal distribution in spherical coordinates?
I need both $N_p(0,I_p)$ , the ...
4
votes
2answers
162 views
How do you identify the variables that separate several groups?
I don't have much background on statistics. I am working on multivariate morphometrics of a sample of frogs. I have a data matrix of 19 variables (continuous characteristics) for around 250 samples. ...
1
vote
0answers
90 views
$\chi^2$ distance and multivariate gaussian distribution
I want to know how to write the $\chi^{2}$ distance between two multivariate Gaussian distributions $f$ and $g$ in terms of their parameters only. The parameters of $f$ is the vector $\mu_{1}$ and a ...
12
votes
1answer
326 views
Does GSVD implement all linear multivariate techniques?
I came across the article by Hervé Abdi about generalized SVD. The author mentioned:
The generalized SVD (GSVD) decomposes a rectangular matrix and takes into account constraints imposed on the ...
2
votes
2answers
122 views
Multi-factor model for a quantitative response variable
I am analyzing data in order to develop a model for power generation of a solar system based on three predictor variables. I have done t-tests showing significant improvement in the generation while ...
10
votes
2answers
1k views
What test can I use to compare slopes from two or more regression models?
I would like to test the difference in response of two variables to one predictor. Here is a minimal reproducible example.
...
0
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0answers
282 views
Multivariate Multilevel regression using lmer function in R?
I am trying to run a multilevel regression with multiple responses (multiple outcome measures) using lmer in R. Or at least that is what I think I want to be doing. My key resource is this article by ...
2
votes
0answers
564 views
Non-normal and heterogeneous data with repeated measures ANOVA
I have run a repeated measures ANOVA using 3 groups and one factor with two levels.
I have discovered that the data are not normally distributed (but not badly), nor is the variance homogeneous in ...
5
votes
0answers
316 views
Random forests for multivariate regression
I have a multi-output regression problem with $d_x$ input features and $d_y$ outputs. The outputs have a complex, non-linear correlation structure.
I'd like to use random forests to do the ...
0
votes
0answers
136 views
Testing threshold cointegration in vector error-correction models
In Hansen and Seo's paper on Testing two regime threshold cointegration in VECM (J. Econometrics, 2002; 110:293), the authors proposed a test based on Lagrange Multiplier for testing treshold in ...
5
votes
2answers
178 views
How do test whether two multivariate distributions are sampled from the same underlying population?
Say you are given two multivariate data sets, say an old one and a new one, and that they are supposed to have been generated by the same process(that you have no model for) but perhaps, somewhere ...
0
votes
3answers
426 views
Multivariate random walks in BUGS
I want to jointly estimate a very simple MV-Normal two-dimensional AR[1] process,
$[x_t,y_t]=[x_{t-1},y_{t-1}]+\text{[Bivariate Gaussian error]}$, in BUGS. But the syntax has been impossible to ...
1
vote
1answer
680 views
Simple Multivariate Regression with Octave
For the last 2 months, I've been trying to do any kind of multivariate regression, but I haven't had much luck. I hear Octave is simpler and more intuitive for these kinds of tasks, so I thought I'd ...
3
votes
0answers
171 views
Distribution of a normalized inverse Wishart times Gaussian
Suppose $z\sim\mathcal{N}\left(\lambda^2 e_1,I_n\right)$ where $e_1$ is the first column of the $n$-dimensional identity matrix, denoted here as $I_n$. Suppose $S\sim\mathcal{W}\left(m,I_n\right)$ is ...
2
votes
0answers
258 views
Controlling for a variable in a GEE using SPSS
I have a dataset which I think would suit GEE. I am trying to assess the relative contribution of a number of simultaneous predictors and their interactions to the intensity of hurt feelings. I asked ...
2
votes
1answer
128 views
Multivariate analysis and PCA
I observe y as a function of x. y is a scalar, x is a vector of dimension n.
I have k observations of y and x.
Let $$X = \begin{bmatrix}x_{1,1} & \cdots & x_{1,n}\\\vdots & \vdots & ...
3
votes
0answers
102 views
How to evaluate a multivariate gaussian condition
I am trying to come up with estimates on the outcomes from a layered-earth inversion calculation whereby the calculation provides a posterior covariance matrix for the best-fitting model parameters ...
2
votes
0answers
165 views
Efficient Portfolio Optimization Through Simulation
Apologies in advance for the (possibly?) poor terminology as I'm a bit of a novice in the field. I was torn whether to ask this on stackoverflow or here, so hope its the right place.
Anyway, my ...
2
votes
0answers
51 views
How can I assess the effect of several categorical predictors on an outcome variable?
I have a function of a dozen discrete variables, $$y = f(x_1, ..., x_n)$$ and $k$ samples of $y$ (a lot), $y$ being continuous.
I can use Matlab to analyse the data, with the statistics toolbox. The ...
2
votes
1answer
109 views
Proof for principal component score
Can we proof that two principal component scores are not equal or one is better than the other in terms of variation? For example, the 1st principal component score is defined as $z_1 = a_{11}(y_1 - ...
3
votes
1answer
282 views
Basic Multivariate Regression Analysis with R
I'm trying to look for simple patterns in weather data. Here's a simplified version of what I'm working with.
...
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0answers
103 views
Repeated measures within and between conditions
I tested reactions to pictures under five conditions (neutral, high status, low status, high adhesion, low adhesion), using an EEG of 16 channels. The pictures were presented in random order for 15 ...
3
votes
1answer
151 views
How can you relate the coefficients of a multivariate regression of ${\bf Y} \sim {\bf X}$ to the coefficients of ${\bf X} \sim {\bf Y}$?
Is anyone aware of a orthogonal multiple regression library that is implemented in say R, Scipy, Matlab, Octave, etc.? (Or even fortran/C...) If I'm not mistaken, it would not be difficult to write ...
