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Questions tagged [multivariate-analysis]

Analyses where there is more than one variable analyzed together at once, and these variables are either dependent (response) ones or the only ones in the analysis. This can be contrasted with "multiple" or "multivariable" analysis, which implies more than one predictor (independent) variable.

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9 views

Decomposition of Mahalanobis distance: Where's my mistake?

Kim (2000) gives the formula for the decomposition of the Mahalanobis distance: $$ (\mathbf{x}-\mathbf{\mu})^{T}\mathbf{\Sigma}^{-1}(\mathbf{x}-\mathbf{\mu}) = \sum_{i = 1}^{d}(1 - \rho_{i}^{2})^{-1/...
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is “multivariable linear regression” the same as logistic regression?

I am new to machine learning and I am simultaneously studying linear and logistic regression. Logistic regression is when there is one dependent variable and there may be more than one independent ...
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1answer
9 views

how to understand an unit of analysis

I came a cross a definition which I cannot understand the logic. is there a way to explain what is the problem ? a longitudinal design for an intervention study in 10 participants where the ...
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13 views

How to generate a Tornado Diagram showing impact of different variables on output mean using 1000 sensitivity runs of a complex model?

How can I generate a Tornado diagram showing % impact of different variables on mean output? I have 1000 simulation runs of a complex model with multiple variables. In addition a normal QCing of ...
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15 views

Multivariate Bayesian Car Model Result

I have developed a multivariate Bayesian Car model for three crash severity level analysis. I found that the covariance for both heterogenous effects and the spatial effect is not significant for any ...
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Help with model selection [on hold]

In my experimental setup, I have a square symmetric matrix of variables (65) which I'll call A. Aij represents some relationship between the variables. I then performed an experiment in which I have ...
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19 views

Can I use LASSO as a variable selector with only three variable?

Can we still use LASSO even when we have a small number of variables?
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1answer
45 views

Simulate multivariate outliers that are hidden in 2D scatterplots

How could I simulate multivariate outliers that are "hidden" in all pairwise 2D scatterplots between the variables? By "hidden" I mean that they can't be seen (as obvious outliers) or detected ...
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1answer
19 views

Measuring variation explained in community matrix using both geographic distance and and environmental variables

So I have this dataset where I have species community data from a variety of sites. I’m trying to explain what are the factors that drive the variation in these data. For each site, I have a ...
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21 views

Can knn be used for multivariate multiple regression?

I am working with MLB data with around 15000 observations for seasonal player stat. The data frame's structure looks like this (I'm making up the stats): ...
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13 views

Bayesian update vs optimization in multivariate case

Say I have a multivariate normal vector $r$~$N(\mu , \Sigma )$ and I observe that $ y \equiv Pr + \epsilon = Q$ where $P$ is a matrix and $Q$ a vector and $\epsilon$~$N(0 , \Omega )$. Now I ...
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Distribution of a quadratic form [closed]

Problem: Let $ x \sim N_{k}(\mu, \sigma^2 I)$. Show that $x^\prime x/\sigma ^2 \sim \chi^2(k, \mu ^\prime \mu/2\sigma ^2)$ I am trying to use the following theorem result but I am kinda confused how ...
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48 views

linear combination and univariate normal

Show that $(X_1,X_2)$ has a bivariate normal distribution with means $\mu_1, \mu_2$, variances $\sigma _1^2 $ and $\sigma _2^2$, and correlation coefficient $\rho $ if and only if every linear ...
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1answer
35 views

Bivariate normal distribution from independent random variables

Let $X_1$ and $X_2$ random variables such that $X_1+X_2$ and $X_1-X_2$ have independent standard normal distributions. Show that $x=(X_1, X_2)$ has a bivariate normal distribution. My work: Since $...
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29 views

Joint distribution of sample means from multivariate normal

Suppose $\mathbf{Z_1}, \dots, \mathbf{Z}_n$ be iid random vectors of normal distribution s.t. $\mathbf{Z}_i \sim N(\boldsymbol{\mu},\boldsymbol{\Sigma})$ where $\mathbf{Z}_i = (X_i, Y_i)^T$, $\...
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7 views

Distribution to Examine Perceived Impact of Aircraft Flyovers [closed]

I am attempting to model the impact of aircraft flyover noise and had a two question survey filled by students 1) The frequency of disruption of their study sessions per day 2) The perceived noise ...
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18 views

What analysis should I use?

I have a dataset with 5 years of data, and am looking at trends in outcomes over time - so I have a categorical independent variable of Year, and 7 dependent variables, 5 of which are boolean, 2 of ...
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13 views

How to choose the suitable Neural Network Architecture for Regression Tasks

so I'm working on a Project where I want to predict the Vehicle Position from the Vehicle Data like speed, acceleration etc.. now the data that I have comes also with a timestamp for each sample ( I ...
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Finding $\mathsf P(\textbf{Y}\mid\textbf{Z})$ where $Z_1,Z_2,\ldots,Z_n$ are conditionally independent

As an extension of my previous question which is described below... Assume $Y_1$, $Y_2$, $\ldots$ ,$Y_n$ are random variables over a regular lattice indexed by $i= 1,2,\ldots,n$ where $Y_i\in\{...
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1answer
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Are my PCA groups significantly different?

I am studying the feeding behaviour of deep sea fishes, and have produced a dataset containing percentages for 20 different fatty acids (totalling 100%) for 32 individual fish. I have performed PCA (...
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28 views

finding the most correlated features in a multivariate time series

Assume I have a multivariate time series with 4 features where feature 1 is the most important one for me but at the same time I am suspecting maybe there is at least one more feature (another column ...
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Treatment variable not in control data set-how to make a dataframe suitable for regression?

I would appreciate some feedback on this particular problem I'm stuck at. Experiment: Between Subjects; Treatment Vs Control. 10 subjects per condition. The subjects are measured over 10 trails. (so ...
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1answer
42 views

Is it possible to forecast multivariate time series using exponential smoothing equations? If yes what are those equations?

I know we can forecast univariate time series using different models of exponential smoothing , but am searching for whether same can be extended to multivariate time series and if yes what are those ...
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How to test if my population is orderable?

I perform repeated experiment, which takes, e.g. 1s, such that time $t \in [0,1]$. I observe variable $x$, which is an event. So for each experiment $i$, $x=1$ at some random time $t_i$, and $x=0$ the ...
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15 views

Logic for testing differences in regression beta weights from a multivariate model

I have several questions regarding the logic of comparing difference scores and using a multivariate model as a means of doing this. To start, let’s say I have a multivariate model whereby I am ...
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20 views

Two sample multivariate t-test?

I am wondering if there is a relatively easy way to implement a multivariate t-test or something analogous in R. I am aware of Hotelling's T-squared test, but in my case p>n and I've read that this ...
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How do I extract VaR estimation from DCC-GARCH model in R?

I have estimated a DCC-GARCH model in R and I need to extract the Value at Risk for an equally weighted portfolio from the estimated model. ...
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15 views

Converting regular time interval to non uniform

I have a time series data set with multiple features. This data set is collected over 8 hours of time at regular intervals of 5 mins. How can i resample and select the data in exponential scale? I ...
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1answer
65 views

Model selection Multivariate Regression

I have a question about the construction of a multivariate regression model. I have one major predictor (continuous: IV1) and 3 continuous dependent variables. As we are registering our study on OSF ...
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1answer
19 views

Why is the standard error of regression parameters not decreasing?

I know that the standard error is calculated from looking at the sum of squared errors divided by square root of n. However, as we add more and more variables, we expect the sum of squared errors ...
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47 views

Correlation between logrank (log-rank) test statistics with common control

Say I have a $K$ arm experiment that generates survival (time-to-event) endpoints. There are $K-1$ experimental arms and a single control arm. Say I compute a log rank test statistic comparing the ...
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1answer
44 views

Will one-hot encoding for categorical predictor violate the independence assumption of linear regression?

we know that for non-numeric categorical features, such as country, color, they can be transform into numeric value by one-hot encoding. For instance, suppose there are 7 color options for a car, ...
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22 views

Multiple cox regression with no events in one group of one variable — survival analysis

I am trying to run a multivariate Cox regression analysis but I have 1 value for 1 variable that has no events reached. This variable was treatment (values = treatment 1, treatment 2, treatment 3, and ...
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1answer
20 views

How to handle clustering analysis of data which has different numbers of levels

For example, if i have data which is along the lines of ...
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6 views

What statistical analysis to use to relate multispectral seed data to other conventional tests?

I'm a PhD student at the University of São Paulo, Brazil, and I'm conducting experiments with multispectral analysis of soybean seeds. I have reflectance data for 8 different soybean seed samples, ...
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8 views

Proof help for multivariate mutual information as a sum of entropies

I'm following this paper on ICA and I got to equation (1) describing the multivariate mutual information contrast function as a sum of entropies. $J(Y) = \int p(y_1,...y_D)log(\frac{p(y_1,...y_D)}{p(...
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26 views

Best Statistical Test for my situation?

For an upcoming project we are trying to create a recommendation algorithm for customers and providers. I will have some number of service providers, probably hundreds to thousands, and some number ...
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18 views

conversion of multivariate time series into functional data analysis

i am trying to generalize the functional autoregressive model of order one to some order p, for this i calculate the functional principle components, and choose a particular pcs which explain a given ...
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6 views

In what circumstances would be consider using PLS-DA rather than Linear Discriminant Analysis?

I'm wondering in what kind of case would be consider using PLS-DA rather than Linear Discriminant Analysis? And what's the difference?
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1answer
61 views

Is the joint distribution $P_{XY}(x,y)$ determined from the marginal $P_X(x)$ and the conditional $P_{X|Y}(x|y)$?

For simplicity assume that $X,Y$ are discrete, finite, random variables, with joint distribution $P_{XY}(x,y) = \mathbb{P}(X=x\wedge Y=y)$. Now suppose that we do not know $P_{XY}(x,y)$, but are ...
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42 views

Convergence in distribution of $\sqrt{n-3}(z -\zeta)$

Let $(x_i,y_i)$ be iid $(x,y), i = 1,..,n$ be any bivariate sample. The correlation coefficient \begin{equation} \begin{split} \rho & = \text{cor}(x,y) \\ & = \frac{\text{cov}(x,y)}{\sqrt{\...
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46 views

Using NbClust on datasets that produce some negative eigenvalues. When to exclude data, when to force to positive, when to exclude test index?

Background on why I am using clustering: I am analyzing data from a multistep biological experiment, where each step is done in batches of varying sizes. I want to account for any biases that might ...
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13 views

compare 2 different sized multivariate samples

I have a two data tables like below. The dataset1 represents failed candidates. The dataset2 represents the successful candidates. I want to know, by applying some inference statistics which var (...
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0answers
17 views

Ranking groups based on multiple criteria

My objective: To give a more sound foundation to the data I have access to. This is an exercise that is aimed to look for some structure and soundness in the interpretation of the data BUT it can be ...
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1answer
43 views

How to show that $X = LY$ where $Y\sim N(0,I)$?

Let $X\sim MVN(0,\Sigma)$ denote a random vector having the multivariate normal distribution with mean $0$ and covariance matrix $\Sigma$. Suppose we want to sample from $X\sim MVN(0,\Sigma)$. ...
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25 views

How to Create a Toy Example of the Curds and Whey Algorithm?

Why is my simulated example failing? I am trying to create a toy example of the Curds and Whey method for multivariate linear regression in python (An example in R would be very helpful as well). I ...
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1answer
60 views

Assessing Continuous Predictor with HR in Cox Model

I would like to recreate the following figure The authors state this about the figure: "Multivariate Cox regression models witha cubic natural spline analysis were used to determine the potential ...
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0answers
39 views

Secret Life of Covariance Matrix

I am currently reading Secret Life of Covariance Matrix: http://www.inf.fu-berlin.de/inst/ag-ki/rojas_home/documents/tutorials/secretcovariance.pdf and am confused by the following: Now, in the ...
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0answers
11 views

Messy cross-section and time series data analysis

I am currently working with a dataset that has the messiest "panel" structure I have seen. Each observation is a customer at certain time, that has several predictors and one dependent variable (debt ...
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1answer
40 views

Doubt about proof of positive semi-definite matrix implies covariance matrix

I have a doubt about the proof of the fact that a positive semi-definite matrix is a covariance matrix. The professor do the following proof: Let $\Sigma$ be a positive semi-definite $p \times p$ ...