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Analyses where there is more than one response or dependent variable of interest. This can be contrasted with "multiple" or "multivariable" analysis, which typically implies more than one predictor or independent variable.

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A function that changes the dimension of a random vector make the random vector discrete?

One of my problems ask the question Let $\vec{x} \in \mathbb{R}^n$ be a random vector, and $g: \mathbb{R}^n \to \mathbb{R}^k$ be measurable. Then show that $g(\vec{x})$ is a discrete random vector. ...
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13 views

Bivariate Distribution [on hold]

Let X,Y ~ N(0,1) and define Z = X, if XY>0 and Z = -X if XY<0. Find the distribution of Z. I'm not sure how to divide the distribution for Z based on the fact that XY<0 or XY>0.
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15 views

Least squares estimate for multivariate regression [on hold]

How can I find the least squares estimate Bhat for a multivariate multiple regression in R Studio? (I have several predictor variables and two DVs)
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13 views

Analysis of multiple dependent variables all influenced by one indepdenent variable

I am analyzing a psychophysiological experiment. I ran a model on my response times and accuracy data, which gave 7 parameters [dependent variable] per participant ( n = 12) all depending on one ...
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1answer
23 views

Variable importance (?) for multivariate time series anomaly detection methods

I'm working on anomaly detection methods for multivariate time series $[\mathbf{x}^{new}_1,\dots,\mathbf{x}^{new}_T]$ where $\mathbf{x}^{new}_{i}$ is $p-$dimensional. I won't go into the details of ...
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0answers
11 views

how i found elements in every cluster in python [closed]

In python i did cluster. I have a table with 26000 cloth's article and 52 weeks. The values in the table are the sold quantity of every article during the weeks. I'm doing clustering of time series.....
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30 views

Cross-Correlation of time series with underlying condition

I want to compare two time series and want to find out if there is a significant correlation. Specifically I want to find out if in certain situations there is a specific lag between the series. I ...
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1answer
17 views

Obtaining point forecasts from a DCC-GARCH model in rmgarch in R [closed]

I am becoming more acquainted with GARCH models in R, but I am not sure my code is right for what I am trying to do, so I would appreciate any help. Based on an xts I create using data from a csv ...
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54 views

Confidence regions on bivariate normal distributions using $\hat{\Sigma}_{MLE}$ or $\mathbf{S}$

Given a $5 \times 2$ dataset $\mathbf{X} =\left( \begin{array}{rr}-0.9&0.2\\2.4&0.7\\-1.4&1.0\\2.9&-0.5\\2.0&-1.0 \end{array} \right)$. Assume that $X\sim N_2(\mu, \Sigma)$. ...
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0answers
10 views

VAR(p) models and its application in describing GDP growth

Im currently reading up on Vector Auto Regression models however I cant wrap my head around how you set a model to describe a variable. My goal is it use interest rate, imports and exchange rate to ...
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16 views

Visit level variables along with merchant level variables

I am using mixed model and my dependent variable is conversion. Records are at visit level. I have merchants selling different products in the data set, and each merchant has attributes: merchant name,...
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17 views

Variability in categorical variables while reducing dimensionality

If a dataset has a variable with categorical values (A, B, C, D, E, F), would converting them to numeric and breaking them down into separate columns (for example, column A that will have 1s for all ...
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1answer
30 views

Cluster analysis of variables or observations?

I'm very new to cluster analysis. In papers such as Richette et al.1 (which tries to see which concomitant diseases cluster together), authors first cluster the variables and then the observations (i....
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0answers
8 views

Any publication suggestion on Dynamic Factor Analysis application for common trends?

I have 38 different Google Search Trend series for online retailing sites in Turkey. Now I want to analyze common trends which can be extracted from these series and see which retailers have similar ...
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0answers
12 views

Distribution of maximum variance explained by 1 variable

Say I do principal component analysis on $n$ variables, and I sort the fractions of variance explained to find the largest. What is the probability distribution for this figure? For context I just ...
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0answers
13 views

Doubt on passage in the derivation of the equation for estimating beta coefficients in the multivariate regression

The equation that I need to derive is this: $$\hat{\beta_1}=\frac{\sum\limits_{i=1}^n\hat{r}_{i1}y_i}{\sum\limits_{i=1}^n\hat{r}_{i1}^2}$$ * $r$ are the residuals regressing $x_{i1}$ on the other ...
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1answer
30 views

multivariate normal distribution range [duplicate]

Simple question about MVN pdf. I understand the domain to be [0,1]. However, why does scipy.stats.multivariate_normal.pdf output values above this range. E.g. <...
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7 views

Variables relationship in large multidimensional datasets

Suppose I have quite a large time series (e.g., daily car accident rates in London for the past 20 years) and I also have further datasets for the same time period (e.g., daily precipitation, wind ...
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1answer
18 views

Will VECM handle multiple seasons?

I have two questions: Since VAR (vector autoregression) will not handle seasonality and trend. VECM comes into play which can handle season as well as trend. I had a doubt whether it will handle ...
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0answers
11 views

multivariate welch test [closed]

Has anyone implemented the use of the multivariate Welch test (https://github.com/alekseyenko/Tw2), implemented in R? I am trying to figure out how to format the inputs and I am not having a lot of ...
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12 views

Comparative Analysis

First I would like to indicate I plan to use Bayesian analysis methods (as instructed) I want to compare the effect of 6 independent variables (IVs) on four dependent variables. The dependent ...
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1answer
30 views

Multivariate regression

I am just wondering about the appropriateness of multivariate regression in my research design. As an example, say I have three different dependent measures of similar constructs (e.g. "academic ...
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19 views

Finding trends for multiple dependent variables

I am analyzing training data to look for trends. The variables I have are training date and then I have 5 metrics of performance. Each metric has 4 time points. So it looks like this: Training Date ...
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1answer
44 views

Interpretation of DCC GARCH output In R

I have got clarifications about almost all the aspects of interpretation a DCC model from a post from 2016. But I have a doubt regarding the interpretation of dcca1...
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1answer
105 views

Robust covariance and OGK outlier detection

I'm calculating the robust covariance of a data set in order to use mahalanobis distance for outlier detection. There are few methods to calculate the covariance in the equation. Using the Fast-MCD ...
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7 views

Hazard model for multiple streams of events

I've got multiple streams of events (suppose that only two) : for two countries we mark day by 1 if there is at least one new infection of rear disease, 0 otherwise, how to treat such dataset (2000 ...
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7 views

Analysis of Multiple Count Dependent Variable and Multiple Binary Independent Variable

I am wondering if Point Biserial Correlation is applicable for multiple binary independent variables and a dependent count variable. I have read how it was derive for a two variable system of one ...
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1answer
21 views

If one dimension of the data is scaled by a factor, how would it affect the probability of the Gaussian distribution?

I have fitted a maximum likelihood Gaussian distribution $N(\mu, \Sigma)$ on a multidimensional data set $X$. I wonder how would $p(X)$ change if one dimension of $X$ is scaled by a factor? It's ...
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15 views

How to handle errors of observed values in multiple linear regression?

I am dealing with a multiple linear regression model such that $$ E[Y] = \alpha + \beta X$$ I have a set of observations lets say $$\bar{y}_i | x_{1i}, x_{2i}, ...$$ where $\bar{y}_i$'s are the ...
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13 views

ANOVA, mutual information, Chi-squared feature selection are widely used and implemented in SKLearn - but where were they first published?

SKlearn is a widely-used, almost 'industry-standard' package for machine learning and implements a number of univariate feature selection methods (ANOVA, mutual information, Chi-squared) ... but the ...
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1answer
73 views

ARIMA with independent variables [closed]

I'm a Data Scientist, but new to time series methods. I primarily use SPSS, but I'm familiar with R. I have read Rob's blog, various books, and taken a few courses. I have a couple of outstanding ...
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50 views

Multivariate distribution with specific (multivariate) marginal distributions

Let suppose I have a 6-variate random variable $\mathbf{x}=(x_1,x_2,x_3,x_4,x_5,x_6)$. What I want is to define a multivariate distribution for $\mathbf{x}$ with some specific multivariate marginals. ...
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1answer
32 views

optimal subset / joint distribution prediction with machine learning

How can I find the optimal subset of classes for a given entity? For context, say that we have some customers and data about these customers transactions, and a set of possible products to advertise ...
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13 views

How can I investigate correlations between tumor location and surface-receptor expression in R-studio?

I am not sure what statistical approach/model I should use for the following example - so I hope you can helt with some inputs. I have four different possible tumour locations in the head area - ...
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0answers
20 views

Expectation of expressions involving sample covariance matrix and inverse of covariance matrix

Let $y_{ij}$, $i=1,2,\cdots,n_j$ be a random sample from $N_p(\mu_j,\Sigma_j)$, $j=1,2$. Let $$\overline{y}_j=\frac{1}{n_j}\sum_{i=1}^{n_j}y_{ij} \hspace{2mm} \mathrm{and}$$ $$S_j=\frac{1}{n_j-1}\sum_{...
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How to combine multiple kernels of large sample datasets?

I have multiple large sample datasets in matrix format (each has 15000 rows and 5-50 columns) corresponding to different experiments. Each matrix contains the same number of samples(rows) but the ...
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14 views

Interpreting Moderator

I have the following regression model $Y = \alpha X + \beta M + \gamma XM$, where $X$ is the main explanatory variable of interest, and $M$ is the moderator. All our variables are continuous variables....
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22 views

Conditions for the Fisher Information matrix to be invertible

The Fisher Information Matrix is positive semi definite. So, it is not necessarily invertible. By the Multivariate Central Limit Theorem we know that $\sqrt{n}(\hat{\theta}−\theta)=S_{n}⟹\mathcal{N}(...
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1answer
26 views

Manipulating primitive form of a VAR model

Given a primitive form of a bivariate VAR(1) below, and correspondingly in a matrix form below. What were the steps involved in manipulating the matrices such that it resulted in this form below as ...
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14 views

Train on Sequential and Make Predictions on Non-Sequential Data using LSTM architecture in Keras

I am working with multivariate time series data with multiple examples to train LSTM on, and Y is either 0 or 1 binary classification. Currently, I am using pad sequence layer in combination with a ...
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21 views

Advantage of RNN over CNN/other architectures for multivariate time series prediction?

I am building a multivariate time series prediction. I want to train and use the network with fixed length series of n events. I know that I could use a RNN for this. What I do not understand though ...
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2answers
50 views

Multivariate vs Multiple time series

While looking through the concepts of multivariate time series I came across the term "Multiple" time series. Is both the terms are pointing to the same meaning. What is the difference between them ...
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8 views

Should I apply Multivariate method on this data set

I have a data set including subject, group, time and 50 different columns Analyt such as Calcium, Potassium and etc. I want to see the if the result (Analyte) change over time in the different ...
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1answer
24 views

How do you calculate P(E1, E2 | H) when E1 and E2 are not independent?

I understand from Bayes Rule that P(H | E1, E2) = P(E1, E2 | H) * P(H) / P(E1, E2) When E1 and E2 are independent, P(E1, E2 | H) = P(E1 | H) * P(E2 | H) How can I calucate P(E1, E2 | H) when E1 ...
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23 views

Multivariate Multiple TIme series

In Bats, we can handle multiple seasonalities In ARIMA, we can handle multivariate problems. Is there is any method/package to handle both Multivariate Multiple Seasonalities?
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2answers
126 views

Multivariate linear mixed model using lmer

I want to detect differences between 4 treatments of a food product based on the results from a sensory evaluation, where 9 panelists assessed the 4 products (i.e. treatments) following a number of ...
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14 views

How to analytically solve the probability of improvement acquisition function in Bayesian Optimization with Vector inputs?

I have been using the probability of improvement acquisition function in my Bayesian Optimization program, but I've run into a problem because I am not optimizing the acquisition function that quickly....
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6 views

Multivariate fixed point iteration: the wrt variable on both sides of update equation and not are different?

I try to understand more about the update in multivariate fixed point iteration. I saw the examples where the updates have the same variable (the wrt. variable of partial differentiation) on both ...
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12 views

Determining which variable is more affected

An illustration of my issue: For e.g. X is a hormone that affects both the growth of hair, feet and nails. A case-control study was conducted with cases having a condition causing excessive hormone ...
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1answer
67 views

re-analysis of someone else's data: 5 treatments x 4 non-exclusive outcomes

I am trying to re-analyze (ETA: used loosely; the original study performed no statistical analysis) some published biological data (below). They used 5 treatments and scored presence/absence of 4 non-...