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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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Does Partial Correlation Affect Likelihood of Multivariate Normal? [duplicate]

Suppose I have a 3-dimensional multivariate normal distribution characterized by the following variance-covariance matrix $$ \begin{bmatrix} V_{X} & C_{XY} & C_{XZ} \\ C_{XY} & V_{Y} & ...
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Constructing Joint Multivariate Normal Distribution from Marginal Distribution (detrended data)

I have two n-length data vectors $X_1 \sim N(\mu_{1},\Sigma_{1})$ and $X_{2} \sim N(\mu_{2}, \Sigma_{2})$ which may or may not have a covariance. To see whether they do or not, I detrend them by ...
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How do you pronounce the notation for partial regression coefficients?

I've been working through Causal Inference in Statistics: A Primer and have hit a bit of a roadblock in my understanding when on page 24 the authors introduced the following notation for the partial ...
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Is partial correlation analysis in spss reasonable [closed]

I had two continuous variables, neither of which were in line with normal distribution. spearman correlation analysis found moderate positive correlation (r=0.597). Then ...
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Partial Correlation and Partial (Linear) Regression

Consider the linear regression model $$\boldsymbol y = \alpha + \beta \boldsymbol x + \gamma \boldsymbol z + \boldsymbol u,$$ and denote the OLSE of $\alpha$, $\beta$ and $\gamma$ by $\hat\alpha$, $\...
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Partial Correlation and 1 Categorical Control Variable with 3 Categories

I'm trying to calculate the partial correlation between continuous variables $X$ and $Y$ while controlling for $Z$ (a categorical variable with three possible categories). Tutorials and answered ...
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Meta-analysis: estimating partial correlation coefficients using estimates from multi-level analyses

I would be very grateful if someone could offer some ideas or point to relevant literature on the calculation of partial correlation coefficients (PCCs) using estimates from multi-level analyses. ...
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Random correlation matrices

Suppose that we simulate random $n\times n$ correlation matrices by assigning iid $U(-1,1)$ random variables to all off-diagonal entries and accept matrices $\boldsymbol\Sigma$ that are positive ...
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Partial correlation with random effects

Partial correlation analysis allows one to assess the correlation between a dependent variable and an independent variable given a set of covariates. Some pairs of observations in my data are related ...
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Using Partial Correlations and Correlations to calculate each other's values

EDIT: I have a correlation matrix with some known values and some unknown values, and i have a partial correlation matrix with the exact opposite known and unknown values. For example, my correlation ...
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How to interpret a partial r statistic?

I am not sure how to interpret a partial r statistic in a research paper I am reading for my class. I’ve attached a photo of the table provided by the researchers but cannot figure it out. I’m not ...
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Compare effects in a small sample

I would like to analyse whether measures A, B, and C have a different influence on a measure D compared to a measure X on D. My exploratory hypothesis is that A, B, or C could influence Z negatively ...
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Controlling for a Variable, do not know if it is a moderating variable

I conducted a Spearman's correlation to determine if there was a relationship between emotional clarity and cognitive empathy. I found that they were positively associated, but the relationship was ...
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How to use partial correlation on compositional (counts) data? (e.g., as described in Erb et al. 2020)

I've read through this paper: https://www.sciencedirect.com/science/article/pii/S2590197420300082 Which introduced me to the concept of partial correlation. I typically use Proportionality when ...
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Should partial (spearman) correlation be used on a time series data?

I'm trying to adapt my workflows to timeseries datasets and stumbled across this youtube video: https://www.youtube.com/watch?v=OpAf4N582bA It discusses partial correlation and it seems like a useful ...
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How exactly do I create a partial regression plot to view the true effect of x on true y?

When creating a scatterplot by plotting each variable in a linear regression against y, we are essentially treating all regressors to be linearly independent. If regressors have multicollinearity, for ...
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Partial spearman correlation with complex survey data

I'm looking for info on how to compute both the partial spearman correlations and p-values for complex survey data. There was a similar question for pearson correlations here: Partial correlation ...
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Selection of covariates for partial correlation?

Are there any recommendations on procedures to identify relevant variables for a partial correlation between $r(X, Y)$? To me, it appears most reasonable to only include those $Z_1, Z_2,\ldots,Z_n$ as ...
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Precision matrix and conditional uncorrelatedness

Let $\mathbf{u}_t = (u_{1t},u_{2t},\ldots,u_{pt})^{\prime}$ be a $p \times 1$ (stationary) random vector, and let $\mathbf{\Sigma}_{u}$ be the covariance matrix of $\mathbf{u}_t$. Further, denote the ...
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The sign of the partial correlation coefficient

The sign of the partial correlation coefficient is consistent with the sign of the corresponding estimated parameter. For example, in the estimated regression equation $\widehat{Y}=\hat{b}_{0}+\hat{b}...
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Relationship between beta and t-value in Shen (2018)

As far as I know [source], $$t_{\widehat{\beta}} = \frac{\widehat{\beta}}{\widehat{SE_{\beta}}}.$$ It means the sign of the t-value should be the same as the sign of beta. In Table S1 of Shen (2018), ...
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Distributions of random (partial) correlations drawn from a given data matrix

Background: Let $X=[x_{j,k}]_{j=1,\ldots,p, k=1,\ldots,n}$ be a $p\times n$ data matrix. Each column is an i.i.d. $p$-dimensional centred random vector. One can compute the sample covariance matrix $$...
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Bivariate correlation across subgroups

I have several variables and I would like to test for possible linear correlations between. However, the data is across 2 groups, and there is a significant group difference in these variables. I know ...
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Can I calculate the correlation coefficient from the beta of fixed effects in a linear mixed model?

I would like to determine a partial correlation from fixed effects in my linear mixed models. If i would run a model for example $Aij = \beta_0 + \beta_1X + \beta_2Y + \beta_2Z + ui$ + ϵij Can I ...
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Partial correlation coefficient in terms of student's t [duplicate]

I would like some help proving this expression of partial correlation in terms of student's t : r(yx.efd.....p)² = t²/[t²+n-k-1] Can you please direct me to a source explaining how to go about this? I ...
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The generalisation of the expression of partial correlation coefficient

I hope you're doing well. How do we use this expression of generalised partial correlation coefficient? I struggle with putting it into work in practical examples of multiple regression models. We ...
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Finding the partial intraclass correlation

How do I calculate the partial correlation with an intraclass correlation? I tried asking earlier, but provided too much detail because it’s not easy to explain what I mean in a short or simple way. I’...
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Confused about partial intraclass correlation

Suppose the correlation between baldness scores in group 1 (fathers) and group 2 (sons) is 0.5. Furthermore, let the correlation between DHT and baldness scores in group 1 (fathers) be 0.4, and the ...
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Does increasing partial correlation covariates affect power?

I'm trying to characterise the relationship between variable A and B. I know the relationship is confounded by age, and maybe also variable C. The partial Spearman correlation coefficient between A ...
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Correlation controlling for group-level variable

I have reaction time data from a repeated measures design. Each participant completed 24 trials and gave four reactions per trial. I want to calculate two difference scores from these four raw ...
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Partial Correlation with Nominal/Categorical Variable

Is there a method to do a partial correlation with a nominal/categorical variable? If so: What is it called and how would you do it in R?
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Can we isolate the effect of two different control variables in a semi-partial correlation?

I know that we are able to use a partial correlation when we want to correlate X and Y but Z affects both of them and that we may use a semi-partial correlation when we want to correlate X and Y and ...
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How to interpret ACF and PACF in time series?

In this following monthly sales time series, how can I interpret ACF and PACF? STL Decomposition ACF: PACF:
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How to turn many variables into one for the PACF equation

I have been trying to calculate the PACF manually, but I encountered some issues with the following equation: $PACF = \frac{Covariance ([Y_{t}|Y_{t-1}, Y_{t-2},...,Y_{t-k+1}],[Y_{t-k}|Y_{t-1}, Y_{t-2}...
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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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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 ...
Ian Wang's user avatar
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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 ...
Ian Wang's user avatar
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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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1 answer
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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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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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$p$-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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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. Suppose there are two linear regression models \begin{aligned} M_1: & y = \beta_0 + x_2\beta_2 + \epsilon \\ M_2: & y = \beta_0 + x_1\beta_1 + x_2\beta_2 + \...
ForStudy's user avatar
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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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