# Tagged Questions

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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### Path Analysis Vs Multinomial Logit

Would anyone be able to explain the logic behind using a Path Analysis over running several multinomial logits. The theoretical model I am testing has X1-3 mediating Y1. Y1 and X1 predict U1-3 (the ...
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### How to incorporate intraspecific variation in discrete characters in comparative analysis?

I'd like to run a multivariate analysis (Pavoine et al. 2011) that aims to disentagle the effect of environmental gradients on traits, considering its autocorrelation with phylogeny and space. It uses ...
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### Sequence analysis with multiple sequences

I would like to recognize different states in a sequence of multiple vectors. To make it little more clear, here is an example: I have 2 (or more) vectors in a sequence: head position(HP) and eye ...
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### How to use Taguchi method when doing online multivariate A/B testing?

I want to run a multivariate test on my website landing page. I have a click on subscribe KPI, and I want to test many different color / calls to action / positions on that button. I heard of ...
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### Test on SUR model

I have a SUR model with 22 equations, where each equation has the same 7 factors. I want to test if a coefficient (b3 in equation 1) is significantly different from another coefficient in another ...
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### Johansen cointegration test: interpret the result

I am trying to develop a stationary time series with 6 variables in Matlab. Can anyone tell me whether the 6 variables are cointegrated? The results I got are:
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### Dirichlet multivariable regression with temporal autocorrelation?

BACKGROUND: I have some animal behaviour data. The time allocated by a group of animals to different behaviours per minute was recorded repeatedly until the end of the experiment. Therefore, I have ...
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### Interpretation of DCC-GARCH output

I have done fitted a DCC-GARCH model using the dccfit function from the "rmgarch" package in R. The output is below: ...
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### Marginal normality and joint normality

Let $X$ and $Y$ be two independent standard normally distributed random variables $N(0,1)$ .If we define a new random variable $Z$ such that : Z = \begin{cases}X & \text{if} &XY > ...
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### How to analyze repeated measurements with categorical/ordered outcomes

I have the following dataset: 100 indiviuals (id) Each individual with 4 measurements at 4 timepoints time1,time2,time3 and time4 Outcome is a categorical or ordered variable 1,2,3,4. I simulated ...
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### Quantifying the most sensitive multivariate responses

I have traditionally been using the r2 obtained via different PERMANOVAs to ascertain which multivariate dataset was most sensitive to a factor consisting of two levels (e.g. impacted versus ...
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### Testing simple mediation model with two separate outcome variables

I'd like to test whether a variable mediates the relationship between an IV and 2 DVs. The DVs will likely be highly correlated, as they're essentially measuring opposite constructs. Should I do this ...
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### Can I use Bray-Curtis distance when performing MRPP or MRBP?

Can I use Bray-Curtis distance when performing MRPP (Multi-response Permutation Procedures) or MRBP (Blocked Multi-response Permutation Procedures)? [See Ch 24 of McCune & Grace (2002) for ...
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### Is this book excerpt an accurate statistical analysis of project risk?

I found this passage on the odds of a project succeeding in a book on risk management. I know this is open-ended, but is the author's math and logical reasoning correct here?
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### Obtaining distribution function for positive linear combination of independent random variables with Poisson distribution [duplicate]

Let $X_1,X_2,...,X_n,Z$ be i.i.d poisson random variables,respectively with mean $\lambda_i$ and $\lambda$ where $"n"$ is definite, $c_i\geq 0$. Assume all the parameters $\lambda_i$'s and $\lambda$ ...
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### different directions of the dimensions of multiple correspondance analysis

I have done a mca. My focus is about supplementary variable, that I want to see their behavior. This variable is significant (v.test) with the dimension 2 and 3. Both for the dimension 2 and dimension ...
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### Seeming disagreement between learning sources about linear/quadratic and Fisher's discriminant analysis

I'm studying discriminant analysis, but I'm having a difficult time reconciling several different explanations. I believe I must be missing something, because I've never encountered this (seeming) ...
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### How can I test for multivariate equivalence?

I have two sets of data and I want to test to see if they were drawn from the same population/distribution. The data sets have around 200 variables, and I want to be able to take into account the ...
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### How to determine the number of random initializations to use in non-metric multidimensional scaling?

I'm trying to determine how many random initializations (restarts) I should use when performing an nMDS ordination. I understand I want to choose the solution that minimizes the stress, but how many ...
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### Specifying the priors for multivariate MCMCglmm mixed model in R (Poisson distribution)

I am trying to build a model using MCMCglmm. Ideally, I would use a negative binomial distribution for my response; however, this is not an option in MCMCglmm. I don't know of any open-source ...
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### Easy explanation of how to fit a multivariate GARCH model (in Gretl)

I have multiple financial time series data (FX-rates, commodity prices) that have been recorded daily (without weekends) for the past six years and want to analyze their effect/influence on the stock ...
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### Multivariate asymmetric generalized gaussian distribution

I would like to write the distribution of a multivariate asymmetric generalized gaussian distribution and plot the result with Matlab. So far I was able to write the code to create a bivariate ...
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### Partial Derivatives of Function of two Random Variables with respect to the Random Variables

We have a function $G(X,Y,\theta)$ of two random variables, $X$, $Y$ and parameter $\theta$. Probability Density function of $X$ and $Y$ is given by $f_{X}$ and $f_{Y}$ respectively. Cummulative ...
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### Appropriate model to score a test dynamically?

I have a test bank of questions with particular difficulties (say, a number from 1 to 10), and people take "tests" consisting of some subset of those questions. Each question is graded on a 1 to 10 ...
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### Multilevel and multivariate statistics

I'm considering classes for next semester and I have a choice between 2: Multivariate statistics and analysis Hierarchical linear modeling and growth models I'm wondering which of these courses ...
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### multivariate point process with simultaneous occurence of jumps

I am doing some little personal research work about multivariate point process where the counting process is not simple, which means that events of different types in my counting processes can happen ...
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### Is one correlation coefficient possible for 3 variables?

I have three variables (X,Y and Z) which were measured on three different days. So, I have ...
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### What is the difference between Covariance matrix and the variance-covariance matrix

I am bit unsure whether there exist any difference at all.. Google tells me that variance-covariance matrix is the matrix where the variance is written in the diagonal of the matrix, and the other ...
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### Discriminant analysis vs logistic regression

I found some pros of discriminant analysis and I've got questions about them. So: When the classes are well-separated, the parameter estimates for logistic regression are surprisingly unstable. ...
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### Motivation befind simultaneous confidence interval?

I am bit unsure what the primary motivation for doing simultaneous confidence interval? The confidence interval for an hoteling $T^2$ should in my head take care of the things that should be taken ...
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### Combining individual terms from the predict() function

I want to merge several variables' estimate and also calculate the confidence intervals from the survival:::predict.coxph function's output. Just like the the ...
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### Why is there no assumptions about IVs' and DV's distribution in multiple linear regression

Many sources say that we do not have to make any assumptions about normality of distribution of IVs and DV. The requirement of normality applies only to the distribution of errors. I wonder why that ...
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### Multivariate analysis with repeated measurement

Unfortunately I did not get any reply yet. I have a dataset of 900 subjects. Each on them belongs to one of the 4 categories of group1 (A,B,C,D) and to one of the 5 categories of group2 (0,1,2,3,4). ...
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### Incorporating prior knowledge in machine learning?

What are recommended methods for incorporating prior knowledge in machine learning tasks? By prior knowledge I am referring to information like which features are a priori considered more important or ...
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### Finding the most important variable for a ranking problem?

I am working on a problem which I believe should be standard in statistics but unable to dig more. I have $N$ objects and two variables $x\in [0,1]$ and $y\in [0,100]$ which take different values for ...
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### correlation estimation with non identical but independent multivariate normal samples

Suppose there are $n$ k-dimensional multivariate normal distributions, each of them has the following form, with mean vector ${\mu_i}=[m_i,m_i,...,m_i]'$ of size $k$ by 1 and covariance matrix ...
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### When should we use Bayesian Anova?

I am studying Anova (and extensions) since a few weeks and am quite confused. It looks to me that many users are struggle with difficulties related to non-gaussianity/inhomogenous-variance/missing ...
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### Stress testing modeling

I try to make an analysis of time series to develop an econometrics model and then estimate the prob. of default with a stress scenario. About the model, i have some question about the step on which ...
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### negative F value in 2-way permanova

I am performing a permanova using a bacterial OTU table (16S-metagenomic data) and I want to examine 2 factors if they affect the composition of my OTUs each of the factors is affecting significantly ...
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### Overview of multivariate statistics for chemometrics (e.g., Raman spectra)

I am looking for an overview of multivariate statistics for chemometrics. I'm reviewing a number of articles that for the most part are analyzing a large number (300+) of various spectra (IR, UV-Vis, ...
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### Multiple regression model from factorial experiment

Given the following factorial experiment, how does one construct an 'equivalent' multiple regression model? This appeared in an exam and left me almost clueless. \begin{align*} \mu_{11} &= \mu + ...
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### multivariate analysis of dependent data

I have some diet data I am analyzing that was collected in different locations at different times (over 3 years). The nature of the sampling resulted in multiple predators at the same location. The ...
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### Best ways to visualize multivariate data with missingness

I have a huge dataset that is multivariate, but not all the samples have data assigned in certain variables. To be more specific, I have data of microbial contamination (in logs) of milk (in two ...
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### multivariate or regular quality control

I want to conduct quality control. Just say the observed variable is X. X consists several indicator variables in it ; X1, X2 and X3. Should I using multivariate quality control method? or combine the ...
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### Contradicting results of a multivariate and pairwise/bivariate Johansens reduced rank test

I was performing Johansen's reduced rank test on a group of 3 commodity price series $X$, $Y$, and $Z$ ($n=3$; lag-length selection based on the SBIC but at least 2; unrestricted constant model (case ...
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### Sampling and design problem

Suppose there are quite many (hundreds/thousands) variables, $X_1$,...,$X_m$, in a computer model, following some multivariate distribution. How can we get a sample of these variables that has good ...
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### A multivariate data problem in search of a technique

About four years ago I took a graduate course in multivariate statistics. Now I'm faced with a data problem which is ringing a bell about something covered toward the end of the semester but even ...
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### Resources for multivariate normal distribution

Is there any particular book/online notes that I can use to better understand the multivariate normal distribution? I could also do with a bunch of questions and solutions.
I was given the following question as a practice question for an exam: Let $X \sim N_k\left(\mu,\Sigma\right)$. For (deterministic) $l \times k$ matrix $A$ and $m \times k$ matrix $B$, show that $AX$ ...