This post provides a function for weighted Pearson correlation in R, i.e. function(x, y, weights). Is a corollary available for the Spearman rank correlation coefficient?
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Max Ghenis
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you mean Spearman with weight? – Colonel Beauvel Sep 04 '15 at 07:04
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I'd like the coefficient to consider a third vector of observation-level weights, which I'd provide. – Max Ghenis Sep 04 '15 at 14:36
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Spearman's rank correlation coefficient r_s is calculated in the same way as Pearson's product moment correlation coefficient, except that ordinal rather than interval data are used. However, there is a way to calculate r_p using weights:
LaTeX:
\begin{align}
\bar{x} & = \frac{\sum_{i=1}^n{w_i x_i}}{\sum_{i=1}^n{w_i}} \quad
\bar{y} = \frac{\sum_{i=1}^n{w_i y_i}}{\sum_{i=1}^n{w_i}} \\
s_{x,y} & = \frac{\sum_{i=1}^n{w_i (x_i - \bar{x}_i) (y_i - \bar{y}_i)}}{\sum_{i=1}^n{w_i}} \quad
s_x = \frac{\sum_{i=1}^n{w_i (x_i - \bar{x})}}{w_i} \quad
s_y = \frac{\sum_{i=1}^n{w_i (y_i - \bar{y})}}{w_i} \\
r(x,y,w) & = \frac{s_{x,y}}{\sqrt{s_x s_y}}
\end{align}
Max Ghenis
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I think that in the weighted variance S_x, the term (x_i - x_bar) should be squared. Similar in S_y – hector Feb 12 '19 at 04:40