Tagged Questions

Multivariate analysis is used when there is more than one variable of interest in the statistical analysis.

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9 views

Covariance of logit transformed variables

I am having trouble evaluating the covariance of a non-linear transformation for two vectors $s_0^*$ and $s_1^*$ $$\left| \begin{array}{c} s_0^*\\s_1^* \end{array} \right| \sim N\left( \left| ...
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28 views

Estimating parameters of multivariate AR(1) with multiple realizations

I have several multivariate realizations of what is believed to be the same process, governed by the same parameters. I would like to fit a first order autoregressive model to the data and estimate ...
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0answers
15 views

Partial $\eta^2$ in multivariate analysis

I wonder why the partial $\eta^2$ values are so small in my SPSS GLM Multivariate analysis. I have 3 DVs and 5 IVs and the sample size is large (n=5000). The main effects and significant but the ...
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22 views

Transforming data with both negative and positive skew

I am attempting to run a MANCOVA of memory assessment data. My IV has three levels (no memory impairment, moderate memory impairment, and severe memory impairment). The covariate is education. The DV ...
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31 views
+50

The distribution of the scalar product of multivariate complex normal vectors

Assume two independent random complex vectors (with real and imaginary parts): $$ \vec{\dot{Z}}=(\dot{z}_1,\dot{z}_2,\ldots,\dot{z}_n)~~~~~~~~~~ \begin{cases} \Re(\dot{z}_i)&=x_i \\ ...
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1answer
32 views

Fit a curve (spline?) through a solid in 3D and map a value onto it

I have a series of xyz data in a unit cube. It forms a sort of tapered & curved cylinder. It will begin and end at 0,0,0 and 1,1,1. I want some sort of best fit curve down the 'axis' of this ...
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0answers
10 views

R: Codes for getting quantiles of multivariate data [migrated]

I have a vector of 365 data, each follow its own normal distribution. I have a vector of average and a diagonal matrix as matrix for standard deviation. I would like to get quantiles (0.1,0.2,...0.9) ...
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0answers
52 views

Regression model where errors are not normally distributed

From a Physics equation I have the following model: $$W=\beta_0+\beta_1Z$$ $\beta_0$, $\beta_1$ are fixed values for which I want to find a $1-\alpha$ confidence region. I have ...
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0answers
30 views

Higher order tensors in Statistics

I am looking for problems in Statistics or application areas in Statistics which deal with three-way data or higher order data or 3-Tensors. Is there a regression setting where the covariates are ...
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0answers
31 views

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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1answer
44 views

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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49 views

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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0answers
22 views

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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22 views

Combining multivariate normal distributions

I hope the title is descriptive enough. I was looking in previous questions but I didn't find a related question. I want to combine two measurements which errors are given by bivariate multinormal ...
4
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1answer
32 views

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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0answers
21 views

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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1answer
161 views

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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2answers
50 views

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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21 views

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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0answers
24 views

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 ...
3
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0answers
49 views

Co-occurrence of properties in a population

I have 150 properties that may occur in a population of 10000 people. Individual people may have none, one or a couple of these properties. The properties are not mutually exclusive and have different ...
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1answer
41 views

Interpreting multivariate tests in repeated measures

I have a within subjects design with 4 DVs and I ran a repeated measures analysis on SPSS. My DV is a physiological measurement and is not expected to be linear. My multivariate Wilks lambda is ...
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41 views

Expression for Sum of Multivariate Gaussian Random Vectors

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 $y=x+z$. ...
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27 views

Multivariate Gaussian with 3 Partitions

Given that we partition a Gaussian random vector $\textbf{x}$ into three groups, $\textbf{x}_a$, $\textbf{x}_b$, and $\textbf{x}_c$, with a corresponding partitioning of the mean vector $\mu$ and of ...
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1answer
58 views

How to analyse a risk assessment questionnaire where each risk is rated for both probability and impact?

I would like your opinion on how to analyze a questionnaire on risk assessment in construction projects. For each question, concerning a specific risk for the project, there are two answers: An ...
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0answers
26 views

Fast multivariate unimodal density estimator

I have a sample $\boldsymbol{x}_i$ for $i$ in $1,\dots, n$, from a $d$ dimensional density $f(\boldsymbol{x})$ and I would like to estimate this unknown density. In addition I know that ...
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22 views

How to find the level curves of a multivariate normal?

I'm trying to get some intuition for multivariate analysis. Thought it would be good to visualise, say, the .95 probability contour for a multivariate normal. I'm looking for suggestions on an ...
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1answer
71 views

Problem with the formulation of a gaussian copula likelihood function

I recently got to hear about copulas which to me sounded like a nice tool to model relationships between variables. I decided to try to implement the likelihood function for a bivariate Gaussian ...
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0answers
87 views

Understanding Naive and Multivariate Gaussian Classifier

Thank you for checking this question out. I am trying to understand how to use the multivariate gaussian classifier. To introduce you better to my problem, I will show how currently I classify data. ...
2
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0answers
62 views

Categorical vs Continuous Variable

I have two variables, one continuous and one categorical which I currently both use as predictor variables in a logistic regression model. Their relationship is shown in the following plot with the ...
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0answers
21 views

Using ANOSIM to analyze randomized complete block design data?

I've used NMDS to explore data collected in a randomized block design, involving three treatments, each applied in 10 spatial unit blocks. Is it possible to use ANOSIM to test for hypotheses of ...
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0answers
32 views

Statistical Distance Within Multivariate Distribution

Suppose you have some multivariate normal distribution $X \sim N(\mu,\Sigma)$. Is there a good way to calculate a measure of distance between an arbitrary $X_{i}$ and $X_{j}$ of $X$ (I suppose the ...
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0answers
28 views

Nonlinear PCA‏ ( R package homals)

I'm using the NLPCA to reduce the dimensionality of nine variables (4 nominal / 3 ordinal /2 numeric) to obtain the object-scores to be used as dependent variable in a regression model. I'm using the ...
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2answers
270 views

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 ...
2
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0answers
89 views

Diagnostic plot for assessing homogeneity of variance-covariance matrices

Is there a handy plot for comparing the variance-covariance matrices of two (or perhaps more) groups? An alternative to looking at lots of marginal plots, especially in the multivariate Normal case?
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0answers
37 views

pdf of multivariate normal distribution

I have a question concerning some sentences in the book Structural Equations with Latent Variables (Bollen) at page 132 (bottom) and page 133 (top) regarding the pdf of the multivariate normal ...
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0answers
83 views

Multivariate linear mixed model in R

I have run into a problem with respect to an application of linear mixed effects model using lme4 package and I wondered if I could seek your help. This is my model in a multivariate setup where ...
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1answer
63 views

Minimize a function with respect to a matrix

I have two sets of vectors, A and B. Vectors from set A live in an m-dimensional space, ...
2
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1answer
40 views

How to prove independentness of marginal/conditional (?) posterior distributions?

This is a question about exercises 4.2 and 4.3 of Jim Albert’s “Bayesian Comptutation With R” (p. 82). Note that while this might be homework, in my case it is not. We are to prove that, given two ...
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0answers
31 views

Joint PDF change of variables

I now understand how to conduct a change of variables for a marginal PDF. Now, given two functions that define parameter's spatially: $C_A(x)$ and $C_B(x)$, is it possible to construct the Joint PDF, ...
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1answer
38 views

Is it normal to obtain better (smaller) P values in multivariate analysis compared to bivariate one?

If a multivariate design controls for other predictors when calculating the effect of a predictor, shouldn't it give paler P values (less significant ones, or less vivid odds ratios)? I am seeing ...
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0answers
70 views

Two-way anova with interaction term: what is the point of a post-hoc test?

I have a statistics interpretation question. I've recently performed a two-way anova to identify an interaction term between my categorical independent variables (genotype + temperature) that ...
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0answers
40 views

Find the moment generating function

Find the moment generating function of $W$, when $W=X+2Y+4Z$. $~X,~Y,~Z$ are independent normal distributions $\mathcal N(1,4),~ \mathcal N(2,9) \text{ and }\mathcal N(3,16)$.
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2answers
85 views

Pre-truncation moments for truncated multivariate normal

Suppose the random variable $Y$ has a multivariate normal (MVN) distribution, and consider truncating $Y$ in some way to create $T$. Given $T$'s mean and covariance matrix, I'd like to obtain $Y$'s ...
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1answer
54 views

How do I set up a multivariate hierarchical multiple linear regression in R?

I have two continuous DVs (measurements taken on individual fish), one continuous individual level IV (fish's size), and two site-level IVs (PC1 and PC4). Sites are either take or no take. There are ...
2
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2answers
93 views

What is the difference between multivariate analysis and econometrics?

I am writing my thesis about how different factors influence stock excess returns after an M&A announcement. I haven't taken a multivariate analysis class and I have only a very basic idea of ...
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0answers
14 views

How does the Cross Validation in PRIM work?

One of the steps described in the PRIM algorithm is, after the peeling and pasting procedure, using Cross Validation to select an appropriate Box from the sequence of boxes obtained by the peeling and ...
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1answer
72 views

Compute sum of vectors drawn from multivariate normal, subject to a linear constraint

I want to compute $S = \sum_{i=1}^n x_i$ where $w^t x_i>-1, \; \forall i$ and $x_i \tilde{} \mathcal{N}(\mu, \Sigma)$ for known $w$, $\mu$ and $\Sigma$. I know $S$ can be approximated by sampling ...
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1answer
32 views

Distance measure for multi-categorical responses

I have a data set of categorical data where each question can have more than one answer. This is a toy example: question one: what did you eat today? ...

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