Calculate the variance-covariance matrix for a Bradley-Terry model
vcovBT(mu, X)
| mu | a vector of Bradley--Terry model parameter estimates |
|---|---|
| X | a square matrix of paired comparisons |
A Fisher information matrix
Other Bradley-Terry model utility functions: BradleyTerry,
hessianBT, loglikelihood,
pseudocount
#> [,1] [,2] [,3] [,4] [,5] [,6] #> [1,] 0.02768722 0.01538249 0.01579889 0.01567693 0.01504243 0.01494286 #> [2,] 0.01538249 0.01737506 0.01524373 0.01563264 0.01509178 0.01497899 #> [3,] 0.01579889 0.01524373 0.03728709 0.01525345 0.01518367 0.01514861 #> [4,] 0.01567693 0.01563264 0.01525345 0.02550116 0.01504333 0.01498037 #> [5,] 0.01504243 0.01509178 0.01518367 0.01504333 0.02214995 0.01534518 #> [6,] 0.01494286 0.01497899 0.01514861 0.01498037 0.01534518 0.01743292 #> [7,] 0.01523441 0.01524744 0.01523388 0.01526516 0.01515966 0.01509708 #> [8,] 0.01488392 0.01494202 0.01496777 0.01490729 0.01527974 0.01529593 #> [9,] 0.01522974 0.01522670 0.01520928 0.01528696 0.01507704 0.01508079 #> [10,] 0.01531665 0.01502065 0.01518271 0.01505747 0.01504960 0.01485347 #> [11,] 0.01559261 0.01521287 0.01538714 0.01532736 0.01510608 0.01495306 #> [12,] 0.01508077 0.01511916 0.01518040 0.01533600 0.01501523 0.01486033 #> [13,] 0.01516042 0.01508487 0.01515218 0.01510597 0.01510904 0.01494038 #> [14,] 0.01487403 0.01489255 0.01493409 0.01487527 0.01498021 0.01500230 #> [15,] 0.01520962 0.01518009 0.01520094 0.01516170 0.01513939 0.01510078 #> [16,] 0.01433313 0.01428364 0.01465225 0.01437132 0.01422337 0.01413343 #> [17,] 0.01499890 0.01501562 0.01533156 0.01500058 0.01511457 0.01546759 #> [18,] 0.01515315 0.01521360 0.01523796 0.01520479 0.01509222 0.01506885 #> [19,] 0.01506180 0.01498871 0.01537649 0.01499881 0.01512758 0.01495033 #> [20,] 0.01483296 0.01488079 0.01503861 0.01484047 0.01620157 0.01534034 #> [21,] 0.01503712 0.01513699 0.01515508 0.01509717 0.01498807 0.01489211 #> [,7] [,8] [,9] [,10] [,11] [,12] #> [1,] 0.01523441 0.01488392 0.01522974 0.01531665 0.01559261 0.01508077 #> [2,] 0.01524744 0.01494202 0.01522670 0.01502065 0.01521287 0.01511916 #> [3,] 0.01523388 0.01496777 0.01520928 0.01518271 0.01538714 0.01518040 #> [4,] 0.01526516 0.01490729 0.01528696 0.01505747 0.01532736 0.01533600 #> [5,] 0.01515966 0.01527974 0.01507704 0.01504960 0.01510608 0.01501523 #> [6,] 0.01509708 0.01529593 0.01508079 0.01485347 0.01495306 0.01486033 #> [7,] 0.01794496 0.01509194 0.01520231 0.01496361 0.01513515 0.01503622 #> [8,] 0.01509194 0.02084149 0.01499657 0.01479343 0.01489190 0.01482394 #> [9,] 0.01520231 0.01499657 0.02510842 0.01501862 0.01519637 0.01510785 #> [10,] 0.01496361 0.01479343 0.01501862 0.02253780 0.01546995 0.01508470 #> [11,] 0.01513515 0.01489190 0.01519637 0.01546995 0.01987298 0.01513822 #> [12,] 0.01503622 0.01482394 0.01510785 0.01508470 0.01513822 0.03708951 #> [13,] 0.01505629 0.01487782 0.01513219 0.01507899 0.01513399 0.01527401 #> [14,] 0.01489776 0.01491468 0.01502717 0.01473668 0.01490347 0.01480518 #> [15,] 0.01520387 0.01507350 0.01527738 0.01500843 0.01519150 0.01504673 #> [16,] 0.01430407 0.01407287 0.01423477 0.01432475 0.01441267 0.01416897 #> [17,] 0.01508534 0.01497351 0.01502662 0.01489872 0.01500200 0.01516704 #> [18,] 0.01517248 0.01504509 0.01518558 0.01493917 0.01506186 0.01508870 #> [19,] 0.01498337 0.01486349 0.01510091 0.01535296 0.01544225 0.01506984 #> [20,] 0.01499582 0.01522300 0.01488495 0.01476899 0.01487699 0.01475685 #> [21,] 0.01509494 0.01494086 0.01497901 0.01494062 0.01497546 0.01515321 #> [,13] [,14] [,15] [,16] [,17] [,18] #> [1,] 0.01516042 0.01487403 0.01520962 0.01433313 0.01499890 0.01515315 #> [2,] 0.01508487 0.01489255 0.01518009 0.01428364 0.01501562 0.01521360 #> [3,] 0.01515218 0.01493409 0.01520094 0.01465225 0.01533156 0.01523796 #> [4,] 0.01510597 0.01487527 0.01516170 0.01437132 0.01500058 0.01520479 #> [5,] 0.01510904 0.01498021 0.01513939 0.01422337 0.01511457 0.01509222 #> [6,] 0.01494038 0.01500230 0.01510078 0.01413343 0.01546759 0.01506885 #> [7,] 0.01505629 0.01489776 0.01520387 0.01430407 0.01508534 0.01517248 #> [8,] 0.01487782 0.01491468 0.01507350 0.01407287 0.01497351 0.01504509 #> [9,] 0.01513219 0.01502717 0.01527738 0.01423477 0.01502662 0.01518558 #> [10,] 0.01507899 0.01473668 0.01500843 0.01432475 0.01489872 0.01493917 #> [11,] 0.01513399 0.01490347 0.01519150 0.01441267 0.01500200 0.01506186 #> [12,] 0.01527401 0.01480518 0.01504673 0.01416897 0.01516704 0.01508870 #> [13,] 0.01700772 0.01502463 0.01518612 0.01432628 0.01509410 0.01502777 #> [14,] 0.01502463 0.04301983 0.01637257 0.01404590 0.01665521 0.01500118 #> [15,] 0.01518612 0.01637257 0.03113811 0.01449509 0.01619939 0.01524426 #> [16,] 0.01432628 0.01404590 0.01449509 0.04341879 0.01414821 0.01426939 #> [17,] 0.01509410 0.01665521 0.01619939 0.01414821 0.03908472 0.01521683 #> [18,] 0.01502777 0.01500118 0.01524426 0.01426939 0.01521683 0.01655566 #> [19,] 0.01512487 0.01478304 0.01509836 0.01447399 0.01500061 0.01492750 #> [20,] 0.01488043 0.01484062 0.01494624 0.01411984 0.01495046 0.01492044 #> [21,] 0.01512478 0.01509339 0.01544739 0.01415603 0.01506009 0.01506540 #> [,19] [,20] [,21] [,22] [,23] [,24] #> [1,] 0.01506180 0.01483296 0.01503712 0.01553624 0.01569017 0.01485008 #> [2,] 0.01498871 0.01488079 0.01513699 0.01542329 0.01548832 0.01484349 #> [3,] 0.01537649 0.01503861 0.01515508 0.01546807 0.01534302 0.01541131 #> [4,] 0.01499881 0.01484047 0.01509717 0.01551043 0.01552270 0.01484441 #> [5,] 0.01512758 0.01620157 0.01498807 0.01506349 0.01516136 0.01524428 #> [6,] 0.01495033 0.01534034 0.01489211 0.01499409 0.01507480 0.01509354 #> [7,] 0.01498337 0.01499582 0.01509494 0.01526559 0.01527793 0.01492432 #> [8,] 0.01486349 0.01522300 0.01494086 0.01493738 0.01499130 0.01525616 #> [9,] 0.01510091 0.01488495 0.01497901 0.01535376 0.01559701 0.01488965 #> [10,] 0.01535296 0.01476899 0.01494062 0.01513812 0.01510974 0.01479627 #> [11,] 0.01544225 0.01487699 0.01497546 0.01540695 0.01541766 0.01490375 #> [12,] 0.01506984 0.01475685 0.01515321 0.01518352 0.01546836 0.01475740 #> [13,] 0.01512487 0.01488043 0.01512478 0.01518299 0.01520045 0.01485688 #> [14,] 0.01478304 0.01484062 0.01509339 0.01493045 0.01492288 0.01496353 #> [15,] 0.01509836 0.01494624 0.01544739 0.01527869 0.01520986 0.01496180 #> [16,] 0.01447399 0.01411984 0.01415603 0.01447796 0.01434305 0.01460878 #> [17,] 0.01500061 0.01495046 0.01506009 0.01501746 0.01505401 0.01492918 #> [18,] 0.01492750 0.01492044 0.01506540 0.01517771 0.01519669 0.01496943 #> [19,] 0.02357200 0.01486672 0.01491395 0.01509936 0.01508361 0.01497082 #> [20,] 0.01486672 0.02591155 0.01479501 0.01485810 0.01490555 0.01504498 #> [21,] 0.01491395 0.01479501 0.02170162 0.01509157 0.01511879 0.01482739 #> [,25] [,26] [,27] [,28] [,29] [,30] #> [1,] 0.01518517 0.01492705 0.01544403 0.01546892 0.01471585 0.01551011 #> [2,] 0.01522564 0.01494343 0.01517908 0.01521724 0.01473485 0.01521699 #> [3,] 0.01514782 0.01503755 0.01539064 0.01538126 0.01494385 0.01531479 #> [4,] 0.01523856 0.01491347 0.01527900 0.01530765 0.01474757 0.01541614 #> [5,] 0.01510911 0.01509437 0.01511832 0.01505169 0.01483218 0.01497223 #> [6,] 0.01499043 0.01516418 0.01495236 0.01492558 0.01471257 0.01489685 #> [7,] 0.01514054 0.01503235 0.01508646 0.01515210 0.01474243 0.01507248 #> [8,] 0.01497344 0.01521681 0.01493484 0.01485526 0.01479515 0.01481736 #> [9,] 0.01520392 0.01505803 0.01518882 0.01516345 0.01491318 0.01518405 #> [10,] 0.01493552 0.01480352 0.01538347 0.01507547 0.01463941 0.01536871 #> [11,] 0.01506857 0.01493327 0.01553093 0.01538944 0.01466959 0.01536620 #> [12,] 0.01506825 0.01479598 0.01516629 0.01502963 0.01475078 0.01555479 #> [13,] 0.01506452 0.01487362 0.01522980 0.01508699 0.01486720 0.01516730 #> [14,] 0.01508563 0.01508054 0.01492528 0.01489928 0.01457315 0.01480776 #> [15,] 0.01525173 0.01518231 0.01510929 0.01525827 0.01496932 0.01517048 #> [16,] 0.01427257 0.01407573 0.01441868 0.01438249 0.01394609 0.01529494 #> [17,] 0.01506765 0.01535456 0.01513828 0.01501325 0.01482625 0.01494000 #> [18,] 0.01511825 0.01502698 0.01504667 0.01506076 0.01467803 0.01508832 #> [19,] 0.01495670 0.01499601 0.01539452 0.01507840 0.01466476 0.01508549 #> [20,] 0.01492115 0.01496761 0.01485466 0.01483242 0.01467054 0.01476170 #> [21,] 0.01515421 0.01494607 0.01500951 0.01496121 0.01493636 0.01496270 #> [,31] [,32] [,33] [,34] [,35] [,36] #> [1,] 0.01510453 0.01576576 0.01525048 0.01477253 0.01511908 0.01531499 #> [2,] 0.01512522 0.01520635 0.01521040 0.01482945 0.01528121 0.01509209 #> [3,] 0.01515839 0.01524395 0.01526693 0.01486969 0.01521975 0.01514856 #> [4,] 0.01511790 0.01527014 0.01533940 0.01477147 0.01512652 0.01516876 #> [5,] 0.01539865 0.01503506 0.01516477 0.01509388 0.01509387 0.01497925 #> [6,] 0.01537309 0.01489422 0.01505885 0.01489550 0.01507896 0.01479883 #> [7,] 0.01526180 0.01515484 0.01521627 0.01483403 0.01519743 0.01501075 #> [8,] 0.01544334 0.01481883 0.01508699 0.01488148 0.01502713 0.01472564 #> [9,] 0.01520295 0.01519749 0.01516129 0.01494141 0.01516101 0.01509160 #> [10,] 0.01500349 0.01518239 0.01493442 0.01469475 0.01495475 0.01518853 #> [11,] 0.01519635 0.01557427 0.01513718 0.01477365 0.01503630 0.01569313 #> [12,] 0.01497744 0.01499651 0.01518224 0.01468827 0.01532426 0.01491386 #> [13,] 0.01504977 0.01508368 0.01508358 0.01491581 0.01519378 0.01502902 #> [14,] 0.01496409 0.01480362 0.01502517 0.01477892 0.01491909 0.01473738 #> [15,] 0.01515144 0.01510916 0.01537181 0.01487633 0.01532737 0.01521199 #> [16,] 0.01443619 0.01429262 0.01420461 0.01486230 0.01427196 0.01479804 #> [17,] 0.01509812 0.01493311 0.01508382 0.01479086 0.01509520 0.01485379 #> [18,] 0.01517931 0.01503821 0.01508774 0.01474671 0.01522140 0.01491955 #> [19,] 0.01513361 0.01520360 0.01498643 0.01475245 0.01500240 0.01527062 #> [20,] 0.01510849 0.01482263 0.01488556 0.01499045 0.01487919 0.01470084 #> [21,] 0.01496818 0.01493262 0.01506529 0.01467641 0.01545027 0.01484845 #> [,37] [,38] [,39] [,40] [,41] [,42] #> [1,] 0.01483613 0.01482456 0.01499531 0.01524638 0.01562734 0.01560022 #> [2,] 0.01483474 0.01486042 0.01499850 0.01517856 0.01525289 0.01525104 #> [3,] 0.01492855 0.01497819 0.01505208 0.01517285 0.01559365 0.01545052 #> [4,] 0.01482796 0.01484004 0.01499641 0.01587554 0.01537738 0.01559763 #> [5,] 0.01555968 0.01541270 0.01519836 0.01508568 0.01514628 0.01505891 #> [6,] 0.01519114 0.01524623 0.01506093 0.01495636 0.01496467 0.01495744 #> [7,] 0.01495444 0.01501767 0.01512345 0.01498026 0.01513509 0.01517451 #> [8,] 0.01522018 0.01526904 0.01525795 0.01481806 0.01494434 0.01490695 #> [9,] 0.01494900 0.01508326 0.01511243 0.01494679 0.01526115 0.01527163 #> [10,] 0.01487942 0.01474127 0.01502302 0.01497864 0.01563242 0.01522189 #> [11,] 0.01488071 0.01483596 0.01497723 0.01505271 0.01619803 0.01558027 #> [12,] 0.01479965 0.01474473 0.01491061 0.01485806 0.01509942 0.01512592 #> [13,] 0.01488202 0.01485523 0.01513747 0.01496346 0.01523794 0.01509600 #> [14,] 0.01508379 0.01506821 0.01489304 0.01470404 0.01488863 0.01483099 #> [15,] 0.01504772 0.01495527 0.01532047 0.01493381 0.01518143 0.01520315 #> [16,] 0.01415534 0.01404515 0.01432213 0.01409029 0.01452218 0.01452285 #> [17,] 0.01501207 0.01493565 0.01498931 0.01483534 0.01501536 0.01495753 #> [18,] 0.01489244 0.01492316 0.01505549 0.01490117 0.01511703 0.01506779 #> [19,] 0.01492964 0.01492113 0.01522255 0.01507977 0.01554522 0.01511036 #> [20,] 0.01556664 0.01519218 0.01494945 0.01484401 0.01495614 0.01481227 #> [21,] 0.01479406 0.01481493 0.01508959 0.01478936 0.01499391 0.01498093 #> [,43] [,44] [,45] [,46] #> [1,] 0.01469860 0.01532360 0.01516817 0.01544921 #> [2,] 0.01474993 0.01543017 0.01514874 0.01547316 #> [3,] 0.01474402 0.01526626 0.01534617 0.01536902 #> [4,] 0.01481210 0.01542875 0.01511810 0.01541716 #> [5,] 0.01479325 0.01510073 0.01501838 0.01511985 #> [6,] 0.01480542 0.01501280 0.01493862 0.01510120 #> [7,] 0.01483597 0.01532718 0.01508336 0.01526785 #> [8,] 0.01487002 0.01496829 0.01485460 0.01496182 #> [9,] 0.01474054 0.01523856 0.01512874 0.01532962 #> [10,] 0.01456533 0.01503356 0.01518925 0.01517024 #> [11,] 0.01468064 0.01519268 0.01534158 0.01536621 #> [12,] 0.01465231 0.01506326 0.01512145 0.01514307 #> [13,] 0.01465175 0.01507558 0.01514306 0.01519876 #> [14,] 0.01473274 0.01489607 0.01484349 0.01524049 #> [15,] 0.01479331 0.01518559 0.01528150 0.01556182 #> [16,] 0.01400300 0.01436961 0.01419894 0.01433032 #> [17,] 0.01479500 0.01502395 0.01520655 0.01533218 #> [18,] 0.01474873 0.01519681 0.01503451 0.01526342 #> [19,] 0.01465299 0.01501215 0.01517665 0.01513305 #> [20,] 0.01474728 0.01491632 0.01491972 0.01495551 #> [21,] 0.01479037 0.01512643 0.01509876 0.01507272 #> [ reached getOption("max.print") -- omitted 25 rows ]