r - 如何解释 corrplot 的输出？

Question

corrplot软件包提供了一些简洁的图表和文档以及示例。

但我不明白输出。我可以看到，如果您有一个矩阵 A_ij，您可以将其绘制为 n 乘 n 方形图 block 的排列，其中tile ij 对应于A_ij 的值。但有些例子似乎有更多的维度:

这里我们可以猜测颜色表示相关系数，椭圆的方向是负相关/正相关。什么是偏心率？

documentation对于方法说:

the visualization method of correlation matrix to be used. Currently, it supports seven methods, named "circle" (default), "square", "ellipse", "number", "pie", "shade" and "color". See examples for details.

The areas of circles or squares show the absolute value of corresponding correlation coefficients. Method "pie" and "shade" came from Michael Friendly’s job (with some adjustment about the shade added on), and "ellipse" came from D.J. Murdoch and E.D. Chow’s job, see in section References.

所以我们知道圆形和正方形的面积应该显示系数。其他维度和其他方法怎么样？

Answer 1

绘图仅显示一维。

MichaelFriendly，在Corrgrams:相关矩阵的探索性显示(corrplot文档混淆地将此称为他的“工作”)中说:

In the shaded row, each cell is shaded blue or red depending on the sign of the correlation, and with the intensity of color scaled 0–100% in proportion to the magnitude of the correlation. (Such scaled colors are easily computed using RGB coding from red, (1, 0, 0), through white (1, 1, 1), to blue (0, 0, 1). For simplicity, we ignore the non-linearities of color reproduction and perception, but note that these are easily accommodated in the color mapping function.) White diagonal lines are added so that the direction of the correlation may still be discerned in black and white. This bipolar scale of color was chosen to leave correlations near 0 empty (white), and to make positive and negative values of equal magnitude approximately equally intensely shaded. Gray scale and other color schemes are implemented in our software (Section 6), but not illustrated here.

The bar and circular symbols also use the same scaled colors, but fill an area proportional to the absolute value of the correlation. For the bars, negative values are filled from the bottom, positive values from the top. The circles are filled clockwise for positive values, anti-clockwise for negative values. The ellipses have their eccentricity parametrically scaled to the correlation value (Murdoch and Chow, 1996). Perceptually, they have the property of becoming visually less prominent as the magnitude of the correlation increases, in contrast to the other glyphs.

(强调我的)

“Murdoch and Chow，1996”是一份描述绘制椭圆方程的出版物(大型相关矩阵的图形显示)。椭圆显然是二元正态分布的漫画:

因此总而言之，显示的唯一维度始终是相关系数(或使用问题术语时的A_ij值)本身。多个表观尺寸是多余的。