Questions tagged [partial-correlation]

Partial correlation is the correlation between two variables when some other variables are controlled for. An example is the partial autocorrelation function in time series.

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Difference between partial correlation and mediation?

If partial correlation looks at the correlation between variables A and B when controlling for C, how is this different from looking at the relationship between A and B with C as a mediator?
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Is there a test for difference in partial correlations without distributional assumptions?

My colleagues and I have what I believe is a niche statistical dilemma. We are interested in whether anyone knows of a standard approach, and if not, if our ad-hoc strategy can be improved. We have ...
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Partial covariance matrix after linear transformations

Let $X=(X_1,\ldots,X_n)$ and $Y=(Y_1,\ldots,Y_m)$ be two multivariate random variables. We denote with $\Sigma(X)$ the $n\times n$ covariance matrix $\text{cov}(X_i,X_j)$ and with $\Sigma(X,Y)$ the $n\...
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Definition of partial correlation

Here (page 415) https://www.stat.cmu.edu/~larry/=sml/DAGs.pdf I found this definition: which confuses me. I am used to see $E[*|Z]$ as a ($Z$-measurable) random variable and as far as I know the ...
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Derivation of pair-wise relationships expression of βyx.z and σyx.z

I'm reading Linear Models: A Useful “Microscope” for Causal Analysis. In the article, when discussing the beta coefficient and standard error of partial correlation, the auther mentioned "express ...
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Proof of Wright’s path-tracing rules

I have a path diagram. According to Wright’s path-tracing rules, correlation of B & D = b + a*f. However, when I tried to proof the above result by solving ...
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Help understanding the terms in a partial correlation equation

I am trying to follow a protocol to calculate partial correlation values for the above matrix. The axes are both the amino acids making up a protein, with the meat of the matrix showing Pearson ...
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Does conditional independence mandate zero partial correlation?

A and B are conditionally independent random variables given C. Does this necessarily imply partial correlation coefficient of A and B adjusted for C (rho_AB.C) is zero? Can you give an example if its ...
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Is Partial Correlation useful for noisy data?

Explaining The Problem Important question in data analysis is testing observed relationships for confounding factors. Partial Correlation is a metric designed to do specifically that. The general idea ...
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ANOVA for multicollinear data? Partial Correlation?

I have experimental data. The data consists of simultaneous observations of some external variable $Y$ and multiple intrinsic variables $\vec{X}$. It is known that all $\vec{X}$ are strongly ...
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How to compute p-values for shrinkage estimates of partial correlation?

I am using the pcor.shrink function from the corpcor R package to compute the shrinkage estimates of partial correlation ...
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Partial effects plot - error update

I would like to replicate JMP's profiler on RShiny tool but I'm not sure how it works. JMP's profiler is interactive partial effect plot like the one bellow Now, if I change the level of hp and keep ...
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Partial Cross-Correlation, and its relationship to Granger Causality?

Definitions: Granger Causality (GC): To the future of the target channel $y(t)$ fit past values of the target channel $y(t-1)$, ... $y(t-n)$ To the future of the target channel $y(t)$ fit past values ...
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After a factor analysis, is there a way to see how much of the relationship between variables is from the latent factor?

Lets imagine a factor analysis on 20 different variables. X1, X2 and X3 all load onto Factor 1. X1 and X2 are highly correlated. Is there a way to know if the relationship between X1 and X2 is: coming ...
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Conditional kendalls vs partial kendalls

I read about conditional kendall's tau for independent test. I also found partial correlation kendalls tau test. My question is, are they different? If yes, how? I tried to calculate the conditional ...
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mutual information and maximual infomation coffecient

I am interested in calculating the strength between random variables. I found that the maximal information coefficient is one of the good methods to use and it is robust to the mutual information ...
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How to test the difference between dependent partial correlations in the presence of autocorrelation?

Background and what I am trying to do: I have a single dependent variable $Y$, and $K$ independent variables of interest ($X_1, X_2... X_k$). I also have a single independent variable of non-interest, ...
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Group-level analysis of incremental predictive power of two correlated variables

Imagine you have two variables X1 and X2 which both predict an outcome Y across different groups (e.g. the size and song length of a bird positively predict its reproductive success across a range of ...
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$p$-Values: Standardized coefficients vs. partial $R^2$ vs. $\Delta R^2$

In this excellent answer, the definitions of, and differences between, the three quantities in the title of this question are laid out. My question concerns the relationship between their $p$-values. ...
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Generalisation of the formula for a semi-partial correlation coefficient

There are several places (e.g. this SE answer), where the formula for the semi-partial correlation coefficient of a variable $x$ with $y$, controlling for another variable $z$, say, is given as $$ r_{...
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What is the difference between partial correlation and removing the linear trend?

From this link https://en.wikipedia.org/wiki/Partial_correlation, the partial correlation of X and Y can be computed while controlling for Z. My question is if I removed the regression line between X ...
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Can a partial correlation test for causation?

I am reading a study and they find no effect of intervention group on their outcome of WM integrity. They then do a partial correlation (controlling for age, gender, attendance) to see if there is a ...
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How to prove the equivalence of partial correlation and coefficient of partial determination?

I am taking a regression course. I do not know how to prove these formulae are equivalent. $$ R_{Y1|2}^2 = \frac{SSE(X_2) - SSE(X_1, X_2)}{SSE(X_2)} $$ $$ R_{Y1|2}^2 = \frac{(r_{Y,X_1} - r_{Y,X_2}r_{...
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Measures of correlation / influence for predictors with bounded outcome

I'm doing a systematic review of epidemic models that project "the % reduction in incidence ($Y$) after K years" given a particular simulated intervention. The models include various ...
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To estimate a Markov random field, do we have to assume a DAG generated the data?

Even if I believe that I understood the Markov Random Fields and DAGs separately, I encountered a question that I have written in the title and cannot come up with a clear-cut answer. Can you help me ...
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Is it possible to reconstruct a regression coefficient from a truncated regression output?

I am trying to help a friend solve an exam question and I fear that I am missing the obvious solution. Problem: Students are provided a regression output from R. Just a simple linear OLS estimation ...
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Difference between autocorrelation and partial autocorrelation

I have read some articles about partial autocorrelation of time series and I have to admit, that I do not really comprehend the difference to a normal autocorrelation. It is often stated that the ...
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Partial correlations with independent variable used as control?

In my recent study I had one independent variable (IV, 2 levels) and a number of different DVs. The aim was to assess the relationship between teamwork (main response - continuous), presence (...
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Inconsistent results from partial Mantel test on (non)distance matrices

Currently I am trying to look at the correlation between three matrices of ecological data. All three are forms of distance matrices (two matrices of pairwise community dissimilarities and one matrix ...
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225 views

Conditional independence, partial correlation

In my work, I am modelling graphs by measuring the zero- and first-order conditional independence between the variables. That is, if there are three variables, say $A$,$B$ and $C$, an edge between the ...
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Why does uncertainty of the autocorrelation coefficient increase as lag increases?

The Python module statsmodels contains functions for ACF and PACF. Below is an example from the docs with a plot that shows the (zero-centered) confidence ...
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Help understanding Autocorrelation and Partial Autorcorrelation (PACF)

I understand the layman concept of PACF - it is the correlation with the linear dependence of the earlier lags removed. However, I am confused as to how this relates to Autocorrelation. Consider ACF(2)...
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partial correlations

Our CGPA (Variable 1) is influenced by Intelligence (Variable 2) ,and examination self -efficacy (variable 3) . Zero order correlations between these three variables are: r12= .50, r13= .60 and r23= ....
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Controlling for baseline in difference scores

I have a dataset of participants receiving various frequency of intervention. We want to see if those who received more intervention had greater improvement between pre-intervention and post-...
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How to equalize results of Partial Correlation Analysis when number of factors exceeds rows?

I didn't notice this bug until I had a dataset where the number of factors was greater than my number of rows. Which lead to an overfitted perfect model when doing partial correlation (i.e. compare ...
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Partial correlation for dichotomous variable in Python

I would like to compute the partial correlation between a target categorical variable y (= A or B) and a number of numerical (discrete or continuous) predictors. In the following post: https://...
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How to run a partial correlation analysis with ID as factor?

I want to make a within-individual correlation between several molecules and molecule X in a repeated measure design, there are 8 measurements per individual. If I have understood this correctly I ...
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Proportion of variance unexplained by one variable but explained by another variable

Suppose you have an dependent variable $ Y $ and two dependent variables $ X_2 $ and $X_3$. You want to know the proportion of variance unexplained by $ X_2 $, but explained by $X_3$. How will you ...
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Partial correlations or multiple regression model

I am interested in the relation between two variables ${A}$ and ${B}$ while controlling for several covariates. Some of these covariates are strongly correlated with ${A}$ and mildly correlated with ${...
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partial correlation for logistic regression

I am looking for an equivalent of partial correlation but for logistic regression. I.e., I want to have a measure of an effect a variable have on the outcome, independent of other variables in the ...
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comparing two partial correlation coefficients (spearman)

I have carried out the following two spearman partial correlations using the "ppcor" package in R: -- Coefficient 1 = Correlation of A1 with B controlling for C; -- Coefficient 2 = Correlation of A2 ...
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Multiple regression and partial correlations with more than 3 predictors

I need to estimate slopes of a multiple regression that has 5 independent variables: $$y = \alpha + \beta_1 x_1 + \beta_2 x_2 + \beta_3 x_3 + \beta_4 x_4 + \beta_5 x_5$$ The challenge is to estimate ...
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Correlogram With Points Beyond -1 and +1?

I made a partial correlation plot of the residual of a dataset using python. I got the pacf graph below with some correlation points going to 2 and -1.5. Everyone finds this strange, does someone have ...
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Trying to understand partial R-squared

I'm trying to understand partial R-squared as computed by package rsq. See the reproducible example on the standard data set: ...
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Can partial correlation help to highlight variable's meaning in the analysis?

I have an interesting problem (interesting at least for beginners like myself :) ). I have a dependent variable Y (class-variable, 2 possible values 0 and 1). I have multiple variables that all ...
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Which test is suitable in below situation?

I want to calculate the correlation of two continuous variables, unfortunately both of them are not normally distributed. (by using Shapiro-Wilk test) There are two categorical confounding variables ...
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Real life use of acf and pacf

I understood ACF usefulness, with a temperature example... If we have a temperature time series, it is useful to know (for example) how correlated the temperature of past month is with this month. ...
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Recurrent PACF expression on ACF and PACF of lower order

Let $\rho_{partial}(n) = Cor(Y_t, Y_{t-n}|Y_{t-1}=\mu,\cdots Y_{t-2}=\mu, Y_{t-n+1}=\mu)$ where $\mu$ is the mean of stationary process. I know that $\rho_{partial}(1)= \rho(1)$ and that $\rho_{...
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What do these ACF and PACF plots tell you about AR and MA orders?

The residual of a seasonal_decompose (from python's statsmodels) yields the following ACF and PACF plots The sampling frequency of the time series is hourly, so the ACF plot hints at daily (24 ...
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Do control variables in a regression analysis cause collinearity?

This is something that bothers me for quite some time, but I didn't find yet a satisfactory answer. I hope that the wisdom of the people hear will help me to clarify this: In a multivariate ...