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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Looking for advice on conceptualizing and modeling this type of data
In a hypothetical experiment, lets assume that there are 30 lakes and I suspect that there is a difference in their chemistry. To test this, I randomly sample 10 rocks from each lake and measure the ...
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16 views
Jacobian transformation
Suppose $J_1 $ be the Jacobian for transforming $(x_1,x_2,...,x_n) \to (y_1,y_2,...,y_n) $ and let $J_2 $ be the Jacobian for transforming $(y_1,y_2,...,y_n) \to (x_1,x_2,..,x_n) $ then prove that $...
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28 views
Inverse moment of Multivariate Normal Norm
Let $x \sim N(\mu, \Sigma)$ with $\mu \in \mathbb{R}^P$; $\Sigma \in \mathbb{R}^{P\times P}$, positive definite. Denote by $||x||_2$ the vector two norm, that is, $||x||_2 = \sqrt{x^\top x}$.
What ...
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Conditional probability involving black-box functions
Let X be a continuous random variable subject to a given probability density function. Let $f: \mathbb{R} \rightarrow \mathbb{R}$ and $g: \mathbb{R} \rightarrow \mathbb{R}$ be two black-box functions, ...
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12 views
How can I predict a variable based on multiple linear correlations? [closed]
I am trying to predict the value of y based on the various correlations I obtained. Let's say that y is correlated with x and z. However, the slope of these relationships differs from one subject to ...
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22 views
Path analysis model fit statistics. RMSEA = 0.106
Hi folks,
My path analysis is using primary data that I've collected for a uni project. After removing the very non-signif variables, I have a model (which I hypothesised) that seems to work pretty ...
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60 views
Understanding the Johnson-Neyman algorithm for finding the region of significance in a trivariate correlation analysis
I'm pretty new to the whole statistics world, so excuse me for being a novice in advance. I'm trying to understand Andrew F. Hayes's PROCESS macro in SPSS [1]. To my best understanding, the macro uses ...
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2answers
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Relation between bivariate survial function and cumulative density function
I am trying to understand why
$Pr(T_1> t_1,T_2 > 2)=1-F_1(t_1)-F_2(t_2)+F_{12}(t_1,t_2)$
My derivation is as follows:
\begin{align} Pr(T_1> t_1,T_2 > t_2) &=Pr(T_1> t_1\mid T_2>...
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1answer
48 views
Multivariate normal distribution - hypothesis testing MLE
Suppose $X_{1}$, $X_{2}$,...,$X_{n}$ are i.i.d. observations from a multivariate normal distribution $N$($\mu$,$\Sigma$) where $\Sigma$ is known.
Use the likelihood ratio procedure to produce a test ...
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1answer
23 views
What is the difference between factors and latent variables?
From what I have read about factor analysis and latent variable models, factors and latent variables are, both unobserved, and both serve the purpose of shrinking the observed data to a smaller data ...
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Aggregating a multivariate distribution
I'm currently trying to investigate how to 'quickly' measure the distance between a sample of data and a larger distribution of data. I have looked at the Kolmogorov-Smirnov test, which in some paper ...
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Testing if there is any new knowledge in a third variable
I am trying to predict the outcome $X$ of an event given a big set of input variables $A$, $B$, $C$, $D$, etc.
Both $X$ and $A$, $B$, $C$, etc. are categorical variables, some of them with a high ...
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20 views
Why does the RMSE value goes high? [duplicate]
I have been trying to predict the glucose values of patients by using regression algorithms. I used Support Vector Regression (RMSE: 65), Logistic Regression (RMSE: 86), Linear Regression(RMSE: 64) ...
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Trying to find if there is a relationship between convictions for corruption and changes in electoral districts after a census
I have a small request for help with some tests of a data set I am working with for my thesis.
I am attempting to see if there is a relationship between the years before during and after a census (...
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33 views
Hotelling's T for Matrix Normal Distribution
Suppose you observe matrix normal $\mathbf{X}_i \sim \mathcal{MN}_{m,p}\left(\mathbf{M},\mathbf{U},\mathbf{V}\right)$, for $i=1,2,\ldots,n$. That is $\mathbf{X}_i$ is an $m\times p$ matrix which is ...
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How to analyse this pre-test and post-test double-blinded RCT study? [duplicate]
I have conducted a study where participants are split between two groups (treatment and control). I want to measure changes in depression and sleep disturbance pre and post-test (before and after ...
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The way PERMANOVA handling continuous explanatory variable
I have read some tutorials which explain the mechanism behind PERMANOVA, e.g., enter link description here. Based on the tutorials, my understanding is PERMANOVA can only handle categorical ...
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How to control for group membership in multivariate community analysis (CCA) when group is confounded with explanatory variables of interest?
I am studying differences in microbiome composition across 11 different populations and attempting to identify correlations between microbiome community beta diversity and population-level covariates. ...
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How to Estimate Covariance Matrix using Wishart Distribution?
I learned that Wishart distribution can help estimate covariance matrix of MVN without sampling directly from MVN. But there are some points that are still unclear for me:
Why we bother to estimate ...
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34 views
Analyze dataset with multidimensional scaling
I am ask to analyze a dataset via multidimensional scaling. There are 9 variables in totals, with 1 of them being factor. I plan to make a Classical MDS plot, but there are 8 variables ( i drop the ...
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Variable selection when dependant variable is a clinical score
I am building a mixed linear model to evaluate the effect of a particuliar variable on the evolution of a clinical score over time.
The clinical score is calculated via an equation using the age, a ...
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1answer
21 views
Multidimensional Scaling - distance?
I am trying to plot a ggscatter plot with a 8 variables and 72 rows, and i am following the steps in the reference (at the bottom as a link). However, the author label the x-axis and the y-asix as ...
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41 views
Why Multivariate Distribution with Covariance Matrix with Rank 1 Works?
So I want to sample from multivariate normal distribution and have this code where mean is 0 and I added covariance matrix with all entries to 1 implying all random variables are equally correlated.
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Are there any methods to detect whole multivariate time-series as anomalous from a set of multivariate time-series?
Consider a scenario with Dataset D as {T1, T2, ..., Tn} and Ti is a multivariate time-series of length mi as {X1, X2, ..., Xmi}. Here each record of the time-series Xi is a vector of attribute values {...
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The second order moments of the Gaussian multivariate distribution
I am really quite confused to how to calculate and get the result from
to
I know the symmetry will recduce the sum of j to sum of i(yiyj to yiyi),but however, it is still difficult for me to think ...
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Second order moment of multivariate Gaussian-completeness of the set of eigenvectors (bishop p. 83)
I don't know how 2.60 euqation is derived. Even if I have read the contents in previous pages, it is still hard for me to get an idea of how the 2.60 euqation is calculated. Also, I don't know the ...
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1answer
55 views
multivariate Gaussian/normal distribution- sigma covariance and eigenvector
For a Multivariate Gaussian Distribution
I am a bit confused about the derivation of sigma
I am confused that I still cannot get the details of the derivation of sigma. Could anyone help me with ...
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1answer
74 views
Statistical analysis of amino acid profiles, quantitative vs qualitative methods?
I work on a study comparing the amino acid profile of 5 sample groups with 3 replicates in each group. This is how the data looks like except that there are 17 columns (one for each amino acid) in ...
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Joint distribution of linear combinations of multivariate normal vectors
I am trying to solve the following exercise:
Let $ \mathbf x \sim N_3(\mathbf \mu, \mathbf \Sigma) $ with $ \mathbf
\mu^T = \gamma(1,1,1) $ and $ \mathbf \Sigma = \sigma^2
\begin{bmatrix} 1 & \...
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Machine Learning with Multivariate Data with and without Time Structure
If you have a set of independent variables $X_1,,,X_{50}$ (where $50$ is just a large number) and a corresponding $Y$.
If you want to predict the next time step of Y what is the difference in ...
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Handling correlation between outcomes and permutations of predictors
My problem is the following:
I have multiple features I wish to predict with
My outcome(s) are numeric, though information about a binary state (0, >0) may be descriptive enough
The features are ...
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Understanding the influence of multiple dimensions on a binary outcome - what method to use?
I've got a large quantity of multi-variate data, including 10 dimensions along with a binary outcome. I want to understand each of the dimension's influence on the binary outcome (ideally ranked) and ...
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Multivariate Natural Logarithmic (Exponential) Regression
I have a list of values with 4 input columns and one output column as follows:
Temperature: Directly Proportional to Severity
Hours of utilization per month: Directly Proportional to Severity
Power ...
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MARS-Model: Forward pass
I study the paper "Multivariate Adaptive Regression Splines" and the introduced "MARS"-model, but I do not understand its forward pass algorithm in detail.
Given the algorithm (just a screenshot of ...
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Mean and variance of a function of random multivariate vector
Let's assume to have a scalar function $Y=f(X)$, that is function of a multivariate normally-distributed random variable $X\sim\mathcal{N}(\mu, \Sigma)$.
Is there a general way to compute, even in an ...
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Multilabel classification and regression on time-series data
I am trying to develop an LSTM network on a vehicle dataset I have obtained from my professor. The dataset in about vehicle driving in a roundabout. I have the following tasks to complete 1. Classify ...
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high-dimensional multivariate regression with R
think of the following data:
two z-standardized dependent variables = continuous (here, both reflect a deviation of age but in different tissues)
many predictors for a rather small data set, possibly ...
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Is it okay to perform PerMANOVA on PCA values?
Is it acceptable to first perform principal components analysis on a dataset, and then use permutational MANOVA on those principal components values, rather than on the original values in the dataset? ...
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How do I interpret the beta from a PCA regression?
Assume I have a time series dataset $X_{t}$ where there are ten variables, and each variable has the exact same unit of measurement, and each variable has a similar mean and a similar standard ...
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Creating non-negative definite matrix for multivariate spatial random field?
I am trying to model a spatial multivariate (three variate) random filed. I have defined correlation matrix using LMC as function of distance lag of interested points $\mathbf{C(h}{{\mathbf{)}}_{3\...
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Bounds for common correlation of uncorrelated random variables with another random variable
Suppose we have a random variable $y$ and a collection $(x_1,\dots,x_n)$ of $n$ random variables that are all uncorrelated: $\operatorname{corr}(x_i,x_j) = 0$ $\forall i \ne j$ and that all have the ...
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Gradient of multivariate normal distribution function?
Let $X\sim\mathcal{N}_J(\mu,\Sigma)$ be a multivariate normal with PDF $f_X$ and CDF $F_X$.
Taking derivatives of $f_X$ wrt $X$, $\mu$ and $\Sigma$ is easy as shown here.
However, I am interested in ...
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1answer
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How to vectorize Multivariate Gaussian distribution?
I was going through Chuong B Do' notes on The Multivariate Gaussian Distribution. The multivariate Gaussian distribution according to it, is given as follows:
$p(x; \mu, \Sigma) = \frac{1}{(2\pi)^{n/...
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Fitting environmental variables to an ordination (artificially replicating data?)
I collected five samples of animal tissue from each of 3 different sampling sites (15 samples total). For each sample, I determined bacterial community composition, so I have a standard multivariate ...
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Should I include all the covariates in a PERMANOVA test (R)?
I have a matrix with abundance ( df_for_abundance) from gut microbiota and a matrix with metadata (26 variables; meta). I would like to calculate the effect of clinical covariates on the composition ...
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2answers
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How to predict future of time series 1 with time series 2 with AR(I)MA?
Hey guys i am new in this forum.
I am also new into programming with R or Stata(and programming in total, but i really would like to learn it). Currently I am writing a thesis about whether its ...
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Jointly Gaussian RVs: Relation between the slope of the major axis and Pearson correlation coefficient
Given a covariance matrix $\Sigma$ and their eigenvectors $V$ and eigenvalues $e$. $\rho$ is Pearson correlation coefficient.
$$
\begin{array}{l}
\Sigma = \left[ {\begin{array}{*{20}{c}}
{.25}&{....
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1answer
37 views
Video lectures on Generalized Linear Models and Extensions
I am looking for some video lectures on Generalized Linear Models and Extensions. Also, some good resources that cover "Fundamental theory of model fitting and inference in generalized linear models, ...
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lunar phase influence on animal abudance in stomach content of predator species
I have a set of data presenting the abundance of prey in the stomach of one predator species. each predator was identified with an ID number and date was recorded among other info. The date was used ...
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145 views
When do we use a multivariate regression?
I understand that multivariate regression models contain more than 1 dependent variable, but what is the difference between running a multivariate regression with dependent a and b to a set of ...
