R Under development (unstable) (2026-01-18 r89306 ucrt) -- "Unsuffered Consequences" Copyright (C) 2026 The R Foundation for Statistical Computing Platform: x86_64-w64-mingw32/x64 R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > > options( digits = 3 ) > library( "sampleSelection" ) Loading required package: maxLik Loading required package: miscTools Please cite the 'maxLik' package as: Henningsen, Arne and Toomet, Ott (2011). maxLik: A package for maximum likelihood estimation in R. Computational Statistics 26(3), 443-458. DOI 10.1007/s00180-010-0217-1. If you have questions, suggestions, or comments regarding the 'maxLik' package, please use a forum or 'tracker' at maxLik's R-Forge site: https://r-forge.r-project.org/projects/maxlik/ > set.seed(0) > # Note: library() may change RNG state! > > ## Leeman Lucas (and many others): binary outcome > > N <- 500 > rho <- 0.7 > suppressPackageStartupMessages( library( "mvtnorm" ) ) > eps <- rmvnorm(N, c(0,0), matrix(c(1,rho,rho,1), 2, 2) ) > simDat <- data.frame( xs = runif(N) ) > simDat$ysX <- 3 * simDat$xs + eps[,1] > simDat$ys <- simDat$ysX > 0 > simDat$xo <- runif(N) > simDat$yoX <- -1 + 2 * simDat$xo + eps[,2] > simDat$yo <- factor( (simDat$yoX > 0) * (simDat$ys > 0)) > # binary outcome, only observable if ys>0 > print(table(simDat$ys, simDat$yo, exclude=NULL)) 0 1 FALSE 74 0 TRUE 202 224 > > # estimation with BHHH method > ss <- selection( ys ~ xs, yo ~ xo, data = simDat, steptol = 1e-12 ) > print( ss ) Call: selection(selection = ys ~ xs, outcome = yo ~ xo, data = simDat, steptol = 1e-12) Coefficients: S:(Intercept) S:xs O:(Intercept) O:xo rho -0.122 3.329 -1.055 1.987 0.817 > summary( ss ) -------------------------------------------- Tobit 2 model with binary outcome (sample selection model) Maximum Likelihood estimation BHHH maximisation, 6 iterations Return code 8: successive function values within relative tolerance limit (reltol) Log-Likelihood: -398 500 observations (74 censored and 426 observed) 5 free parameters (df = 495) Probit selection equation: Estimate Std. Error t value Pr(>|t|) (Intercept) -0.122 0.130 -0.94 0.35 xs 3.329 0.393 8.48 2.7e-16 *** Outcome equation: Estimate Std. Error t value Pr(>|t|) (Intercept) -1.055 0.121 -8.71 <2e-16 *** xo 1.987 0.228 8.73 <2e-16 *** Error terms: Estimate Std. Error t value Pr(>|t|) rho 0.817 0.141 5.77 1.4e-08 *** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 -------------------------------------------- > coef( ss ) S:(Intercept) S:xs O:(Intercept) O:xo rho -0.122 3.329 -1.055 1.987 0.817 > coef( ss, part = "outcome" ) (Intercept) xo -1.05 1.99 > coef( summary( ss ) ) Estimate Std. Error t value Pr(>|t|) (Intercept) -0.122 0.130 -0.944 3.46e-01 xs 3.329 0.393 8.476 2.69e-16 (Intercept) -1.055 0.121 -8.713 4.46e-17 xo 1.987 0.228 8.727 4.01e-17 rho 0.817 0.141 5.772 1.38e-08 > coef( summary( ss ), part = "outcome" ) Estimate Std. Error t value Pr(>|t|) (Intercept) -1.05 0.121 -8.71 4.46e-17 xo 1.99 0.228 8.73 4.01e-17 > stdEr( ss ) (Intercept) xs (Intercept) xo rho 0.130 0.393 0.121 0.228 0.141 > vcov( ss ) (Intercept) xs (Intercept) xo rho (Intercept) 0.01681 -0.04000 0.001870 -0.00409 0.006358 xs -0.04000 0.15422 -0.003141 0.01406 -0.015359 (Intercept) 0.00187 -0.00314 0.014652 -0.02269 0.000289 xo -0.00409 0.01406 -0.022694 0.05186 -0.009832 rho 0.00636 -0.01536 0.000289 -0.00983 0.020017 > vcov( ss, part = "outcome" ) (Intercept) xo (Intercept) 0.0147 -0.0227 xo -0.0227 0.0519 > nobs( ss ) [1] 500 > nObs( ss ) [1] 500 > round( fitted( ss ), 3 ) 1 2 3 4 5 6 7 8 9 10 11 12 13 0.338 0.496 0.182 0.737 0.415 0.818 NA 0.772 0.154 0.251 0.386 0.329 0.498 14 15 16 17 18 19 20 21 22 23 24 25 26 0.653 0.800 NA 0.214 0.561 0.820 0.193 0.766 0.349 0.454 0.241 0.361 0.241 27 28 29 30 31 32 33 34 35 36 37 38 39 0.596 0.279 0.767 NA 0.783 0.474 NA NA 0.265 0.327 0.746 0.253 0.738 40 41 42 43 44 45 46 47 48 49 50 51 52 0.796 0.305 0.731 NA 0.674 0.433 0.801 0.582 0.233 0.403 0.814 0.223 NA 53 54 55 56 57 58 59 60 61 62 63 64 65 0.253 NA 0.699 0.657 0.670 NA NA 0.441 0.291 NA 0.425 0.684 0.212 66 67 68 69 70 71 72 73 74 75 76 77 78 0.816 0.713 0.815 0.163 0.529 0.399 0.442 0.400 0.533 0.295 0.753 0.821 0.786 79 80 81 82 83 84 85 86 87 88 89 90 91 0.817 0.600 0.325 0.748 0.610 0.467 0.577 0.625 0.611 NA 0.623 0.824 0.289 92 93 94 95 96 97 98 99 100 101 102 103 104 0.459 0.153 0.290 0.343 0.611 0.667 0.354 0.309 0.659 0.576 0.581 0.266 0.772 105 106 107 108 109 110 111 112 113 114 115 116 117 NA 0.236 0.619 0.204 NA 0.793 0.224 0.546 0.755 0.242 0.453 NA 0.196 118 119 120 121 122 123 124 125 126 127 128 129 130 0.316 0.285 0.648 0.504 0.323 NA 0.775 0.161 0.552 0.225 0.537 0.440 NA 131 132 133 134 135 136 137 138 139 140 141 142 143 0.496 NA 0.786 NA 0.285 0.754 0.245 0.191 0.281 0.744 0.726 0.369 0.248 144 145 146 147 148 149 150 151 152 153 154 155 156 NA 0.429 0.457 NA 0.190 NA 0.583 0.255 0.296 0.337 NA 0.171 NA 157 158 159 160 161 162 163 164 165 166 167 168 169 0.533 0.163 0.154 0.253 0.353 0.312 0.247 0.258 NA 0.402 0.748 0.306 0.670 170 171 172 173 174 175 176 177 178 179 180 181 182 0.353 0.803 0.577 0.734 0.208 0.520 0.687 0.295 0.475 0.543 0.464 0.561 0.155 183 184 185 186 187 188 189 190 191 192 193 194 195 0.384 0.384 0.179 NA 0.679 0.705 0.258 0.779 NA NA 0.486 0.215 0.351 196 197 198 199 200 201 202 203 204 205 206 207 208 0.264 NA NA 0.350 0.221 NA 0.172 0.566 0.694 0.539 0.497 0.406 0.654 209 210 211 212 213 214 215 216 217 218 219 220 221 0.758 0.204 NA 0.372 0.291 0.208 0.541 NA 0.539 0.547 0.813 0.286 0.458 222 223 224 225 226 227 228 229 230 231 232 233 234 0.231 0.696 0.194 NA 0.183 NA 0.252 0.643 0.801 0.663 0.293 NA 0.215 235 236 237 238 239 240 241 242 243 244 245 246 247 0.243 0.185 0.303 0.429 0.640 NA 0.225 0.554 0.763 0.389 NA 0.709 0.206 248 249 250 251 252 253 254 255 256 257 258 259 260 0.679 0.211 0.740 0.505 0.552 0.746 0.748 0.174 NA 0.354 0.720 0.499 0.426 261 262 263 264 265 266 267 268 269 270 271 272 273 0.173 0.287 0.396 0.202 NA NA 0.737 NA NA 0.645 0.193 0.459 0.211 274 275 276 277 278 279 280 281 282 283 284 285 286 0.298 0.273 0.246 0.154 0.310 0.208 0.402 0.696 0.199 0.354 0.348 NA NA 287 288 289 290 291 292 293 294 295 296 297 298 299 0.695 0.702 0.271 0.449 0.339 0.511 0.810 0.224 0.370 NA 0.544 0.507 0.752 300 301 302 303 304 305 306 307 308 309 310 311 312 0.682 0.437 0.791 0.522 0.532 0.200 0.389 0.813 0.269 0.269 0.311 0.207 NA 313 314 315 316 317 318 319 320 321 322 323 324 325 0.312 0.589 0.803 0.181 0.164 0.165 0.411 0.290 0.201 0.744 0.225 0.514 0.484 326 327 328 329 330 331 332 333 334 335 336 337 338 NA 0.619 0.667 0.799 0.369 0.357 0.440 NA 0.499 0.147 0.745 0.521 NA 339 340 341 342 343 344 345 346 347 348 349 350 351 0.798 0.769 0.627 NA 0.447 NA 0.428 0.809 0.309 0.814 0.619 0.773 0.609 352 353 354 355 356 357 358 359 360 361 362 363 364 0.408 0.787 0.224 0.154 0.536 NA 0.316 0.307 0.561 NA 0.317 NA 0.718 365 366 367 368 369 370 371 372 373 374 375 376 377 NA 0.817 0.567 0.726 0.279 0.683 0.174 0.487 0.744 0.817 0.395 0.451 0.413 378 379 380 381 382 383 384 385 386 387 388 389 390 0.778 0.462 0.793 0.210 0.526 0.655 NA 0.577 NA 0.188 0.614 NA 0.194 391 392 393 394 395 396 397 398 399 400 401 402 403 0.397 NA 0.700 0.574 0.401 0.147 0.561 0.549 0.775 NA NA 0.292 NA 404 405 406 407 408 409 410 411 412 413 414 415 416 0.496 0.439 0.493 0.188 0.553 0.619 0.515 NA 0.321 0.312 NA 0.235 0.779 417 418 419 420 421 422 423 424 425 426 427 428 429 0.820 0.667 0.470 0.788 0.568 0.391 0.253 0.647 0.789 0.626 0.762 0.274 0.513 430 431 432 433 434 435 436 437 438 439 440 441 442 0.260 0.505 0.808 0.706 0.258 0.398 0.723 0.429 0.394 0.160 0.216 0.615 0.176 443 444 445 446 447 448 449 450 451 452 453 454 455 0.823 0.204 NA 0.158 0.201 0.439 0.704 0.727 NA 0.311 0.588 NA 0.505 456 457 458 459 460 461 462 463 464 465 466 467 468 0.422 0.650 0.239 0.338 0.388 NA 0.308 0.643 0.344 0.556 0.495 0.744 0.502 469 470 471 472 473 474 475 476 477 478 479 480 481 0.202 NA 0.176 0.636 NA 0.691 0.693 0.517 0.740 0.262 0.275 NA 0.432 482 483 484 485 486 487 488 489 490 491 492 493 494 0.601 0.184 0.355 0.709 0.359 0.171 0.746 0.521 NA 0.677 0.512 0.458 0.358 495 496 497 498 499 500 NA 0.798 0.296 0.200 0.291 0.243 > all.equal( fitted( ss ), fitted( ss, part = "outcome" ) ) [1] TRUE > round( fitted( ss, part = "selection" ), 3 ) 1 2 3 4 5 6 7 8 9 10 11 12 13 0.878 0.997 0.999 0.997 0.909 0.697 0.560 0.966 0.545 0.949 0.926 0.515 0.968 14 15 16 17 18 19 20 21 22 23 24 25 26 0.994 0.969 0.488 0.884 0.591 0.483 0.996 0.833 0.804 0.996 0.896 0.465 0.521 27 28 29 30 31 32 33 34 35 36 37 38 39 0.990 0.549 0.545 0.977 0.895 0.905 0.558 0.788 0.994 0.572 0.788 0.630 0.982 40 41 42 43 44 45 46 47 48 49 50 51 52 0.999 0.720 0.868 0.607 0.993 0.538 0.994 0.614 0.993 0.860 0.973 0.998 0.590 53 54 55 56 57 58 59 60 61 62 63 64 65 0.988 0.655 0.773 0.993 0.968 0.577 0.657 0.986 0.780 0.807 0.960 0.848 0.999 66 67 68 69 70 71 72 73 74 75 76 77 78 0.723 0.967 0.892 0.953 0.995 0.465 0.983 0.998 0.892 0.998 0.995 0.521 0.999 79 80 81 82 83 84 85 86 87 88 89 90 91 0.938 0.937 0.708 0.984 0.955 0.972 0.817 0.664 0.997 0.680 0.966 0.999 0.951 92 93 94 95 96 97 98 99 100 101 102 103 104 0.995 0.980 0.993 0.497 0.959 0.609 0.985 0.998 0.959 0.964 0.945 0.981 0.967 105 106 107 108 109 110 111 112 113 114 115 116 117 0.557 0.654 0.999 0.999 0.805 0.994 0.985 0.887 0.885 0.998 0.996 0.777 0.685 118 119 120 121 122 123 124 125 126 127 128 129 130 0.999 0.996 0.849 0.996 0.465 0.723 0.998 0.516 0.997 0.980 0.728 0.464 0.556 131 132 133 134 135 136 137 138 139 140 141 142 143 0.992 0.495 0.993 0.883 0.994 0.495 0.864 0.715 0.999 0.961 0.911 0.995 0.666 144 145 146 147 148 149 150 151 152 153 154 155 156 0.714 0.850 0.916 0.587 0.970 0.584 0.999 0.965 0.670 0.946 0.523 0.805 0.494 157 158 159 160 161 162 163 164 165 166 167 168 169 0.895 0.988 0.909 0.928 0.873 0.993 0.999 0.912 0.788 0.980 0.992 0.967 0.864 170 171 172 173 174 175 176 177 178 179 180 181 182 0.942 0.640 0.778 0.676 0.998 0.960 0.846 0.794 0.991 0.960 0.961 0.976 0.999 183 184 185 186 187 188 189 190 191 192 193 194 195 0.993 0.992 0.650 0.865 0.998 0.937 0.488 0.916 0.487 0.475 0.997 0.999 0.998 196 197 198 199 200 201 202 203 204 205 206 207 208 0.997 0.614 0.731 0.985 0.979 0.572 0.969 0.999 0.620 0.948 0.999 0.911 0.888 209 210 211 212 213 214 215 216 217 218 219 220 221 0.863 0.963 0.591 0.981 0.994 0.659 0.938 0.633 0.985 0.930 0.715 0.988 0.838 222 223 224 225 226 227 228 229 230 231 232 233 234 0.949 0.968 0.992 0.504 0.976 0.672 0.987 0.776 0.558 0.988 0.991 0.672 0.723 235 236 237 238 239 240 241 242 243 244 245 246 247 0.631 0.828 0.981 0.920 0.731 0.517 0.996 0.921 0.511 0.836 0.852 0.747 0.717 248 249 250 251 252 253 254 255 256 257 258 259 260 0.800 0.809 0.998 0.992 0.589 0.992 0.896 0.730 0.460 0.491 0.761 0.730 0.817 261 262 263 264 265 266 267 268 269 270 271 272 273 0.998 0.999 0.935 0.669 0.694 0.697 0.940 0.559 0.994 0.962 0.999 0.997 0.987 274 275 276 277 278 279 280 281 282 283 284 285 286 0.603 0.660 0.840 0.999 0.998 0.951 0.758 0.998 0.991 0.998 0.980 0.479 0.578 287 288 289 290 291 292 293 294 295 296 297 298 299 0.999 0.998 0.919 0.994 0.708 0.821 0.950 0.687 0.951 0.850 0.943 0.994 0.911 300 301 302 303 304 305 306 307 308 309 310 311 312 0.797 0.999 0.492 0.997 0.912 0.976 0.993 0.791 0.613 0.998 0.890 0.992 0.597 313 314 315 316 317 318 319 320 321 322 323 324 325 0.842 0.955 0.820 0.914 0.889 0.933 0.910 0.778 0.980 0.750 0.995 0.995 0.967 326 327 328 329 330 331 332 333 334 335 336 337 338 0.954 0.513 0.902 0.978 0.452 0.997 0.585 0.578 0.993 0.490 0.845 0.994 0.601 339 340 341 342 343 344 345 346 347 348 349 350 351 0.852 0.836 0.986 0.854 0.891 0.817 0.999 0.985 0.998 0.999 0.991 0.996 0.994 352 353 354 355 356 357 358 359 360 361 362 363 364 0.998 0.996 0.867 0.997 0.995 0.680 0.663 0.999 0.913 0.555 0.999 0.472 0.936 365 366 367 368 369 370 371 372 373 374 375 376 377 0.903 0.873 0.990 0.790 0.980 0.993 0.989 0.999 0.954 0.981 0.786 0.885 0.959 378 379 380 381 382 383 384 385 386 387 388 389 390 0.999 0.999 0.727 0.882 0.990 0.985 0.841 0.985 0.651 0.998 0.998 0.632 0.499 391 392 393 394 395 396 397 398 399 400 401 402 403 0.855 0.873 0.973 0.941 0.842 0.835 0.963 0.519 0.887 0.772 0.670 0.530 0.521 404 405 406 407 408 409 410 411 412 413 414 415 416 0.999 0.994 0.493 0.954 0.475 0.993 0.992 0.465 0.995 0.997 0.900 0.977 0.898 417 418 419 420 421 422 423 424 425 426 427 428 429 0.831 0.992 0.987 0.998 0.972 0.525 0.990 0.998 0.987 0.964 0.961 0.864 0.958 430 431 432 433 434 435 436 437 438 439 440 441 442 0.998 0.783 0.996 0.983 0.998 0.807 0.877 0.998 0.993 0.954 0.996 0.998 0.812 443 444 445 446 447 448 449 450 451 452 453 454 455 0.861 0.999 0.899 0.960 0.994 0.929 0.997 0.987 0.620 0.980 0.994 0.751 0.997 456 457 458 459 460 461 462 463 464 465 466 467 468 0.929 0.835 0.999 0.992 0.926 0.769 0.876 0.808 0.993 0.905 0.980 0.753 0.805 469 470 471 472 473 474 475 476 477 478 479 480 481 0.999 0.634 0.931 0.995 0.840 0.955 0.518 0.985 0.948 0.877 0.727 0.517 0.842 482 483 484 485 486 487 488 489 490 491 492 493 494 0.949 0.859 0.999 0.513 0.547 0.983 0.662 0.965 0.571 0.980 0.857 0.700 0.984 495 496 497 498 499 500 0.492 0.910 0.999 0.895 0.998 0.582 > round( residuals( ss ), 3 ) 1 2 3 4 5 6 7 8 9 10 11 -0.909 1.184 -0.633 0.781 1.326 0.633 NA 0.720 -0.579 -0.759 1.381 12 13 14 15 16 17 18 19 20 21 22 1.492 1.181 0.924 0.669 NA -0.694 1.075 0.629 -0.655 0.731 -0.926 23 24 25 26 27 28 29 30 31 32 33 -1.100 -0.743 -0.946 -0.742 1.017 -0.809 0.729 NA 0.700 -1.133 NA 34 35 36 37 38 39 40 41 42 43 44 NA -0.785 -0.890 0.766 1.658 0.780 -1.783 1.540 0.792 NA 0.889 45 46 47 48 49 50 51 52 53 54 55 1.293 0.667 -1.321 -0.729 1.348 0.642 -0.710 NA -0.765 NA 0.847 56 57 58 59 60 61 62 63 64 65 66 -1.462 0.895 NA NA 1.280 -0.830 NA 1.309 0.872 -0.691 0.637 67 68 69 70 71 72 73 74 75 76 77 0.822 0.640 -0.596 -1.227 1.356 -1.080 -1.011 -1.234 -0.837 0.754 0.628 78 79 80 81 82 83 84 85 86 87 88 0.693 0.635 -1.354 -0.887 0.762 0.994 1.234 -1.312 0.970 -1.374 NA 89 90 91 92 93 94 95 96 97 98 99 -1.396 -1.865 -0.826 1.249 -0.576 -0.827 1.464 0.993 0.899 1.441 -0.860 100 101 102 103 104 105 106 107 108 109 110 -1.468 -1.310 1.042 1.628 0.719 NA -0.734 -1.389 1.784 NA -1.774 111 112 113 114 115 116 117 118 119 120 121 -0.712 1.100 -1.678 -0.744 1.259 NA 1.806 -0.872 -0.820 0.931 -1.185 122 123 124 125 126 127 128 129 130 131 132 1.504 NA 0.715 -0.593 1.090 1.727 1.115 1.282 NA 1.183 NA 133 134 135 136 137 138 139 140 141 142 143 0.695 NA -0.819 0.752 -0.749 -0.651 1.593 -1.652 -1.608 1.411 1.670 144 145 146 147 148 149 150 151 152 153 154 NA -1.059 1.251 NA -0.649 NA 1.039 1.654 1.560 -0.906 NA 155 156 157 158 159 160 161 162 163 164 165 -0.612 NA 1.122 1.904 -0.579 -0.764 -0.933 -0.864 1.673 -0.773 NA 166 167 168 169 170 171 172 173 174 175 176 1.350 0.762 -0.855 0.894 -0.933 0.662 1.049 0.786 -0.684 -1.211 0.866 177 178 179 180 181 182 183 184 185 186 187 -0.836 1.220 1.106 -1.116 1.074 1.929 -0.985 -0.984 -0.627 NA 0.880 188 189 190 191 192 193 194 195 196 197 198 0.836 -0.773 -1.738 NA NA 1.201 1.755 1.447 1.632 NA NA 199 200 201 202 203 204 205 206 207 208 209 -0.928 -0.708 NA -0.614 -1.291 0.855 1.112 1.182 -1.020 0.921 0.744 210 211 212 213 214 215 216 217 218 219 220 1.783 NA -0.965 -0.830 1.773 1.108 NA -1.244 -1.259 0.644 -0.821 221 222 223 224 225 226 227 228 229 230 231 1.250 1.712 0.851 -0.656 NA -0.636 NA -0.762 -1.435 0.666 0.907 232 233 234 235 236 237 238 239 240 241 242 -0.832 NA -0.695 -0.746 1.837 -0.850 1.302 0.944 NA -0.714 -1.271 243 244 245 246 247 248 249 250 251 252 253 0.736 1.374 NA 0.830 -0.679 0.880 -0.688 0.776 1.169 -1.267 0.766 254 255 256 257 258 259 260 261 262 263 264 0.761 -0.619 NA 1.441 0.810 1.179 -1.054 -0.616 -0.822 1.361 1.788 265 266 267 268 269 270 271 272 273 274 275 NA NA 0.780 NA NA -1.439 -0.656 1.248 -0.689 -0.842 -0.799 276 277 278 279 280 281 282 283 284 285 286 -0.751 -0.578 -0.862 -0.683 1.349 0.851 1.796 -0.934 -0.924 NA NA 287 288 289 290 291 292 293 294 295 296 297 0.853 -1.556 -0.795 -1.092 -0.911 -1.196 -1.821 -0.713 -0.961 NA -1.254 298 299 300 301 302 303 304 305 306 307 308 -1.190 0.754 0.874 -1.072 0.684 1.140 -1.232 -0.668 -0.993 0.644 -0.792 309 310 311 312 313 314 315 316 317 318 319 -0.791 -0.863 -0.681 NA -0.865 1.028 0.662 -0.631 -0.598 -0.600 1.334 320 321 322 323 324 325 326 327 328 329 330 1.573 -0.669 0.769 -0.715 1.153 1.204 NA 0.980 0.899 0.670 -0.960 331 332 333 334 335 336 337 338 339 340 341 -0.940 1.282 NA 1.180 1.958 -1.653 -1.213 NA 0.672 -1.711 0.966 342 343 344 345 346 347 348 349 350 351 352 NA -1.088 NA 1.303 0.652 -0.860 0.642 0.980 0.717 0.996 1.340 353 354 355 356 357 358 359 360 361 362 363 -1.759 -0.712 -0.578 1.116 NA 1.518 -0.856 1.075 NA -0.873 NA 364 365 366 367 368 369 370 371 372 373 374 0.813 NA 0.636 -1.294 0.801 -0.810 0.872 -0.619 -1.156 0.769 0.636 375 376 377 378 379 380 381 382 383 384 385 1.363 1.263 -1.033 0.709 1.243 0.680 1.768 1.133 0.920 NA 1.049 386 387 388 389 390 391 392 393 394 395 396 NA -0.646 0.988 NA 1.811 1.360 NA 0.845 1.054 -1.013 1.958 397 398 399 400 401 402 403 404 405 406 407 1.074 1.096 0.715 NA NA -0.831 NA 1.185 -1.076 1.190 -0.646 408 409 410 411 412 413 414 415 416 417 418 1.089 -1.390 -1.203 NA -0.879 1.526 NA -0.733 0.707 0.630 -1.483 419 420 421 422 423 424 425 426 427 428 429 -1.126 0.691 1.063 1.370 1.657 -1.442 0.689 0.968 -1.693 -0.801 -1.199 430 431 432 433 434 435 436 437 438 439 440 -0.776 -1.186 0.652 0.835 -0.773 1.357 0.805 -1.059 1.365 -0.591 -0.698 441 442 443 444 445 446 447 448 449 450 451 0.987 -0.622 0.624 -0.675 NA -0.586 -0.669 1.282 0.838 -1.612 NA 452 453 454 455 456 457 458 459 460 461 462 -0.863 1.030 NA 1.169 1.314 0.929 -0.740 1.473 -0.992 NA -0.858 463 464 465 466 467 468 469 470 471 472 473 -1.436 1.461 1.084 -1.168 0.769 1.175 -0.672 NA 1.863 -1.421 NA 474 475 476 477 478 479 480 481 482 483 484 -1.532 -1.536 -1.207 0.775 -0.779 -0.802 NA 1.295 -1.356 1.840 -0.936 485 486 487 488 489 490 491 492 493 494 495 0.830 1.431 -0.612 0.766 -1.213 NA -1.503 1.157 1.249 -0.941 NA 496 497 498 499 500 0.672 -0.838 1.795 1.571 -0.747 > all.equal( residuals( ss ), residuals( ss, part = "outcome" ) ) [1] TRUE > all.equal( residuals( ss ), + residuals( ss, part = "outcome", type = "deviance" ) ) [1] TRUE > round( residuals( ss, type = "pearson" ), 3 ) 1 2 3 4 5 6 7 8 9 10 11 -0.715 1.007 -0.471 0.597 1.187 0.471 NA 0.544 -0.427 -0.578 1.262 12 13 14 15 16 17 18 19 20 21 22 1.429 1.004 0.730 0.501 NA -0.522 0.884 0.468 -0.489 0.553 -0.731 23 24 25 26 27 28 29 30 31 32 33 -0.911 -0.564 -0.752 -0.563 0.823 -0.622 0.552 NA 0.527 -0.949 NA 34 35 36 37 38 39 40 41 42 43 44 NA -0.601 -0.697 0.584 1.719 0.596 -1.975 1.508 0.607 NA 0.696 45 46 47 48 49 50 51 52 53 54 55 1.144 0.499 -1.181 -0.551 1.217 0.478 -0.535 NA -0.583 NA 0.657 56 57 58 59 60 61 62 63 64 65 66 -1.383 0.702 NA NA 1.126 -0.641 NA 1.164 0.680 -0.519 0.475 67 68 69 70 71 72 73 74 75 76 77 0.634 0.477 -0.441 -1.060 1.228 -0.890 -0.817 -1.068 -0.648 0.573 0.467 78 79 80 81 82 83 84 85 86 87 88 0.521 0.472 -1.225 -0.694 0.580 0.800 1.068 -1.168 0.775 -1.253 NA 89 90 91 92 93 94 95 96 97 98 99 -1.284 -2.167 -0.637 1.086 -0.425 -0.639 1.385 0.798 0.706 1.350 -0.669 100 101 102 103 104 105 106 107 108 109 110 -1.391 -1.165 0.849 1.662 0.543 NA -0.556 -1.275 1.977 NA -1.956 111 112 113 114 115 116 117 118 119 120 121 -0.537 0.911 -1.756 -0.565 1.100 NA 2.027 -0.680 -0.632 0.736 -1.009 122 123 124 125 126 127 128 129 130 131 132 1.449 NA 0.539 -0.439 0.901 1.855 0.928 1.129 NA 1.007 NA 133 134 135 136 137 138 139 140 141 142 143 0.522 NA -0.631 0.571 -0.569 -0.485 1.599 -1.707 -1.627 1.307 1.742 144 145 146 147 148 149 150 151 152 153 154 NA -0.867 1.089 NA -0.485 NA 0.846 1.711 1.541 -0.713 NA 155 156 157 158 159 160 161 162 163 164 165 -0.454 NA 0.936 2.264 -0.427 -0.582 -0.739 -0.673 1.747 -0.590 NA 166 167 168 169 170 171 172 173 174 175 176 1.219 0.580 -0.664 0.701 -0.738 0.495 0.856 0.602 -0.513 -1.040 0.674 177 178 179 180 181 182 183 184 185 186 187 -0.647 1.052 0.918 -0.930 0.884 2.331 -0.790 -0.789 -0.466 NA 0.687 188 189 190 191 192 193 194 195 196 197 198 0.647 -0.590 -1.878 NA NA 1.028 1.913 1.360 1.670 NA NA 199 200 201 202 203 204 205 206 207 208 209 -0.733 -0.533 NA -0.456 -1.141 0.664 0.926 1.006 -0.826 0.727 0.564 210 211 212 213 214 215 216 217 218 219 220 1.975 NA -0.770 -0.641 1.954 0.920 NA -1.081 -1.100 0.480 -0.633 221 222 223 224 225 226 227 228 229 230 231 1.089 1.826 0.661 -0.490 NA -0.473 NA -0.580 -1.341 0.499 0.714 232 233 234 235 236 237 238 239 240 241 242 -0.643 NA -0.523 -0.567 2.098 -0.659 1.155 0.750 NA -0.539 -1.115 243 244 245 246 247 248 249 250 251 252 253 0.558 1.254 NA 0.641 -0.510 0.688 -0.517 0.593 0.990 -1.110 0.584 254 255 256 257 258 259 260 261 262 263 264 0.580 -0.459 NA 1.350 0.623 1.002 -0.862 -0.457 -0.634 1.235 1.986 265 266 267 268 269 270 271 272 273 274 275 NA NA 0.597 NA NA -1.348 -0.490 1.085 -0.518 -0.652 -0.613 276 277 278 279 280 281 282 283 284 285 286 -0.571 -0.426 -0.671 -0.512 1.218 0.661 2.005 -0.739 -0.730 NA NA 287 288 289 290 291 292 293 294 295 296 297 0.663 -1.535 -0.610 -0.903 -0.717 -1.022 -2.062 -0.538 -0.766 NA -1.093 298 299 300 301 302 303 304 305 306 307 308 -1.015 0.574 0.682 -0.881 0.513 0.957 -1.066 -0.500 -0.798 0.480 -0.607 309 310 311 312 313 314 315 316 317 318 319 -0.606 -0.671 -0.511 NA -0.674 0.835 0.495 -0.469 -0.442 -0.444 1.198 320 321 322 323 324 325 326 327 328 329 330 1.565 -0.501 0.586 -0.540 0.972 1.032 NA 0.785 0.706 0.501 -0.765 331 332 333 334 335 336 337 338 339 340 341 -0.745 1.129 NA 1.003 2.408 -1.708 -1.042 NA 0.503 -1.822 0.771 342 343 344 345 346 347 348 349 350 351 352 NA -0.898 NA 1.157 0.486 -0.668 0.478 0.785 0.541 0.801 1.206 353 354 355 356 357 358 359 360 361 362 363 -1.923 -0.537 -0.426 0.930 NA 1.472 -0.665 0.884 NA -0.681 NA 364 365 366 367 368 369 370 371 372 373 374 0.626 NA 0.473 -1.144 0.615 -0.623 0.681 -0.459 -0.975 0.586 0.473 375 376 377 378 379 380 381 382 383 384 385 1.237 1.104 -0.840 0.534 1.080 0.510 1.942 0.949 0.726 NA 0.856 386 387 388 389 390 391 392 393 394 395 396 NA -0.482 0.793 NA 2.039 1.233 NA 0.655 0.862 -0.819 2.409 397 398 399 400 401 402 403 404 405 406 407 0.884 0.907 0.539 NA NA -0.642 NA 1.009 -0.885 1.014 -0.482 408 409 410 411 412 413 414 415 416 417 418 0.899 -1.275 -1.030 NA -0.687 1.484 NA -0.555 0.533 0.469 -1.415 419 420 421 422 423 424 425 426 427 428 429 -0.941 0.519 0.872 1.248 1.717 -1.353 0.518 0.773 -1.787 -0.615 -1.025 430 431 432 433 434 435 436 437 438 439 440 -0.593 -1.010 0.487 0.645 -0.590 1.230 0.618 -0.867 1.241 -0.437 -0.525 441 442 443 444 445 446 447 448 449 450 451 0.792 -0.462 0.463 -0.506 NA -0.433 -0.501 1.129 0.649 -1.633 NA 452 453 454 455 456 457 458 459 460 461 462 -0.672 0.837 NA 0.990 1.171 0.734 -0.561 1.400 -0.797 NA -0.667 463 464 465 466 467 468 469 470 471 472 473 -1.343 1.381 0.894 -0.989 0.587 0.997 -0.504 NA 2.162 -1.321 NA 474 475 476 477 478 479 480 481 482 483 484 -1.495 -1.502 -1.035 0.592 -0.596 -0.616 NA 1.146 -1.228 2.106 -0.741 485 486 487 488 489 490 491 492 493 494 495 0.641 1.336 -0.454 0.584 -1.042 NA -1.446 0.977 1.087 -0.746 NA 496 497 498 499 500 0.503 -0.649 2.001 1.561 -0.567 > all.equal( residuals( ss, type = "pearson" ), + residuals( ss, part = "outcome", type = "pearson" ) ) [1] TRUE > round( residuals( ss, type = "deviance" ), 3 ) 1 2 3 4 5 6 7 8 9 10 11 -0.909 1.184 -0.633 0.781 1.326 0.633 NA 0.720 -0.579 -0.759 1.381 12 13 14 15 16 17 18 19 20 21 22 1.492 1.181 0.924 0.669 NA -0.694 1.075 0.629 -0.655 0.731 -0.926 23 24 25 26 27 28 29 30 31 32 33 -1.100 -0.743 -0.946 -0.742 1.017 -0.809 0.729 NA 0.700 -1.133 NA 34 35 36 37 38 39 40 41 42 43 44 NA -0.785 -0.890 0.766 1.658 0.780 -1.783 1.540 0.792 NA 0.889 45 46 47 48 49 50 51 52 53 54 55 1.293 0.667 -1.321 -0.729 1.348 0.642 -0.710 NA -0.765 NA 0.847 56 57 58 59 60 61 62 63 64 65 66 -1.462 0.895 NA NA 1.280 -0.830 NA 1.309 0.872 -0.691 0.637 67 68 69 70 71 72 73 74 75 76 77 0.822 0.640 -0.596 -1.227 1.356 -1.080 -1.011 -1.234 -0.837 0.754 0.628 78 79 80 81 82 83 84 85 86 87 88 0.693 0.635 -1.354 -0.887 0.762 0.994 1.234 -1.312 0.970 -1.374 NA 89 90 91 92 93 94 95 96 97 98 99 -1.396 -1.865 -0.826 1.249 -0.576 -0.827 1.464 0.993 0.899 1.441 -0.860 100 101 102 103 104 105 106 107 108 109 110 -1.468 -1.310 1.042 1.628 0.719 NA -0.734 -1.389 1.784 NA -1.774 111 112 113 114 115 116 117 118 119 120 121 -0.712 1.100 -1.678 -0.744 1.259 NA 1.806 -0.872 -0.820 0.931 -1.185 122 123 124 125 126 127 128 129 130 131 132 1.504 NA 0.715 -0.593 1.090 1.727 1.115 1.282 NA 1.183 NA 133 134 135 136 137 138 139 140 141 142 143 0.695 NA -0.819 0.752 -0.749 -0.651 1.593 -1.652 -1.608 1.411 1.670 144 145 146 147 148 149 150 151 152 153 154 NA -1.059 1.251 NA -0.649 NA 1.039 1.654 1.560 -0.906 NA 155 156 157 158 159 160 161 162 163 164 165 -0.612 NA 1.122 1.904 -0.579 -0.764 -0.933 -0.864 1.673 -0.773 NA 166 167 168 169 170 171 172 173 174 175 176 1.350 0.762 -0.855 0.894 -0.933 0.662 1.049 0.786 -0.684 -1.211 0.866 177 178 179 180 181 182 183 184 185 186 187 -0.836 1.220 1.106 -1.116 1.074 1.929 -0.985 -0.984 -0.627 NA 0.880 188 189 190 191 192 193 194 195 196 197 198 0.836 -0.773 -1.738 NA NA 1.201 1.755 1.447 1.632 NA NA 199 200 201 202 203 204 205 206 207 208 209 -0.928 -0.708 NA -0.614 -1.291 0.855 1.112 1.182 -1.020 0.921 0.744 210 211 212 213 214 215 216 217 218 219 220 1.783 NA -0.965 -0.830 1.773 1.108 NA -1.244 -1.259 0.644 -0.821 221 222 223 224 225 226 227 228 229 230 231 1.250 1.712 0.851 -0.656 NA -0.636 NA -0.762 -1.435 0.666 0.907 232 233 234 235 236 237 238 239 240 241 242 -0.832 NA -0.695 -0.746 1.837 -0.850 1.302 0.944 NA -0.714 -1.271 243 244 245 246 247 248 249 250 251 252 253 0.736 1.374 NA 0.830 -0.679 0.880 -0.688 0.776 1.169 -1.267 0.766 254 255 256 257 258 259 260 261 262 263 264 0.761 -0.619 NA 1.441 0.810 1.179 -1.054 -0.616 -0.822 1.361 1.788 265 266 267 268 269 270 271 272 273 274 275 NA NA 0.780 NA NA -1.439 -0.656 1.248 -0.689 -0.842 -0.799 276 277 278 279 280 281 282 283 284 285 286 -0.751 -0.578 -0.862 -0.683 1.349 0.851 1.796 -0.934 -0.924 NA NA 287 288 289 290 291 292 293 294 295 296 297 0.853 -1.556 -0.795 -1.092 -0.911 -1.196 -1.821 -0.713 -0.961 NA -1.254 298 299 300 301 302 303 304 305 306 307 308 -1.190 0.754 0.874 -1.072 0.684 1.140 -1.232 -0.668 -0.993 0.644 -0.792 309 310 311 312 313 314 315 316 317 318 319 -0.791 -0.863 -0.681 NA -0.865 1.028 0.662 -0.631 -0.598 -0.600 1.334 320 321 322 323 324 325 326 327 328 329 330 1.573 -0.669 0.769 -0.715 1.153 1.204 NA 0.980 0.899 0.670 -0.960 331 332 333 334 335 336 337 338 339 340 341 -0.940 1.282 NA 1.180 1.958 -1.653 -1.213 NA 0.672 -1.711 0.966 342 343 344 345 346 347 348 349 350 351 352 NA -1.088 NA 1.303 0.652 -0.860 0.642 0.980 0.717 0.996 1.340 353 354 355 356 357 358 359 360 361 362 363 -1.759 -0.712 -0.578 1.116 NA 1.518 -0.856 1.075 NA -0.873 NA 364 365 366 367 368 369 370 371 372 373 374 0.813 NA 0.636 -1.294 0.801 -0.810 0.872 -0.619 -1.156 0.769 0.636 375 376 377 378 379 380 381 382 383 384 385 1.363 1.263 -1.033 0.709 1.243 0.680 1.768 1.133 0.920 NA 1.049 386 387 388 389 390 391 392 393 394 395 396 NA -0.646 0.988 NA 1.811 1.360 NA 0.845 1.054 -1.013 1.958 397 398 399 400 401 402 403 404 405 406 407 1.074 1.096 0.715 NA NA -0.831 NA 1.185 -1.076 1.190 -0.646 408 409 410 411 412 413 414 415 416 417 418 1.089 -1.390 -1.203 NA -0.879 1.526 NA -0.733 0.707 0.630 -1.483 419 420 421 422 423 424 425 426 427 428 429 -1.126 0.691 1.063 1.370 1.657 -1.442 0.689 0.968 -1.693 -0.801 -1.199 430 431 432 433 434 435 436 437 438 439 440 -0.776 -1.186 0.652 0.835 -0.773 1.357 0.805 -1.059 1.365 -0.591 -0.698 441 442 443 444 445 446 447 448 449 450 451 0.987 -0.622 0.624 -0.675 NA -0.586 -0.669 1.282 0.838 -1.612 NA 452 453 454 455 456 457 458 459 460 461 462 -0.863 1.030 NA 1.169 1.314 0.929 -0.740 1.473 -0.992 NA -0.858 463 464 465 466 467 468 469 470 471 472 473 -1.436 1.461 1.084 -1.168 0.769 1.175 -0.672 NA 1.863 -1.421 NA 474 475 476 477 478 479 480 481 482 483 484 -1.532 -1.536 -1.207 0.775 -0.779 -0.802 NA 1.295 -1.356 1.840 -0.936 485 486 487 488 489 490 491 492 493 494 495 0.830 1.431 -0.612 0.766 -1.213 NA -1.503 1.157 1.249 -0.941 NA 496 497 498 499 500 0.672 -0.838 1.795 1.571 -0.747 > all.equal( residuals( ss, type = "deviance" ), + residuals( ss, part = "outcome", type = "deviance" ) ) [1] TRUE > all.equal( residuals( ss, part = "outcome", type = "response" ), + ( simDat$yo == 1 ) - fitted( ss, part = "outcome" ) ) [1] TRUE > round( residuals( ss, part = "selection" ), 3 ) 1 2 3 4 5 6 7 8 9 10 11 0.510 0.074 0.044 0.076 0.437 0.849 -1.282 0.265 1.103 0.324 0.391 12 13 14 15 16 17 18 19 20 21 22 1.152 0.254 0.110 0.250 -1.158 0.497 1.025 1.206 0.086 0.605 0.660 23 24 25 26 27 28 29 30 31 32 33 0.094 0.470 1.238 1.142 0.145 1.096 1.103 -2.750 0.471 0.446 -1.277 34 35 36 37 38 39 40 41 42 43 44 -1.762 0.108 1.057 0.691 0.962 0.193 0.041 0.811 0.533 -1.367 0.114 45 46 47 48 49 50 51 52 53 54 55 1.113 0.114 0.988 0.117 0.549 0.234 0.058 -1.336 0.155 -1.458 0.718 56 57 58 59 60 61 62 63 64 65 66 0.119 0.254 -1.312 -1.464 0.165 0.704 -1.813 0.286 0.575 0.037 0.805 67 68 69 70 71 72 73 74 75 76 77 0.257 0.477 0.310 0.100 1.237 0.184 0.071 0.479 0.066 0.101 1.143 78 79 80 81 82 83 84 85 86 87 88 0.048 0.358 0.359 0.831 0.180 0.302 0.240 0.636 0.905 0.084 -1.509 89 90 91 92 93 94 95 96 97 98 99 0.262 0.043 0.317 0.100 0.203 0.121 1.182 0.290 0.996 0.176 0.059 100 101 102 103 104 105 106 107 108 109 110 0.288 0.272 0.337 0.198 0.260 -1.276 0.921 0.040 0.038 -1.808 0.111 111 112 113 114 115 116 117 118 119 120 121 0.175 0.489 0.495 0.068 0.095 -1.731 0.870 0.047 0.088 0.572 0.086 122 123 124 125 126 127 128 129 130 131 132 1.238 -1.602 0.059 1.151 0.074 0.199 0.796 1.240 -1.275 0.123 -1.170 133 134 135 136 137 138 139 140 141 142 143 0.119 -2.071 0.113 1.185 0.542 0.819 0.045 0.283 0.432 0.103 0.902 144 145 146 147 148 149 150 151 152 153 154 -1.581 0.569 0.419 -1.331 0.248 -1.325 0.047 0.267 0.895 0.334 -1.217 155 156 157 158 159 160 161 162 163 164 165 0.659 -1.168 0.471 0.158 0.436 0.386 0.521 0.116 0.046 0.428 -1.760 166 167 168 169 170 171 172 173 174 175 176 0.202 0.130 0.259 0.540 0.345 0.945 0.709 0.885 0.065 0.286 0.579 177 178 179 180 181 182 183 184 185 186 187 0.678 0.134 0.286 0.283 0.218 0.045 0.122 0.126 0.928 -2.000 0.059 188 189 190 191 192 193 194 195 196 197 198 0.361 1.198 0.420 -1.156 -1.136 0.074 0.047 0.066 0.080 -1.379 -1.620 199 200 201 202 203 204 205 206 207 208 209 0.173 0.205 -1.303 0.253 0.050 0.978 0.327 0.054 0.431 0.488 0.543 210 211 212 213 214 215 216 217 218 219 220 0.275 -1.338 0.198 0.105 0.913 0.357 -1.416 0.174 0.380 0.818 0.153 221 222 223 224 225 226 227 228 229 230 231 0.594 0.322 0.255 0.127 -1.184 0.220 -1.493 0.161 0.712 1.081 0.156 232 233 234 235 236 237 238 239 240 241 242 0.132 -1.492 0.805 0.960 0.615 0.196 0.409 0.792 -1.207 0.085 0.406 243 244 245 246 247 248 249 250 251 252 253 1.160 0.600 -1.954 0.764 0.815 0.668 0.650 0.066 0.125 1.030 0.128 254 255 256 257 258 259 260 261 262 263 264 0.469 0.793 -1.110 1.192 0.739 0.794 0.636 0.061 0.052 0.366 0.897 265 266 267 268 269 270 271 272 273 274 275 -1.538 -1.545 0.352 -1.279 -3.208 0.277 0.044 0.072 0.162 1.006 0.911 276 277 278 279 280 281 282 283 284 285 286 0.591 0.039 0.059 0.316 0.745 0.057 0.131 0.063 0.203 -1.142 -1.314 287 288 289 290 291 292 293 294 295 296 297 0.049 0.068 0.412 0.112 0.831 0.628 0.322 0.867 0.319 -1.948 0.344 298 299 300 301 302 303 304 305 306 307 308 0.109 0.432 0.674 0.053 1.192 0.083 0.429 0.219 0.116 0.684 0.989 309 310 311 312 313 314 315 316 317 318 319 0.066 0.482 0.130 -1.349 0.586 0.303 0.629 0.424 0.484 0.373 0.435 320 321 322 323 324 325 326 327 328 329 330 0.708 0.203 0.759 0.099 0.101 0.259 -2.479 1.155 0.453 0.212 1.260 331 332 333 334 335 336 337 338 339 340 341 0.076 1.036 -1.313 0.117 1.194 0.580 0.112 -1.355 0.567 0.599 0.168 342 343 344 345 346 347 348 349 350 351 352 -1.962 0.481 -1.842 0.046 0.173 0.069 0.053 0.137 0.087 0.106 0.066 353 354 355 356 357 358 359 360 361 362 363 0.091 0.535 0.074 0.105 -1.510 0.906 0.050 0.427 -1.273 0.040 -1.131 364 365 366 367 368 369 370 371 372 373 374 0.363 -2.159 0.520 0.141 0.686 0.199 0.116 0.151 0.041 0.306 0.196 375 376 377 378 379 380 381 382 383 384 385 0.694 0.495 0.289 0.041 0.045 0.799 0.501 0.143 0.172 -1.918 0.173 386 387 388 389 390 391 392 393 394 395 396 -1.451 0.067 0.068 -1.414 1.179 0.559 -2.030 0.235 0.349 0.587 0.601 397 398 399 400 401 402 403 404 405 406 407 0.275 1.146 0.489 -1.719 -1.489 1.126 -1.213 0.043 0.108 1.189 0.307 408 409 410 411 412 413 414 415 416 417 418 1.221 0.118 0.129 -1.119 0.097 0.080 -2.147 0.217 0.464 0.608 0.124 419 420 421 422 423 424 425 426 427 428 429 0.162 0.058 0.239 1.135 0.141 0.062 0.164 0.270 0.282 0.540 0.292 430 431 432 433 434 435 436 437 438 439 440 0.065 0.699 0.093 0.183 0.064 0.656 0.512 0.062 0.115 0.307 0.093 441 442 443 444 445 446 447 448 449 450 451 0.056 0.646 0.546 0.046 -2.140 0.284 0.105 0.383 0.074 0.165 -1.391 452 453 454 455 456 457 458 459 460 461 462 0.203 0.106 -1.667 0.077 0.383 0.600 0.038 0.127 0.392 -1.712 0.515 463 464 465 466 467 468 469 470 471 472 473 0.654 0.122 0.448 0.199 0.752 0.658 0.054 -1.417 0.378 0.104 -1.914 474 475 476 477 478 479 480 481 482 483 484 0.302 1.146 0.176 0.326 0.512 0.799 -1.206 0.585 0.324 0.551 0.038 485 486 487 488 489 490 491 492 493 494 495 1.156 1.099 0.183 0.908 0.268 -1.302 0.199 0.555 0.844 0.179 -1.163 496 497 498 499 500 0.435 0.043 0.472 0.057 1.041 > all.equal( residuals( ss, part = "selection" ), + residuals( ss, part = "selection", type = "deviance" ) ) [1] TRUE > round( residuals( ss, part = "selection", type = "pearson" ), digits = 3 ) 1 2 3 4 5 6 7 8 9 10 0.372 0.052 0.031 0.054 0.316 0.659 -1.129 0.189 0.915 0.232 11 12 13 14 15 16 17 18 19 20 0.282 0.970 0.181 0.078 0.178 -0.977 0.362 0.831 1.034 0.061 21 22 23 24 25 26 27 28 29 30 0.449 0.493 0.067 0.341 1.073 0.959 0.103 0.907 0.915 -6.543 31 32 33 34 35 36 37 38 39 40 0.343 0.324 -1.123 -1.929 0.077 0.865 0.519 0.767 0.137 0.029 41 42 43 44 45 46 47 48 49 50 0.624 0.390 -1.243 0.081 0.926 0.081 0.793 0.083 0.403 0.166 51 52 53 54 55 56 57 58 59 60 0.041 -1.200 0.110 -1.377 0.542 0.084 0.181 -1.169 -1.385 0.117 61 62 63 64 65 66 67 68 69 70 0.530 -2.043 0.204 0.424 0.026 0.618 0.184 0.347 0.222 0.071 71 72 73 74 75 76 77 78 79 80 1.072 0.131 0.050 0.348 0.047 0.072 0.960 0.034 0.257 0.258 81 82 83 84 85 86 87 88 89 90 0.642 0.128 0.216 0.171 0.473 0.711 0.059 -1.457 0.187 0.030 91 92 93 94 95 96 97 98 99 100 0.227 0.071 0.145 0.086 1.006 0.207 0.801 0.125 0.042 0.206 101 102 103 104 105 106 107 108 109 110 0.194 0.241 0.140 0.185 -1.122 0.727 0.028 0.027 -2.030 0.079 111 112 113 114 115 116 117 118 119 120 0.124 0.357 0.361 0.048 0.067 -1.864 0.679 0.033 0.062 0.422 121 122 123 124 125 126 127 128 129 130 0.061 1.073 -1.616 0.042 0.969 0.052 0.142 0.611 1.075 -1.119 131 132 133 134 135 136 137 138 139 140 0.087 -0.991 0.084 -2.744 0.080 1.009 0.397 0.631 0.031 0.202 141 142 143 144 145 146 147 148 149 150 0.313 0.073 0.708 -1.578 0.419 0.303 -1.193 0.177 -1.185 0.033 151 152 153 154 155 156 157 158 159 160 0.191 0.702 0.240 -1.048 0.492 -0.989 0.342 0.112 0.316 0.278 161 162 163 164 165 166 167 168 169 170 0.381 0.082 0.032 0.310 -1.926 0.143 0.092 0.185 0.397 0.248 171 172 173 174 175 176 177 178 179 180 0.750 0.534 0.692 0.046 0.204 0.427 0.509 0.095 0.204 0.202 181 182 183 184 185 186 187 188 189 190 0.155 0.032 0.086 0.089 0.733 -2.529 0.042 0.259 1.024 0.304 191 192 193 194 195 196 197 198 199 200 -0.975 -0.952 0.052 0.033 0.047 0.057 -1.260 -1.648 0.123 0.146 201 202 203 204 205 206 207 208 209 210 -1.157 0.180 0.036 0.783 0.235 0.038 0.312 0.355 0.398 0.196 211 212 213 214 215 216 217 218 219 220 -1.203 0.141 0.074 0.719 0.257 -1.313 0.123 0.274 0.631 0.109 221 222 223 224 225 226 227 228 229 230 0.439 0.231 0.182 0.090 -1.008 0.157 -1.430 0.114 0.537 0.891 231 232 233 234 235 236 237 238 239 240 0.111 0.094 -1.430 0.618 0.766 0.456 0.139 0.295 0.607 -1.035 241 242 243 244 245 246 247 248 249 250 0.060 0.293 0.979 0.444 -2.398 0.583 0.628 0.500 0.485 0.047 251 252 253 254 255 256 257 258 259 260 0.089 0.836 0.091 0.341 0.608 -0.923 1.017 0.560 0.609 0.474 261 262 263 264 265 266 267 268 269 270 0.043 0.037 0.263 0.704 -1.505 -1.516 0.253 -1.125 -13.072 0.198 271 272 273 274 275 276 277 278 279 280 0.031 0.051 0.115 0.811 0.717 0.437 0.028 0.042 0.226 0.565 281 282 283 284 285 286 287 288 289 290 0.040 0.093 0.044 0.144 -0.958 -1.170 0.034 0.048 0.297 0.079 291 292 293 294 295 296 297 298 299 300 0.643 0.467 0.230 0.675 0.228 -2.380 0.247 0.077 0.313 0.505 301 302 303 304 305 306 307 308 309 310 0.038 1.017 0.059 0.311 0.156 0.082 0.513 0.794 0.047 0.351 311 312 313 314 315 316 317 318 319 320 0.092 -1.218 0.433 0.217 0.468 0.307 0.353 0.268 0.315 0.534 321 322 323 324 325 326 327 328 329 330 0.144 0.578 0.070 0.072 0.185 -4.536 0.974 0.329 0.151 1.101 331 332 333 334 335 336 337 338 339 340 0.054 0.843 -1.170 0.083 1.019 0.428 0.080 -1.227 0.417 0.443 341 342 343 344 345 346 347 348 349 350 0.119 -2.421 0.350 -2.111 0.033 0.123 0.049 0.037 0.097 0.062 351 352 353 354 355 356 357 358 359 360 0.075 0.047 0.064 0.392 0.052 0.074 -1.458 0.713 0.035 0.309 361 362 363 364 365 366 367 368 369 370 -1.117 0.028 -0.946 0.261 -3.048 0.381 0.100 0.515 0.141 0.082 371 372 373 374 375 376 377 378 379 380 0.107 0.029 0.219 0.139 0.522 0.361 0.207 0.029 0.032 0.613 381 382 383 384 385 386 387 388 389 390 0.365 0.101 0.122 -2.300 0.122 -1.366 0.047 0.048 -1.310 1.002 391 392 393 394 395 396 397 398 399 400 0.411 -2.618 0.167 0.251 0.433 0.445 0.196 0.964 0.356 -1.840 401 402 403 404 405 406 407 408 409 410 -1.424 0.941 -1.043 0.030 0.077 1.014 0.219 1.052 0.083 0.091 411 412 413 414 415 416 417 418 419 420 -0.933 0.068 0.057 -3.005 0.155 0.337 0.451 0.088 0.115 0.041 421 422 423 424 425 426 427 428 429 430 0.170 0.951 0.100 0.044 0.117 0.193 0.202 0.396 0.209 0.046 431 432 433 434 435 436 437 438 439 440 0.526 0.066 0.130 0.045 0.490 0.374 0.044 0.082 0.220 0.066 441 442 443 444 445 446 447 448 449 450 0.039 0.481 0.401 0.032 -2.979 0.203 0.074 0.276 0.052 0.117 451 452 453 454 455 456 457 458 459 460 -1.277 0.144 0.075 -1.736 0.054 0.276 0.444 0.027 0.090 0.283 461 462 463 464 465 466 467 468 469 470 -1.824 0.377 0.488 0.086 0.325 0.142 0.572 0.492 0.038 -1.316 471 472 473 474 475 476 477 478 479 480 0.272 0.074 -2.290 0.216 0.964 0.125 0.233 0.374 0.613 -1.034 481 482 483 484 485 486 487 488 489 490 0.432 0.232 0.405 0.027 0.975 0.911 0.130 0.714 0.191 -1.154 491 492 493 494 495 496 497 498 499 500 0.141 0.408 0.654 0.127 -0.984 0.315 0.030 0.343 0.041 0.848 > round( residuals( ss, part = "selection", type = "response" ), digits = 3 ) 1 2 3 4 5 6 7 8 9 10 11 0.122 0.003 0.001 0.003 0.091 0.303 -0.560 0.034 0.455 0.051 0.074 12 13 14 15 16 17 18 19 20 21 22 0.485 0.032 0.006 0.031 -0.488 0.116 0.409 0.517 0.004 0.167 0.196 23 24 25 26 27 28 29 30 31 32 33 0.004 0.104 0.535 0.479 0.010 0.451 0.455 -0.977 0.105 0.095 -0.558 34 35 36 37 38 39 40 41 42 43 44 -0.788 0.006 0.428 0.212 0.370 0.018 0.001 0.280 0.132 -0.607 0.007 45 46 47 48 49 50 51 52 53 54 55 0.462 0.006 0.386 0.007 0.140 0.027 0.002 -0.590 0.012 -0.655 0.227 56 57 58 59 60 61 62 63 64 65 66 0.007 0.032 -0.577 -0.657 0.014 0.220 -0.807 0.040 0.152 0.001 0.277 67 68 69 70 71 72 73 74 75 76 77 0.033 0.108 0.047 0.005 0.535 0.017 0.002 0.108 0.002 0.005 0.479 78 79 80 81 82 83 84 85 86 87 88 0.001 0.062 0.063 0.292 0.016 0.045 0.028 0.183 0.336 0.003 -0.680 89 90 91 92 93 94 95 96 97 98 99 0.034 0.001 0.049 0.005 0.020 0.007 0.503 0.041 0.391 0.015 0.002 100 101 102 103 104 105 106 107 108 109 110 0.041 0.036 0.055 0.019 0.033 -0.557 0.346 0.001 0.001 -0.805 0.006 111 112 113 114 115 116 117 118 119 120 121 0.015 0.113 0.115 0.002 0.004 -0.777 0.315 0.001 0.004 0.151 0.004 122 123 124 125 126 127 128 129 130 131 132 0.535 -0.723 0.002 0.484 0.003 0.020 0.272 0.536 -0.556 0.008 -0.495 133 134 135 136 137 138 139 140 141 142 143 0.007 -0.883 0.006 0.505 0.136 0.285 0.001 0.039 0.089 0.005 0.334 144 145 146 147 148 149 150 151 152 153 154 -0.714 0.150 0.084 -0.587 0.030 -0.584 0.001 0.035 0.330 0.054 -0.523 155 156 157 158 159 160 161 162 163 164 165 0.195 -0.494 0.105 0.012 0.091 0.072 0.127 0.007 0.001 0.088 -0.788 166 167 168 169 170 171 172 173 174 175 176 0.020 0.008 0.033 0.136 0.058 0.360 0.222 0.324 0.002 0.040 0.154 177 178 179 180 181 182 183 184 185 186 187 0.206 0.009 0.040 0.039 0.024 0.001 0.007 0.008 0.350 -0.865 0.002 188 189 190 191 192 193 194 195 196 197 198 0.063 0.512 0.084 -0.487 -0.475 0.003 0.001 0.002 0.003 -0.614 -0.731 199 200 201 202 203 204 205 206 207 208 209 0.015 0.021 -0.572 0.031 0.001 0.380 0.052 0.001 0.089 0.112 0.137 210 211 212 213 214 215 216 217 218 219 220 0.037 -0.591 0.019 0.006 0.341 0.062 -0.633 0.015 0.070 0.285 0.012 221 222 223 224 225 226 227 228 229 230 231 0.162 0.051 0.032 0.008 -0.504 0.024 -0.672 0.013 0.224 0.442 0.012 232 233 234 235 236 237 238 239 240 241 242 0.009 -0.672 0.277 0.369 0.172 0.019 0.080 0.269 -0.517 0.004 0.079 243 244 245 246 247 248 249 250 251 252 253 0.489 0.164 -0.852 0.253 0.283 0.200 0.191 0.002 0.008 0.411 0.008 254 255 256 257 258 259 260 261 262 263 264 0.104 0.270 -0.460 0.509 0.239 0.270 0.183 0.002 0.001 0.065 0.331 265 266 267 268 269 270 271 272 273 274 275 -0.694 -0.697 0.060 -0.559 -0.994 0.038 0.001 0.003 0.013 0.397 0.340 276 277 278 279 280 281 282 283 284 285 286 0.160 0.001 0.002 0.049 0.242 0.002 0.009 0.002 0.020 -0.479 -0.578 287 288 289 290 291 292 293 294 295 296 297 0.001 0.002 0.081 0.006 0.292 0.179 0.050 0.313 0.049 -0.850 0.057 298 299 300 301 302 303 304 305 306 307 308 0.006 0.089 0.203 0.001 0.508 0.003 0.088 0.024 0.007 0.209 0.387 309 310 311 312 313 314 315 316 317 318 319 0.002 0.110 0.008 -0.597 0.158 0.045 0.180 0.086 0.111 0.067 0.090 320 321 322 323 324 325 326 327 328 329 330 0.222 0.020 0.250 0.005 0.005 0.033 -0.954 0.487 0.098 0.022 0.548 331 332 333 334 335 336 337 338 339 340 341 0.003 0.415 -0.578 0.007 0.510 0.155 0.006 -0.601 0.148 0.164 0.014 342 343 344 345 346 347 348 349 350 351 352 -0.854 0.109 -0.817 0.001 0.015 0.002 0.001 0.009 0.004 0.006 0.002 353 354 355 356 357 358 359 360 361 362 363 0.004 0.133 0.003 0.005 -0.680 0.337 0.001 0.087 -0.555 0.001 -0.472 364 365 366 367 368 369 370 371 372 373 374 0.064 -0.903 0.127 0.010 0.210 0.020 0.007 0.011 0.001 0.046 0.019 375 376 377 378 379 380 381 382 383 384 385 0.214 0.115 0.041 0.001 0.001 0.273 0.118 0.010 0.015 -0.841 0.015 386 387 388 389 390 391 392 393 394 395 396 -0.651 0.002 0.002 -0.632 0.501 0.145 -0.873 0.027 0.059 0.158 0.165 397 398 399 400 401 402 403 404 405 406 407 0.037 0.481 0.113 -0.772 -0.670 0.470 -0.521 0.001 0.006 0.507 0.046 408 409 410 411 412 413 414 415 416 417 418 0.525 0.007 0.008 -0.465 0.005 0.003 -0.900 0.023 0.102 0.169 0.008 419 420 421 422 423 424 425 426 427 428 429 0.013 0.002 0.028 0.475 0.010 0.002 0.013 0.036 0.039 0.136 0.042 430 431 432 433 434 435 436 437 438 439 440 0.002 0.217 0.004 0.017 0.002 0.193 0.123 0.002 0.007 0.046 0.004 441 442 443 444 445 446 447 448 449 450 451 0.002 0.188 0.139 0.001 -0.899 0.040 0.006 0.071 0.003 0.013 -0.620 452 453 454 455 456 457 458 459 460 461 462 0.020 0.006 -0.751 0.003 0.071 0.165 0.001 0.008 0.074 -0.769 0.124 463 464 465 466 467 468 469 470 471 472 473 0.192 0.007 0.095 0.020 0.247 0.195 0.001 -0.634 0.069 0.005 -0.840 474 475 476 477 478 479 480 481 482 483 484 0.045 0.482 0.015 0.052 0.123 0.273 -0.517 0.158 0.051 0.141 0.001 485 486 487 488 489 490 491 492 493 494 495 0.487 0.453 0.017 0.338 0.035 -0.571 0.020 0.143 0.300 0.016 -0.492 496 497 498 499 500 0.090 0.001 0.105 0.002 0.418 > all.equal( residuals( ss, part = "selection", type = "response" ), + simDat$ys - fitted( ss, part = "selection" ) ) [1] TRUE > model.matrix( ss ) (Intercept) xo 1 1 0.32067 2 1 0.52602 3 1 0.07334 4 1 0.84974 5 1 0.42306 6 1 0.98810 7 NA NA 8 1 0.90569 9 1 0.01851 10 1 0.19214 11 1 0.38431 12 1 0.30744 13 1 0.52829 14 1 0.72823 15 1 0.95356 16 NA NA 17 1 0.13202 18 1 0.60847 19 1 0.99187 20 1 0.09471 21 1 0.89528 22 1 0.33486 23 1 0.47218 24 1 0.17712 25 1 0.35166 26 1 0.17656 27 1 0.65305 28 1 0.23610 29 1 0.89716 30 NA NA 31 1 0.92380 32 1 0.49774 33 NA NA 34 NA NA 35 1 0.21483 36 1 0.30531 37 1 0.86350 38 1 0.19572 39 1 0.85095 40 1 0.94697 41 1 0.27456 42 1 0.83986 43 NA NA 44 1 0.75705 45 1 0.44613 46 1 0.95543 47 1 0.63533 48 1 0.16410 49 1 0.40697 50 1 0.97976 51 1 0.14694 52 NA NA 53 1 0.19670 54 NA NA 55 1 0.79254 56 1 0.73380 57 1 0.75172 58 NA NA 59 NA NA 60 1 0.45588 61 1 0.25400 62 NA NA 63 1 0.43530 64 1 0.77113 65 1 0.12916 66 1 0.98392 67 1 0.81418 68 1 0.98168 69 1 0.03634 70 1 0.56741 71 1 0.40172 72 1 0.45705 73 1 0.40332 74 1 0.57221 75 1 0.26025 76 1 0.87409 77 1 0.99309 78 1 0.93020 79 1 0.98653 80 1 0.65834 81 1 0.30239 82 1 0.86742 83 1 0.67126 84 1 0.48920 85 1 0.62858 86 1 0.69066 87 1 0.67229 88 NA NA 89 1 0.68774 90 1 0.99986 91 1 0.25054 92 1 0.47847 93 1 0.01510 94 1 0.25202 95 1 0.32666 96 1 0.67213 97 1 0.74844 98 1 0.34244 99 1 0.28026 100 1 0.73738 101 1 0.62697 102 1 0.63354 103 1 0.21598 104 1 0.90594 105 NA NA 106 1 0.16858 107 1 0.68320 108 1 0.11399 109 NA NA 110 1 0.94151 111 1 0.14895 112 1 0.58912 113 1 0.87828 114 1 0.17816 115 1 0.47083 116 NA NA 117 1 0.09938 118 1 0.29035 119 1 0.24548 120 1 0.72256 121 1 0.53627 122 1 0.29900 123 NA NA 124 1 0.91018 125 1 0.03297 126 1 0.59632 127 1 0.15091 128 1 0.57765 129 1 0.45448 130 NA NA 131 1 0.52621 132 NA NA 133 1 0.92890 134 NA NA 135 1 0.24476 136 1 0.87626 137 1 0.18266 138 1 0.09032 139 1 0.23916 140 1 0.86143 141 1 0.83256 142 1 0.36291 143 1 0.18791 144 NA NA 145 1 0.44079 146 1 0.47671 147 NA NA 148 1 0.08918 149 NA NA 150 1 0.63567 151 1 0.19854 152 1 0.26161 153 1 0.31876 154 NA NA 155 1 0.05209 156 NA NA 157 1 0.57226 158 1 0.03691 159 1 0.01809 160 1 0.19655 161 1 0.34098 162 1 0.28365 163 1 0.18633 164 1 0.20442 165 NA NA 166 1 0.40610 167 1 0.86717 168 1 0.27581 169 1 0.75255 170 1 0.34063 171 1 0.96010 172 1 0.62854 173 1 0.84531 174 1 0.12228 175 1 0.55571 176 1 0.77643 177 1 0.25938 178 1 0.49898 179 1 0.58442 180 1 0.48475 181 1 0.60854 182 1 0.02086 183 1 0.38280 184 1 0.38162 185 1 0.06741 186 NA NA 187 1 0.76474 188 1 0.80158 189 1 0.20403 190 1 0.91786 191 NA NA 192 NA NA 193 1 0.51343 194 1 0.13278 195 1 0.33798 196 1 0.21300 197 NA NA 198 NA NA 199 1 0.33625 200 1 0.14465 201 NA NA 202 1 0.05432 203 1 0.61388 204 1 0.78563 205 1 0.57945 206 1 0.52717 207 1 0.41051 208 1 0.73052 209 1 0.88360 210 1 0.11448 211 NA NA 212 1 0.36676 213 1 0.25395 214 1 0.12075 215 1 0.58297 216 NA NA 217 1 0.57975 218 1 0.59065 219 1 0.97719 220 1 0.24613 221 1 0.47724 222 1 0.16025 223 1 0.78917 224 1 0.09575 225 NA NA 226 1 0.07575 227 NA NA 228 1 0.19411 229 1 0.71458 230 1 0.95579 231 1 0.74186 232 1 0.25603 233 NA NA 234 1 0.13282 235 1 0.18019 236 1 0.07994 237 1 0.27118 238 1 0.44013 239 1 0.71146 240 NA NA 241 1 0.15047 242 1 0.59951 243 1 0.89062 244 1 0.38870 245 NA NA 246 1 0.80721 247 1 0.11808 248 1 0.76427 249 1 0.12625 250 1 0.85453 251 1 0.53677 252 1 0.59619 253 1 0.86305 254 1 0.86744 255 1 0.05909 256 NA NA 257 1 0.34248 258 1 0.82457 259 1 0.52929 260 1 0.43724 261 1 0.05643 262 1 0.24777 263 1 0.39809 264 1 0.11121 265 NA NA 266 NA NA 267 1 0.85053 268 NA NA 269 NA NA 270 1 0.71772 271 1 0.09516 272 1 0.47922 273 1 0.12714 274 1 0.26424 275 1 0.22704 276 1 0.18450 277 1 0.01726 278 1 0.28163 279 1 0.12104 280 1 0.40643 281 1 0.78917 282 1 0.10587 283 1 0.34159 284 1 0.33359 285 NA NA 286 NA NA 287 1 0.78717 288 1 0.79759 289 1 0.22391 290 1 0.46616 291 1 0.32234 292 1 0.54453 293 1 0.97157 294 1 0.14930 295 1 0.36368 296 NA NA 297 1 0.58661 298 1 0.53979 299 1 0.87389 300 1 0.76943 301 1 0.45084 302 1 0.93905 303 1 0.55859 304 1 0.57100 305 1 0.10731 306 1 0.38876 307 1 0.97748 308 1 0.22145 309 1 0.22006 310 1 0.28217 311 1 0.11922 312 NA NA 313 1 0.28445 314 1 0.64428 315 1 0.96036 316 1 0.07109 317 1 0.03792 318 1 0.04046 319 1 0.41692 320 1 0.25226 321 1 0.10859 322 1 0.86088 323 1 0.15139 324 1 0.54888 325 1 0.51072 326 NA NA 327 1 0.68298 328 1 0.74844 329 1 0.95252 330 1 0.36261 331 1 0.34629 332 1 0.45423 333 NA NA 334 1 0.52909 335 1 0.00282 336 1 0.86187 337 1 0.55689 338 NA NA 339 1 0.95033 340 1 0.90017 341 1 0.69395 342 NA NA 343 1 0.46319 344 NA NA 345 1 0.43910 346 1 0.96992 347 1 0.27955 348 1 0.97947 349 1 0.68293 350 1 0.90801 351 1 0.66998 352 1 0.41306 353 1 0.93139 354 1 0.14916 355 1 0.01702 356 1 0.57650 357 NA NA 358 1 0.28937 359 1 0.27640 360 1 0.60834 361 NA NA 362 1 0.29098 363 NA NA 364 1 0.82154 365 NA NA 366 1 0.98572 367 1 0.61545 368 1 0.83248 369 1 0.23662 370 1 0.77090 371 1 0.05877 372 1 0.51490 373 1 0.86101 374 1 0.98540 375 1 0.39676 376 1 0.46828 377 1 0.42066 378 1 0.91563 379 1 0.48231 380 1 0.94241 381 1 0.12418 382 1 0.56371 383 1 0.73124 384 NA NA 385 1 0.62836 386 NA NA 387 1 0.08576 388 1 0.67620 389 NA NA 390 1 0.09610 391 1 0.39890 392 NA NA 393 1 0.79457 394 1 0.62454 395 1 0.40501 396 1 0.00259 397 1 0.60858 398 1 0.59234 399 1 0.91016 400 NA NA 401 NA NA 402 1 0.25509 403 NA NA 404 1 0.52525 405 1 0.45407 406 1 0.52172 407 1 0.08570 408 1 0.59755 409 1 0.68352 410 1 0.54936 411 NA NA 412 1 0.29624 413 1 0.28450 414 NA NA 415 1 0.16767 416 1 0.91739 417 1 0.99091 418 1 0.74767 419 1 0.49254 420 1 0.93281 421 1 0.61704 422 1 0.39170 423 1 0.19638 424 1 0.72008 425 1 0.93417 426 1 0.69264 427 1 0.88858 428 1 0.22867 429 1 0.54657 430 1 0.20700 431 1 0.53705 432 1 0.96928 433 1 0.80323 434 1 0.20405 435 1 0.40065 436 1 0.82912 437 1 0.44113 438 1 0.39505 439 1 0.03089 440 1 0.13587 441 1 0.67718 442 1 0.06249 443 1 0.99754 444 1 0.11385 445 NA NA 446 1 0.02559 447 1 0.10831 448 1 0.45408 449 1 0.80019 450 1 0.83482 451 NA NA 452 1 0.28282 453 1 0.64290 454 NA NA 455 1 0.53711 456 1 0.43145 457 1 0.72412 458 1 0.17412 459 1 0.32032 460 1 0.38798 461 NA NA 462 1 0.27792 463 1 0.71545 464 1 0.32855 465 1 0.60146 466 1 0.52392 467 1 0.86055 468 1 0.53277 469 1 0.11142 470 NA NA 471 1 0.06294 472 1 0.70529 473 NA NA 474 1 0.78132 475 1 0.78414 476 1 0.55258 477 1 0.85511 478 1 0.20987 479 1 0.23006 480 NA NA 481 1 0.44478 482 1 0.66007 483 1 0.07782 484 1 0.34325 485 1 0.80745 486 1 0.34898 487 1 0.05208 488 1 0.86328 489 1 0.55692 490 NA NA 491 1 0.76130 492 1 0.54554 493 1 0.47788 494 1 0.34743 495 NA NA 496 1 0.95077 497 1 0.26138 498 1 0.10681 499 1 0.25376 500 1 0.18090 attr(,"assign") [1] 0 1 > all.equal( model.matrix( ss ), model.matrix( ss, part = "outcome" ) ) [1] TRUE > model.matrix( ss, part = "selection" ) (Intercept) xs 1 1 0.387113 2 1 0.871805 3 1 0.967197 4 1 0.866916 5 1 0.437715 6 1 0.191938 7 1 0.082294 8 1 0.583452 9 1 0.070361 10 1 0.527663 11 1 0.472288 12 1 0.048191 13 1 0.594541 14 1 0.791271 15 1 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0.058774 372 TRUE 0.982406 0 0.514900 373 TRUE 0.543323 1 0.861013 374 TRUE 0.659888 1 0.985402 375 TRUE 0.275039 1 0.396762 376 TRUE 0.396944 1 0.468284 377 TRUE 0.559185 0 0.420656 378 TRUE 0.980950 1 0.915635 379 TRUE 0.964967 1 0.482314 380 TRUE 0.218040 1 0.942408 381 TRUE 0.393171 1 0.124179 382 TRUE 0.734231 1 0.563708 383 TRUE 0.691589 1 0.731237 384 FALSE 0.336752 0 0.000571 385 TRUE 0.690482 1 0.628356 386 FALSE 0.153450 0 0.370726 387 TRUE 0.890399 0 0.085762 388 TRUE 0.888446 1 0.676197 389 FALSE 0.138003 0 0.609158 390 TRUE 0.035949 1 0.096099 391 TRUE 0.355017 1 0.398905 392 FALSE 0.378946 0 0.098322 393 TRUE 0.614777 1 0.794568 394 TRUE 0.506189 1 0.624536 395 TRUE 0.337955 0 0.405014 396 TRUE 0.329130 1 0.002587 397 TRUE 0.573297 1 0.608580 398 TRUE 0.050710 1 0.592337 399 TRUE 0.400963 1 0.910157 400 FALSE 0.260631 0 0.393951 401 FALSE 0.168700 0 0.964200 402 TRUE 0.059731 0 0.255094 403 FALSE 0.052582 0 0.140772 404 TRUE 0.972770 1 0.525254 405 TRUE 0.794608 0 0.454067 406 TRUE 0.031668 1 0.521722 407 TRUE 0.543285 0 0.085697 408 TRUE 0.017597 1 0.597549 409 TRUE 0.776670 0 0.683516 410 TRUE 0.757301 0 0.549356 411 FALSE 0.010548 0 0.620225 412 TRUE 0.817914 0 0.296236 413 TRUE 0.856346 1 0.284500 414 FALSE 0.422310 0 0.601983 415 TRUE 0.634296 0 0.167672 416 TRUE 0.418075 1 0.917387 417 TRUE 0.324664 1 0.990910 418 TRUE 0.765787 0 0.747668 419 TRUE 0.704656 0 0.492539 420 TRUE 0.919051 1 0.932810 421 TRUE 0.610137 1 0.617039 422 TRUE 0.055855 1 0.391704 423 TRUE 0.736152 1 0.196378 424 TRUE 0.903968 0 0.720079 425 TRUE 0.701815 1 0.934172 426 TRUE 0.577700 1 0.692644 427 TRUE 0.565839 0 0.888581 428 TRUE 0.367176 0 0.228666 429 TRUE 0.556922 0 0.546569 430 TRUE 0.897090 0 0.206999 431 TRUE 0.272231 0 0.537050 432 TRUE 0.826333 1 0.969278 433 TRUE 0.675996 1 0.803234 434 TRUE 0.899367 0 0.204047 435 TRUE 0.296660 1 0.400647 436 TRUE 0.385464 1 0.829125 437 TRUE 0.905350 0 0.441127 438 TRUE 0.781176 1 0.395053 439 TRUE 0.542551 0 0.030889 440 TRUE 0.826008 0 0.135866 441 TRUE 0.925736 1 0.677184 442 TRUE 0.302508 0 0.062488 443 TRUE 0.363235 1 0.997538 444 TRUE 0.960561 0 0.113849 445 FALSE 0.419576 0 0.625333 446 TRUE 0.564240 0 0.025587 447 TRUE 0.800476 0 0.108310 448 TRUE 0.478195 1 0.454083 449 TRUE 0.871664 1 0.800191 450 TRUE 0.701587 0 0.834824 451 FALSE 0.128367 0 0.724688 452 TRUE 0.651634 0 0.282822 453 TRUE 0.799508 1 0.642903 454 FALSE 0.240165 0 0.958786 455 TRUE 0.863995 1 0.537109 456 TRUE 0.478795 1 0.431453 457 TRUE 0.329742 1 0.724119 458 TRUE 0.995426 0 0.174124 459 TRUE 0.759542 1 0.320324 460 TRUE 0.471065 0 0.387978 461 FALSE 0.257584 0 0.054494 462 TRUE 0.383511 0 0.277925 463 TRUE 0.297954 0 0.715454 464 TRUE 0.768626 1 0.328546 465 TRUE 0.429740 1 0.601455 466 TRUE 0.655967 0 0.523921 467 TRUE 0.242657 1 0.860549 468 TRUE 0.295185 1 0.532769 469 TRUE 0.929919 0 0.111422 470 FALSE 0.139466 0 0.775893 471 TRUE 0.482361 1 0.062940 472 TRUE 0.801726 0 0.705285 473 FALSE 0.335298 0 0.049256 474 TRUE 0.547301 0 0.781317 475 TRUE 0.050614 0 0.784139 476 TRUE 0.685185 0 0.552576 477 TRUE 0.526017 1 0.855108 478 TRUE 0.385401 0 0.209872 479 TRUE 0.218078 0 0.230055 480 FALSE 0.049256 0 0.673410 481 TRUE 0.338604 1 0.444783 482 TRUE 0.527543 0 0.660065 483 TRUE 0.360100 1 0.077822 484 TRUE 0.991589 0 0.343248 485 TRUE 0.046358 1 0.807455 486 TRUE 0.071902 1 0.348975 487 TRUE 0.676367 0 0.052082 488 TRUE 0.162360 1 0.863283 489 TRUE 0.580374 0 0.556919 490 FALSE 0.090766 0 0.909955 491 TRUE 0.656099 0 0.761297 492 TRUE 0.357507 1 0.545542 493 TRUE 0.194491 1 0.477882 494 TRUE 0.681934 0 0.347431 495 FALSE 0.030555 0 0.568208 496 TRUE 0.439074 1 0.950769 497 TRUE 0.973690 0 0.261379 498 TRUE 0.412593 1 0.106805 499 TRUE 0.919770 1 0.253758 500 TRUE 0.098764 0 0.180904 > logLik( ss ) 'log Lik.' -398 (df=5) > > # estimation with BFGS method > ssBFGS <- selection( ys ~ xs, yo ~ xo, data = simDat, maxMethod = "BFGS" ) > print( ssBFGS ) Call: selection(selection = ys ~ xs, outcome = yo ~ xo, data = simDat, maxMethod = "BFGS") Coefficients: S:(Intercept) S:xs O:(Intercept) O:xo rho -0.122 3.329 -1.055 1.987 0.817 > summary( ssBFGS ) -------------------------------------------- Tobit 2 model with binary outcome (sample selection model) Maximum Likelihood estimation BFGS maximization, 31 iterations Return code 0: successful convergence Log-Likelihood: -398 500 observations (74 censored and 426 observed) 5 free parameters (df = 495) Probit selection equation: Estimate Std. Error t value Pr(>|t|) (Intercept) -0.122 0.132 -0.92 0.36 xs 3.329 0.397 8.39 4.9e-16 *** Outcome equation: Estimate Std. Error t value Pr(>|t|) (Intercept) -1.055 0.122 -8.66 <2e-16 *** xo 1.987 0.232 8.56 <2e-16 *** Error terms: Estimate Std. Error t value Pr(>|t|) rho 0.817 0.145 5.64 2.9e-08 *** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 -------------------------------------------- > all.equal( coef( ssBFGS ), coef( ss ), tol = 1e-2 ) [1] TRUE > all.equal( stdEr( ssBFGS ), stdEr( ss ), tol = 1e-1 ) [1] TRUE > all.equal( vcov( ssBFGS ), vcov( ss ), tol = 1e-1 ) [1] TRUE > nobs( ssBFGS ) [1] 500 > nObs( ssBFGS ) [1] 500 > all.equal( fitted( ss ), fitted( ssBFGS ), tol = 1e-2 ) [1] TRUE > all.equal( fitted( ss, part = "selection" ), + fitted( ssBFGS, part = "selection" ), tol = 1e-2 ) [1] TRUE > all.equal( fitted( ssBFGS ), fitted( ssBFGS, part = "outcome" ) ) [1] TRUE > all.equal( residuals( ss ), residuals( ssBFGS ), tol = 1e-2 ) [1] TRUE > all.equal( residuals( ss, part = "selection" ), + residuals( ssBFGS, part = "selection" ), tol = 1e-2 ) [1] TRUE > all.equal( residuals( ssBFGS ), residuals( ssBFGS, part = "outcome" ) ) [1] TRUE > all.equal( model.matrix( ss ), model.matrix( ssBFGS ) ) [1] TRUE > all.equal( model.matrix( ss, part = "selection" ), + model.matrix( ssBFGS, part = "selection" ) ) [1] TRUE > all.equal( model.matrix( ssBFGS ), model.matrix( ssBFGS, part = "outcome" ) ) [1] TRUE > all.equal( logLik( ss ), logLik( ssBFGS ), tol = 1e-3 ) [1] TRUE > > proc.time() user system elapsed 6.21 0.29 6.50