minor

Author: DominiqueMakowski

paper/paper.md

@@ -62,12 +62,10 @@ $$\tau_{xy} = \frac{2}{n(n-1)}\sum_{i<j}^{}sign(x_i - x_j) \times sign(y_i - y_j
 
 - **Tetrachoric correlation**: Special case of the polychoric correlation applicable when both observed variables are dichotomous.
 
-- **Partial correlation**: Correlation between two variables after adjusting for the (linear) the effect of one or more variables. The correlation test is here run after having partialized the dataset, independently from it. In other words, it considers partialization as an independent step generating a different dataset, rather than belonging to the same model. This is why some discrepancies are to be expected for the *t*- and the *p*-values (but not the correlation coefficient) compared to other implementations such as **ppcor**.
+- **Partial correlation**: Correlation between two variables after adjusting for the (linear) the effect of one or more variables. The correlation test is here run after having partialized the dataset, independently from it. In other words, it considers partialization as an independent step generating a different dataset, rather than belonging to the same model. This is why some discrepancies are to be expected for the *t*- and the *p*-values (but not the correlation coefficient) compared to other implementations such as **ppcor**. Let $e_{x.z}$ be the residuals from the linear prediction of $x$ by $z$ (note that this can be expanded to a multivariate $z$):
 
 $$r_{xy.z} = r_{e_{x.z},e_{y.z}}$$
 
-*Where $e_{x.z}$ are the residuals from the linear prediction of $x$ by $z$. This can be expanded to a multivariate $z$.*
-
 - **Multilevel correlation**: Multilevel correlations are a special case of partial correlations where the variable to be adjusted for is a factor and is included as a random effect in a mixed model.
 
 These methods allow for different ways of quantifying the link between two variables (see **Figure 1**).

vignettes/types.Rmd

@@ -72,11 +72,10 @@ $$\tau_{xy} = \frac{2}{n(n-1)}\sum_{i<j}^{}sign(x_i - x_j) \times sign(y_i - y_j
 
 - **Tetrachoric correlation**: Special case of the polychoric correlation applicable when both observed variables are dichotomous.
 
-- **Partial correlation**: Correlation between two variables after adjusting for the (linear) the effect of one or more variables. The correlation test is here run after having partialized the dataset, independently from it. In other words, it considers partialization as an independent step generating a different dataset, rather than belonging to the same model. This is why some discrepancies are to be expected for the *t*- and the *p*-values (but not the correlation coefficient) compared to other implementations such as `ppcor`.
+- **Partial correlation**: Correlation between two variables after adjusting for the (linear) the effect of one or more variables. The correlation test is here run after having partialized the dataset, independently from it. In other words, it considers partialization as an independent step generating a different dataset, rather than belonging to the same model. This is why some discrepancies are to be expected for the *t*- and the *p*-values (but not the correlation coefficient) compared to other implementations such as `ppcor`. Let $e_{x.z}$ be the residuals from the linear prediction of $x$ by $z$ (note that this can be expanded to a multivariate $z$):
 
 $$r_{xy.z} = r_{e_{x.z},e_{y.z}}$$
 
-*Where $e_{x.z}$ are the residuals from the linear prediction of $x$ by $z$. This can be expanded to a multivariate $z$.*
 
 - **Multilevel correlation**: Multilevel correlations are a special case of partial correlations where the variable to be adjusted for is a factor and is included as a random effect in a mixed model.