As with residuals.copreg, two flavours are available:
type = "structural" gives mu + P alpha + W beta (the causal model
without the copula terms), type = "augmented" adds the copula
control functions, C gamma, back in.
References
Qian, Y., A. Koschmann, and H. Xie (2025). A practical guide to endogeneity correction using copulas. Journal of Marketing.
Examples
set.seed(1)
n <- 150
w <- rnorm(n)
p <- 0.4 * w + rt(n, df = 3)
xi <- 0.5 * p + rnorm(n)
y <- 1 + 2 * p + 1.5 * w + xi
dat <- data.frame(y = y, p = p, w = w)
fit <- endogCopula:::.copreg_fit(
formula = y ~ p | w, data = dat,
ctor = endogCopula:::.ctor_twostage(TRUE),
method = "2sCOPE", cdf = "rank.n", ties = "max",
nboots = 25, verbose = FALSE)
fitted(fit)
#> 1 2 3 4 5 6
#> 0.85068540 7.04895584 -2.81162664 -2.04848540 3.18540066 1.32313294
#> 7 8 9 10 11 12
#> 1.10405874 -0.31002028 0.54931481 -3.69243248 4.43303094 -4.02853276
#> 13 14 15 16 17 18
#> 1.51118406 -7.67205027 6.63327181 0.47069046 -2.01427158 -0.23424496
#> 19 20 21 22 23 24
#> 13.84469473 -6.42280274 3.31077683 1.78387825 4.34309493 -5.03384945
#> 25 26 27 28 29 30
#> 2.74239239 -2.45514135 6.72623640 12.79649600 -6.36820854 -0.69218543
#> 31 32 33 34 35 36
#> -1.16748437 -4.46693794 3.05051984 1.67358862 -4.05530450 -0.20050702
#> 37 38 39 40 41 42
#> 3.10023466 -1.20625234 -5.85835504 2.48948123 -4.00150677 0.98452465
#> 43 44 45 46 47 48
#> 6.12052918 2.08515675 -3.81972778 0.02508309 -0.46536734 3.93194441
#> 49 50 51 52 53 54
#> -8.72992559 0.96632525 9.50402986 7.85172606 3.51676879 -4.97661479
#> 55 56 57 58 59 60
#> 6.05993621 12.63915717 2.63625388 2.54105987 -4.70102603 6.32479163
#> 61 62 63 64 65 66
#> 8.83875047 0.56942491 6.46083181 8.80851428 4.01932801 5.40518030
#> 67 68 69 70 71 72
#> -12.87024635 2.28732060 7.67943700 5.25789060 4.13811114 0.90652967
#> 73 74 75 76 77 78
#> -0.30742924 1.30502623 -1.35360496 -0.77523598 -0.07174603 -0.78742603
#> 79 80 81 82 83 84
#> 6.55936883 -0.57825607 -3.94039407 0.05643882 7.67717968 -1.05133558
#> 85 86 87 88 89 90
#> 2.02627600 6.74816817 2.33871459 -5.34174629 -0.98808690 -3.77956205
#> 91 92 93 94 95 96
#> -8.26467599 -1.90764388 1.36247908 -1.40301204 -2.02221435 6.74884502
#> 97 98 99 100 101 102
#> 4.78043114 1.05590645 -0.89631569 -0.80339379 8.15651091 0.51858941
#> 103 104 105 106 107 108
#> -2.17082349 0.06873905 -0.62668323 14.84571598 4.89528709 10.90939674
#> 109 110 111 112 113 114
#> 2.18863783 -2.35065035 0.45355978 -3.37032919 4.65889826 -1.01144688
#> 115 116 117 118 119 120
#> 4.40767377 3.01175228 -0.12534950 3.54845838 4.37386410 -0.22679330
#> 121 122 123 124 125 126
#> -0.78431716 2.74664688 -0.10360041 -5.53774736 2.28165444 0.66515976
#> 127 128 129 130 131 132
#> -1.28543167 -4.59754148 2.42571020 0.22834597 -3.53879026 5.22045623
#> 133 134 135 136 137 138
#> -0.67617643 26.71565565 -0.42919612 -5.98140876 -2.42170387 0.09698808
#> 139 140 141 142 143 144
#> -0.75033783 6.69653763 -20.55494277 7.47989237 -2.37242821 -3.23579033
#> 145 146 147 148 149 150
#> -8.98783718 -3.83464718 6.16761899 -1.91485820 -4.38562185 -6.94723040
fitted(fit, type = "augmented")
#> 1 2 3 4 5
#> 0.632386995 6.361715838 -2.595246478 -1.268003083 2.934708444
#> 6 7 8 9 10
#> 0.987559279 1.175310338 0.042024335 0.760934526 -3.237055516
#> 11 12 13 14 15
#> 4.366179661 -3.308692163 1.221750307 -7.254725508 6.280093435
#> 16 17 18 19 20
#> 0.470607688 -1.673725991 0.166922575 12.810322016 -5.501501326
#> 21 22 23 24 25
#> 3.211706011 1.841638297 3.925889279 -4.867239687 2.641501457
#> 26 27 28 29 30
#> -2.079076564 5.978952030 11.407850943 -5.588817183 -0.384072086
#> 31 32 33 34 35
#> -0.580487133 -3.870776691 2.838989336 1.516016903 -3.830519699
#> 36 37 38 39 40
#> -0.208570466 2.697640445 -0.984531752 -4.814550144 2.438906990
#> 41 42 43 44 45
#> -3.476179964 0.846790270 5.704503927 2.033155420 -3.454588944
#> 46 47 48 49 50
#> -0.138392475 -0.214469250 3.724664159 -7.687815325 1.218514357
#> 51 52 53 54 55
#> 8.698670939 7.003232426 3.249101087 -4.589358179 5.785735283
#> 56 57 58 59 60
#> 11.847481594 2.290402567 2.013419054 -3.846216423 5.667047437
#> 61 62 63 64 65
#> 8.548627428 0.553821635 6.000317247 8.004489009 3.457332757
#> 66 67 68 69 70
#> 4.928578251 -11.909078133 2.511383679 6.940217857 5.278052590
#> 71 72 73 74 75
#> 3.841809393 0.634538133 0.001364126 0.932050590 -1.457311208
#> 76 77 78 79 80
#> -0.494645162 -0.124043877 -0.590432753 5.947760388 -0.581997831
#> 81 82 83 84 85
#> -3.523571007 0.109438233 7.218065150 -1.284106736 1.992192618
#> 86 87 88 89 90
#> 6.170206800 2.394705790 -4.624915240 -0.658835655 -3.182621034
#> 91 92 93 94 95
#> -7.328255372 -1.261064638 1.642963113 -0.942543422 -1.282246814
#> 96 97 98 99 100
#> 6.244540024 3.992109558 0.822256201 -1.081890721 -0.714781390
#> 101 102 103 104 105
#> 7.206308944 0.537605766 -2.063321739 0.233224926 -0.655269508
#> 106 107 108 109 110
#> 13.981188901 4.584935847 10.074712406 2.086110516 -1.462814518
#> 111 112 113 114 115
#> 0.259758479 -2.990748060 4.529737420 -0.958094529 3.939975884
#> 116 117 118 119 120
#> 2.621810019 -0.116708248 3.124625311 4.047999435 -0.143954611
#> 121 122 123 124 125
#> -0.716701037 2.816705184 -0.051260733 -4.786231475 2.042874324
#> 126 127 128 129 130
#> 0.919363729 -1.055847460 -3.933531582 2.014184310 0.158716791
#> 131 132 133 134 135
#> -3.011872944 4.569163189 -0.341612310 25.320958933 -0.203086211
#> 136 137 138 139 140
#> -5.575785357 -2.104217455 -0.016953732 -0.733857548 6.007129016
#> 141 142 143 144 145
#> -19.473174020 7.048986380 -2.428159350 -2.869693506 -8.198542982
#> 146 147 148 149 150
#> -3.491400439 6.046905173 -1.581684316 -4.112266497 -6.404945015