# Tagged Questions

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

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### 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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### 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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### 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, ...
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### 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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### Statistics for multi-test replicated correlation analysis

I'm analyzing pairwise correlations of time series between two different types of microarrays done for several samples as biological replicates. So, I have M1 number of variables on type 1 array, M2 ...
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### Canonical correlation analysis with rank correlation

Canonical correlation analysis (CCA) aims to maximize the usual Pearson product-moment correlation (i.e. linear correlation coefficient) of the linear combinations of the two data sets. Now, consider ...
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### Smoothing 2D data

The data consist of optical spectra (light intensity against frequency) recorded at varying times. The points were acquired on a regular grid in x (time) , y (frequency). In order to analyse the time ...
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### 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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### Choosing the right test

I am having trouble choosing the right test to analyze my data. I have recorded six behaviors every ten minutes and pooled them into one data set. I would like to compare the time spent in one ...
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### Constructing a measure versus using an interaction

My dataset is sports data and the outcome variable is wins in a season and I am trying to see the affect of the characteristics of the players on the team on this outcome. My question is, is it easier ...
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### 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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### 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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### 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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### 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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### Prediction and explanation of user rating based on multiple criteria

I'm trying to figure out a way to both predict how a user would rate a certain document, as well as an explanation of why certain documents are rated a certain way. A user is represented by: ...
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### How to analyze data with more than one associated categorical dependent variables?

I have some dependent variables related to the growth of a company having categories like (e.g. for variables indicating net profit, financial turnover etc.) (1) decreasing, (2) stable, (3) ...
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### Regression with some associated ordinal dependent variables

I have some associated categorical dependent variables that are ordinal in nature (with 4 or 5 categories). If I want to see the effect of a set of independent variables (which can be both continuous ...
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### Multivariate linear regression in R

I an trying to perform a multivariate linear regression in R. I have two dependent variables (outcomes) and one independent variable (predictor). The model would be something like: ...
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I want to perform quadrat count analysis on several point processes (or one marked point process), to then apply some dimensionality reduction techniques. The marks are not identically distributed, ...
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### How to test for differences in 3 related measures assessed pre- & post- treatment on the same sample?

I am designing a study to compare whether one specific treatment improves Quality of life. I am using a convenience sample ($N=20$). I hope to administer three ...
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### Help with choosing a DM method [closed]

I'm a student using Oracle for a data mining project, and i'm wondering if you can assist me with picking the right DM method for my data set. I'm doing an electricity consumption prediction and i ...
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### Distribution of random variable

The chloride concentration at depth $x$ mm at time $t$ is: $$\text{C}(x,t)=\text{Cs}(1-\text{erf}(x/(2(D*t)^{0.5}))$$ where $\text{Cs}$ is chloride surface concentration with Lognormal ...
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### PCA and varimax references?

After doing PCA it is common that the first component describes the largest part of variability. This is important in i.e. study of body measurements where it is commonly known (Jolliffe, 2002) that ...
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### Dealing with 'Don't Know' answers for a categorical outcome variable

I have a survey data with categorical outcome variable (yes, no, don't know) which reflects the acceptance of some situation by respondents. My concern is how to deal with Don't know answers, I really ...
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### Proof for two-sample Hotelling $T^2$ statistic?

I've been reading "A primer of multivariate statistics" by Richard J. Harris, page 546, which shows how to derive the Hotelling $T^2$ statistic, after seeing this related but different question (I ...
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### Two IVs (schools) and 3 IVs (grade levels in each) where there are 2 DVs (math and reading scores)

Is MANOVA the correct test? I am looking at 3 grade levels in each of the two middle schools. I want to compare the standardized scores (reading and math) of students in each grade level to the same ...
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### Errors in Variables and Deming's multivariate regression: Assumptions

There has been extensive literature that puts forth a standard set of assumptions for the Ordinary Least Squares (OLS) estimator. I am very interested in working around the two classical problems of ...
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### How should I analyze a data set with 1 IV and 2DVs (all scale variables)?

Hello wonderful statisticians, I'm writing a proposal for a dissertation where I'd like to look at whether heart rate can predict 1) narrative coherence (as judged on a scale - but could also be ...
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### PCs scores from Correlation and Covariance matrices through matrix computations and prcomp

I'm want to get PCs scores through matrix approach. My calculated PCs scores for correlation matrix matches with prcomp results but the PCs scores for covariance ...
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### geographic distance and mahalanobis distance

I am trying to match individuals based on monthly consumption and geographic consumption in a dense metro area. Essentially I want to create treatment and control pairs with the having both geo ...
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### Is there a multivariate version of logistic regression?

Based on readings with logistic regression, it appears that you could use this analysis to make predictions about categorical variables. Does logistic regression allow you to predict multiple ...
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### Interpretation of MDS factor plot

Suppose I run Multidimensional Scaling and I got the resulting plot. Can anybody suggest me how to interpret the plot. Please find one of my result below. Here I've 5 concepts which I run the MDS ...
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### Simulated single value based on multiple chains in RJAGS

I am using RJAGS to simulate the posterior distribution of event that a certain candidate will win the presidential election. I need to find the actual percentage that one of the candidates will have. ...
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### Draw conditioned beta distributed random variables

I am trying to draw a beta distributed random variable (recovery rate), conditioned on another beta distributed random variable (default rate). I have shape parameters $(\alpha= 0.6, \beta = 55.5)$ ...
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### How to find quantiles for multivariate data using R?

Quantile for a single variable is easy to implement in R. However, it is not an easy task to quantile for multivariate data. There are several papers have been proposed to quantile for multivariate ...
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### Moment generating function of the inner product of two gaussian random vectors

Can anybody please suggest how I can compute the moment generating function of the inner product of two gaussian random vectors, each distributed as $\mathcal N(0,\sigma^2)$, independent of each ...