The Mahalanobis distance (in squared units) measures the distance in multivariate space taking into account the covariance structure of the data. Because a few extreme outliers can skew the covariance estimate, the bootstrapped version is considered as more robust.
distance_mahalanobis(data, ci = 0.95, iterations = 1000, robust = TRUE, ...)
data | A data frame. |
---|---|
ci | Confidence/Credible Interval level. If "default", then it is set to 0.95 (95% CI). |
iterations | The number of draws to simulate/bootstrap (when |
robust | If |
... | Arguments passed to or from other methods. |
Description of the Mahalanobis distance.
Schwarzkopf, D. S., De Haas, B., & Rees, G. (2012). Better ways to improve standards in brain-behavior correlation analysis. Frontiers in human neuroscience, 6, 200.
distance_mahalanobis(iris[, 1:4])#> # Description of Posterior Distributions #> #> Distance | CI_low | CI_high #> --------------------------- #> 2.182 | 1.482 | 2.980 #> 2.929 | 2.253 | 3.780 #> 2.153 | 1.558 | 2.743 #> 2.532 | 1.952 | 3.170 #> 2.516 | 1.756 | 3.409 #> 3.997 | 2.806 | 5.380 #> 2.976 | 2.353 | 3.743 #> 1.884 | 1.332 | 2.558 #> 3.488 | 2.708 | 4.356 #> 2.442 | 1.973 | 3.018 #> 3.356 | 2.464 | 4.636 #> 2.888 | 2.222 | 3.729 #> 2.685 | 2.081 | 3.335 #> 3.718 | 3.008 | 4.714 #> 9.060 | 6.949 | 11.891 #> 9.991 | 7.364 | 12.992 #> 5.944 | 4.320 | 7.726 #> 2.389 | 1.681 | 3.198 #> 4.667 | 3.408 | 6.180 #> 3.543 | 2.532 | 4.696 #> 2.722 | 2.111 | 3.524 #> 3.015 | 2.255 | 4.072 #> 3.735 | 2.929 | 4.716 #> 2.316 | 1.706 | 3.000 #> 5.492 | 4.215 | 6.929 #> 2.511 | 1.909 | 3.178 #> 1.826 | 1.312 | 2.458 #> 2.246 | 1.620 | 3.068 #> 2.582 | 1.861 | 3.349 #> 2.551 | 1.977 | 3.252 #> 2.046 | 1.581 | 2.620 #> 4.762 | 3.650 | 6.081 #> 8.618 | 6.494 | 10.949 #> 7.445 | 5.435 | 9.789 #> 2.041 | 1.595 | 2.641 #> 3.524 | 2.653 | 4.394 #> 5.490 | 4.306 | 6.944 #> 3.566 | 2.737 | 4.665 #> 3.251 | 2.599 | 4.148 #> 1.946 | 1.361 | 2.624 #> 2.629 | 1.943 | 3.486 #> 11.733 | 8.881 | 15.566 #> 3.453 | 2.763 | 4.303 #> 3.849 | 3.066 | 4.835 #> 4.656 | 3.559 | 5.934 #> 3.061 | 2.249 | 3.919 #> 4.572 | 3.371 | 5.880 #> 2.444 | 1.914 | 3.159 #> 3.073 | 2.133 | 4.188 #> 1.986 | 1.438 | 2.604 #> 4.682 | 3.408 | 6.312 #> 0.692 | 0.356 | 1.040 #> 3.182 | 2.235 | 4.429 #> 3.655 | 2.734 | 4.987 #> 2.130 | 1.522 | 3.008 #> 3.414 | 2.422 | 4.510 #> 1.346 | 0.860 | 1.927 #> 4.411 | 3.404 | 5.774 #> 2.882 | 2.020 | 3.980 #> 3.294 | 2.341 | 4.234 #> 7.776 | 5.901 | 10.100 #> 0.468 | 0.188 | 0.749 #> 7.716 | 6.130 | 10.251 #> 1.597 | 1.103 | 2.366 #> 1.098 | 0.753 | 1.565 #> 2.940 | 2.053 | 3.853 #> 3.606 | 2.683 | 4.737 #> 3.439 | 2.595 | 4.575 #> 7.558 | 5.862 | 9.934 #> 2.231 | 1.686 | 3.065 #> 3.376 | 2.334 | 4.538 #> 1.406 | 0.928 | 1.959 #> 2.453 | 1.782 | 3.333 #> 4.657 | 3.479 | 6.296 #> 1.677 | 1.121 | 2.356 #> 2.452 | 1.661 | 3.266 #> 4.380 | 3.181 | 5.880 #> 1.508 | 0.933 | 2.125 #> 0.345 | 0.185 | 0.556 #> 2.159 | 1.545 | 3.008 #> 2.840 | 2.147 | 3.885 #> 3.189 | 2.343 | 4.204 #> 0.881 | 0.561 | 1.308 #> 2.592 | 1.889 | 3.519 #> 6.427 | 4.871 | 8.107 #> 2.903 | 2.036 | 3.851 #> 1.907 | 1.246 | 2.682 #> 6.705 | 5.174 | 8.800 #> 1.726 | 1.232 | 2.423 #> 2.038 | 1.454 | 2.758 #> 5.093 | 3.761 | 6.639 #> 1.224 | 0.740 | 1.784 #> 1.400 | 0.953 | 1.971 #> 4.659 | 3.474 | 6.121 #> 1.532 | 0.993 | 2.057 #> 2.774 | 1.942 | 3.715 #> 1.229 | 0.790 | 1.740 #> 0.698 | 0.352 | 1.053 #> 4.964 | 3.633 | 6.590 #> 0.660 | 0.392 | 0.984 #> 9.236 | 6.514 | 12.044 #> 3.083 | 2.128 | 4.038 #> 2.585 | 1.829 | 3.418 #> 3.660 | 2.638 | 4.806 #> 2.457 | 1.690 | 3.329 #> 6.308 | 4.472 | 8.693 #> 10.517 | 8.019 | 13.336 #> 7.871 | 5.390 | 10.610 #> 3.423 | 2.469 | 4.483 #> 7.636 | 5.887 | 10.307 #> 2.378 | 1.538 | 3.437 #> 1.289 | 0.959 | 1.711 #> 2.561 | 1.742 | 3.659 #> 4.948 | 3.727 | 6.335 #> 11.896 | 8.513 | 15.421 #> 6.137 | 4.011 | 8.286 #> 2.045 | 1.407 | 2.857 #> 13.187 | 9.638 | 18.095 #> 7.456 | 5.480 | 9.723 #> 4.481 | 3.414 | 5.764 #> 4.224 | 2.690 | 5.661 #> 5.578 | 3.793 | 7.276 #> 9.156 | 6.602 | 12.227 #> 1.871 | 1.330 | 2.585 #> 2.989 | 2.080 | 4.027 #> 6.068 | 3.971 | 8.353 #> 1.506 | 1.009 | 2.151 #> 1.191 | 0.696 | 1.746 #> 1.746 | 1.263 | 2.386 #> 7.332 | 5.192 | 10.079 #> 5.934 | 4.241 | 7.867 #> 13.548 | 9.629 | 18.179 #> 2.649 | 1.826 | 3.652 #> 2.481 | 1.641 | 3.393 #> 13.228 | 10.078 | 17.257 #> 10.071 | 7.569 | 13.131 #> 8.470 | 6.144 | 11.453 #> 3.360 | 2.451 | 4.546 #> 1.529 | 0.953 | 2.275 #> 3.636 | 2.430 | 4.998 #> 6.240 | 4.066 | 8.395 #> 12.773 | 9.426 | 17.584 #> 3.083 | 2.128 | 4.038 #> 3.231 | 2.135 | 4.365 #> 7.794 | 5.295 | 10.436 #> 9.411 | 6.732 | 12.780 #> 4.183 | 3.119 | 5.378 #> 1.869 | 1.077 | 2.632 #> 7.944 | 5.698 | 10.715 #> 3.597 | 2.649 | 4.813 #>distance_mahalanobis(iris[, 1:4], robust = FALSE)#> Distance #> 1 2.1344679 #> 2 2.8491187 #> 3 2.0813387 #> 4 2.4523816 #> 5 2.4621545 #> 6 3.8834177 #> 7 2.8621081 #> 8 1.8333003 #> 9 3.3840731 #> 10 2.3752179 #> 11 3.2831069 #> 12 2.7747975 #> 13 2.6132975 #> 14 3.6034324 #> 15 8.7375184 #> 16 9.7127899 #> 17 5.7605877 #> 18 2.3213894 #> 19 4.4996899 #> 20 3.4388658 #> 21 2.6360071 #> 22 2.9292496 #> 23 3.6134114 #> 24 2.2371731 #> 25 5.3023607 #> 26 2.4453103 #> 27 1.7658286 #> 28 2.1971806 #> 29 2.5027712 #> 30 2.4643980 #> 31 1.9849638 #> 32 4.5911380 #> 33 8.3583413 #> 34 7.2213139 #> 35 1.9820679 #> 36 3.4173031 #> 37 5.3372175 #> 38 3.4513350 #> 39 3.1549793 #> 40 1.8926197 #> 41 2.5485013 #> 42 11.4240288 #> 43 3.3144697 #> 44 3.7085855 #> 45 4.4840560 #> 46 2.9786602 #> 47 4.4333077 #> 48 2.3594309 #> 49 3.0076970 #> 50 1.9285641 #> 51 4.4528311 #> 52 0.6273996 #> 53 3.0186280 #> 54 3.6125278 #> 55 2.0404590 #> 56 3.3195858 #> 57 1.2763441 #> 58 4.3093305 #> 59 2.7426578 #> 60 3.1665229 #> 61 7.6832930 #> 62 0.4323176 #> 63 7.5614023 #> 64 1.5482870 #> 65 1.0372548 #> 66 2.7865631 #> 67 3.4732716 #> 68 3.3289796 #> 69 7.3923779 #> 70 2.1837666 #> 71 3.2615033 #> 72 1.3601100 #> 73 2.3885294 #> 74 4.5073307 #> 75 1.6095193 #> 76 2.3362612 #> 77 4.1982905 #> 78 1.4219664 #> 79 0.3194730 #> 80 2.1112223 #> 81 2.8147732 #> 82 3.1338323 #> 83 0.8579871 #> 84 2.5178289 #> 85 6.2164814 #> 86 2.7910313 #> 87 1.7971852 #> 88 6.5544318 #> 89 1.6677135 #> 90 2.0056841 #> 91 4.9630348 #> 92 1.1821941 #> 93 1.3713881 #> 94 4.5698858 #> 95 1.4932609 #> 96 2.6869276 #> 97 1.1870542 #> 98 0.6575354 #> 99 4.8207427 #> 100 0.6341019 #> 101 8.9395988 #> 102 2.9682833 #> 103 2.4451456 #> 104 3.5551146 #> 105 2.3541837 #> 106 6.0617111 #> 107 10.1378044 #> 108 7.5880086 #> 109 3.3301655 #> 110 7.3453376 #> 111 2.2611037 #> 112 1.2342978 #> 113 2.4316524 #> 114 4.7588845 #> 115 11.4105735 #> 116 5.8815414 #> 117 1.9743869 #> 118 12.8130732 #> 119 7.1768159 #> 120 4.3974981 #> 121 4.0399248 #> 122 5.3595987 #> 123 8.7973122 #> 124 1.7967966 #> 125 2.8868280 #> 126 5.8835660 #> 127 1.4473698 #> 128 1.1348285 #> 129 1.6688603 #> 130 7.0710485 #> 131 5.6935238 #> 132 13.1010925 #> 133 2.5441171 #> 134 2.4087367 #> 135 12.8803310 #> 136 9.6569355 #> 137 8.2028004 #> 138 3.2575803 #> 139 1.4687445 #> 140 3.4924068 #> 141 5.9713581 #> 142 12.4413843 #> 143 2.9682833 #> 144 3.1069367 #> 145 7.4592052 #> 146 9.0639497 #> 147 4.0366487 #> 148 1.7670035 #> 149 7.6824724 #> 150 3.4787688