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29 views

Understanding Partial Correlation

I'm having some trouble fully understanding partial correlation and I was wondering if some of you can shred some light on my confusion. Let's consider the following scenario: It is a known fact ...
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39 views

Is there a relationship between partial correlation and spectral decomposition?

I am wondering if there is a known relationship between the matrix of partial correlation (for example, I would like to regress out the influence of the first PC on the data) and the correlation ...
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1answer
62 views

What is the relationship between regression and partial correlation

There is a well-answered question here. But unfortunately, I don't even understand how the first equation in the answer is derived. Could someone help explain that? $$\text{Beta:} \quad \beta_{x_1}...
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25 views

Correlation analysis with compound variables: controling for a second correlation

We want to test for the existence of a correlation between a variable $X$ and a second variable $Y=ab$ ($a$ and $b$ being independent variables representing observational data). We know that the ...
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11 views

how to prove the PACF(k) equals the regression coefficient of last lag (assume stationary process)

assume AR(p), $$ y_t = \phi_1y_{t-1}+\phi_2y_{t-2}+...+\phi_ky_{t-k}+\epsilon_t $$ $$ corr(y_t, y_{t-k}|y_{t-1}...y_{t-k+1}) = \frac{cov(y_t, y_{t-k}|y_{t-1}...y_{t-k+1})}{\sqrt{var(y_t|y_{t-1}...y_{...
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1answer
97 views

What is the difference between the anti-image covariance and the anti-image correlation?

What is the difference between the anti-image covariance and the anti-image correlation? How are the matrices of these coefficients computed, and what is the meaning of their elements?
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8 views

True or false: γ12.3 and γ12 (and similar comparisons) have the same sign

I know that $y_{12.3}=\frac{y_{12}-y_{13}y_{23}}{\sqrt{(1-y_{13}^2)(1-y_{23}^2)}}$ $y_{12}= \frac{\Sigma x_{2i}y_{i}}{\sqrt{\Sigma x_{2i}^2 \Sigma y_{i}^2 }}$ I can see that the denominator is ...
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288 views

How would I interpret this correlogram from EViews?

This is a correlogram on stock market data generated in EViews. How would I interpret it, in regards to AR and MA? Also, why are all my p-values 0? I would assume they wouldn't be as stock markets ...
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1answer
28 views

Removing/Adding the effect of third variable

If two variables say X and Y with 100 observations are having a relationship(significant correlation) and we know that the third variable Z is having some effect on the that relationship. Then how can ...
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22 views

Is ANCOVA partial or semi-partial?

I thought I had it figured out, but I just wanted to verify: I understand that HMR is just like running a series of ANCOVAs after each level. Am I right to assume that when we run an ANCOVA or HMR, we ...
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13 views

Is there a way to find the components that contribute in a relevant way to the correlation?

Given two vectors $x$ and $y$ of size $N$, suppose that they are not correlated in the subspace composed by $M$ components, but are correlated in the remaining $F=N-M$ components. I would like to ...
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11 views

Is it possible to calculate multiple correlation when predictor intercorrelations are known?

I have two tables with correlations between 7 variables (Var1-Var6 and Y). The first one mentions the correlations of each of ...
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0answers
34 views

PACF MA(1) via correlation of prediction errors

It is known (see e.g., Brockwell and Davis, Introduction to Time Series and Forecasting, p. 95) that the $h$th partial autocorrelation $\phi_{hh}$ of a stationary process can be derived by first ...
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10 views

Multi-response Multivariate Coefficient of Determinations

For the linear model, $$ \bf{Y} = \mu_{Y} + \bf{B}^t \left(\bf{X}-\bf{\mu_X}\right) + \boldsymbol{\epsilon} $$ Where, $\bf{Y}$ is a $n \times q$ matrix of $q$ responses, and $\bf{X}$ is a $n \times ...
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12 views

See if there is a significant difference between regressions for two groups

I'm trying to copy the methods of a paper similar to my study, and I want to check if got it right. It refers to the test as a simple slope test. Mine, like theirs, is a regression with one ...
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1answer
147 views

Interpreting Ljung -Box test results from statsmodels.stats.diagnostic.acorr_ljungbox function (python)

I have a set of daily trading strategy returns and I am trying to prove whether the daily returns are autocorrelated at all. I am hoping to fail to reject the null hypothesis that they are not ...
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19 views

Hierarchical Multiple Regression & Partial or Semi-partial correlation

When conducting a hierarchical multiple regression, I understand that all covariates are entered into the first step in order to control for them. However, does SPSS control for the covariates using a ...
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22 views

Partial Correlation - Quantifying the effect of removing confounding variables on the correlation

I'm conducting partial correlation in order to quantify the association between two variables, X and Y, after the effect of a set of confounding variables Z has been removed from both X and Y. In ...
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2answers
122 views

Can we identify ARIMA model without looking at ACF and PACF plot?

Can we identify ARIMA($p,d,q$) model without looking at the ACF and PACF plots? I am trying to write a generalized R programme for fitting time series models. We may find out the orders $p$, $d$ and $...
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26 views

Partial correlation, semi partial correlation and what's this?

Assuming that I have IV x1, x2 ... xn and DV y: regressing x1 on (x2 + ... + xn) yields residuals e1, regressing y on (x2 + ... + xn) yields residuals ey, Then if I understand it correctly, r(e1,y) ...
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64 views

Interpretation of Mantel r correlations

I am using mantel in R package Ecodist to perform a series of partial mantel tests. I am examining the correlation between a species composition (Bray-curtis ...
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2answers
40 views

How can including an IV uncorrelated with the DV improve a multiple regression model?

Let's say $Y$ is my DV, and $X_1$,and $X_2$ are IVs: \begin{align} \newcommand{\Cor}{\rm Cor} \Cor(Y,X_1) &= 0.7994172 \\ \Cor(Y,X_2) &= -0.00041 \\ \Cor(X_1,X_2) &= 0.505 \\[...
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16 views

Estimation of partial correlations strength after/during Glasso

I've been asked to run some estimations of partial correlation using the glasso algorithm. Luckily, now I'm in a situation where my number of data points is not that low ($N > 2\times p $), with N ...
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54 views

Difference between Partial Correlation and Semi-Partial Correlation

Partial Correlation is when there are three things connected each other(A,B,C), when comparing A and B, we should think about the effect of C so when we calculate the pure relationship between A and B,...
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28 views

Is partial Pearson correlation considered as a linear measure of association?

I know Pearson's correlation is considered to be a linear measure of association, for it is intimately linked to simple least square regression. It is known to have poor performance on non-linear data ...
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0answers
11 views

Is the following regression procedure equivalent to semi-partial correlation?

Take the residuals of A (as explained by B), regress these residuals against C. Is this equivalent to the semi-partial correlation of A on C, holding a fixed against B? (Excepting the usual ...
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1answer
181 views

How could I get a correlation value that accounts for gender?

For instance if I were trying to relate Age and Height, I would do something like this: df <- data.frame(Age, Height) cor(df) How could I get Pearson's r ...
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137 views

How to report partial correlation results?

I received the proofs of a scientific article and the editor changed the way we reported partial correlation results from symbol r = ... to ...
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3answers
51 views

Why do ACF and PACF plots tend closer to each other with the increase of observations?

I have an AR(2) process: $Y_t=0.6Y_{t-1}+0.1Y_{t-2}+\varepsilon_t$. When I plot its autocorrelation function & partial autocorrelation function on the same plane, I notice that their separate ...
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99 views

performing a partial correlation using cosine similarity

I wonder if it's possible to carry out a partial correlation using correlation measures other than the Pearson or Spearman correlation. In particular, I want to assess the cosine similarity between X ...
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1answer
37 views

Two moderate zero-order correlations leading to two weak to null partial correlations: What does it mean?

I am trying (operative word) to validate a scale composed of two highly correlated (~.7) subscales, let's call them A and B. In order to establish convergent validity with other measures, I am looking ...
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208 views

Testing for conditional independence: What's the correct way?

My goal is to check if two variables $X$ and $Y$ are conditionally independent given $Z$. For simplicity, let's assume the joint distribution is multivariate normal. In this case, we can compute ...
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1answer
347 views

How do I interpret this ACF and PACF plot?

I am very new to time-series analysis and have got some time-series data regarding product prices. The data set is monthly data collect since 1993 to 2014. I have tried plotting the ACF and PACF but ...
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32 views

How to describe this study design + MLM adequate for analysis?

I have recently encountered a rather particular study design and wonder how it could be adequately described and if a multilevel model should be used to analyze it. There are 3 factors in this ...
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1answer
75 views

Correlation among two variables shared by a third set of variables

I am interested in a measure that quantifies the correlation between two variables X,Y that is also shared by a third set of variables Z. That is, a measure that is in some way the converse of the ...
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25 views

meaning of partial correlation in regression with no significant association

When I have a simple multivariate regression with two independent variables $$y = \alpha_0 + \beta_1 X_1 + \beta_2 X_2 + \epsilon $$ and I want to compute the partial correlation squared ($pr^2$) of ...
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1answer
50 views

Deriving Pearson correlation from regression results

If the common regression results as typically reported in an empirical primary study (sample size n, regression coefficients (Betas), t-statistic, p-value, R^2, adj. R^2) are given in the case of more ...
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3answers
308 views

In linear regression, what does $\beta_1 = 0$ really mean?

If granted omniscience and we know that $\beta_1$ in a multiple linear regression model is truly 0, what does that mean in words (and math notation)? The model is: $Y = \beta_0 + \beta_1X_1 + \...
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0answers
89 views

Constructing Bayes Factor comparing a single correlation coefficient in the entire sample vs. separate coefficients by group?

I have a sample consisting of 4 independent groups of participants. For any two variables within the sample, I would like to quantify the improvement in fit to the data from estimating a separate ...
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1answer
1k views

Why does inversion of a covariance matrix yield partial correlations between random variables?

I heard that partial correlations between random variables can be found by inverting the covariance matrix and taking appropriate cells from such resulting precision matrix (this fact is mentioned in ...
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0answers
124 views

Copulas for generating uniform random variables with correlations

I want to generate uniform random variables which have a correlation structure defined by a graph i.e. a variable is only correlated with its neighbors in the graph and is uncorrelated with the rest ...
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2answers
3k views

ACF and PACF Formula

I want to create a code for plotting ACF and PACF from time-series data. Just like this generated plot from minitab (below). I have tried to search the formula, but I still don't understand it ...
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1answer
27 views

what's the definition of partial correlation for a population?

is partial correlation only defined for a given sample? the definition based on residuals as on wikipedia seem to imply that's the case. is there a population definition for partial correlation?
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41 views

Semi partial correlation importance variables

I have some SAS code that is used to calculate the importance of variables using semi-partial correlations: ...
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1answer
346 views

How to interpret redundancy?

I have trouble making sense (i.e. real-world sense…) out of some of my results. I have Y and X1 and X2 for different geographic areas. Meaning they are the same variables, but their actual values are ...
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127 views

Partial Correlation VS. Correlation Threshold in brain network graph

Partial correlation (or inverse of covariance matrix) and correlation threshold are two common methods to construct the brain network in fMRI data. Theoretically, partial correlation should perform ...
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1answer
229 views

Get correlation matrix of 3 variables from any combination of 3 simples/partials

Here is the situation. (This is not a homework problem.) I am writing a program that does Cool And Interesting Things starting with a correlation matrix among 3 variables: call them $X$, $Y$, and $Z$....
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1answer
46 views

Partial correlations among three distance matrices

I am trying to test the hypothesis that related species should deviate more in niche space the more they overlap in geographic space. In other words, related species either forage similarly and don't ...
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262 views

Reporting Fixed Effects as (partial) correlations?

I'm doing a linear mixed effects analysis in which I'm really only interested in one of the fixed effects. I have several other fixed effects and a random intercept term, but none of them are relevant,...
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100 views

Strange: Partial Correlation changed correlations values to be negative?

I am trying to investigate the correlation values. A big problem happens. The method I used is in corpcor package in R. I have a column as missing data. I firstly calculate the correlation matrix. ...