Estimates the parameters of the Heckman-t model
HeckmantS(selection, outcome, data = sys.frame(sys.parent()), df, start = NULL)Selection equation.
Primary Regression Equation.
Database.
Initial start to the degree of freedom.
initial values.
Returns a list with the following components.
Coefficients: Returns a numerical vector with the best estimated values of the model parameters;
Value: The value of function to be minimized (or maximized) corresponding to par.
loglik: Negative of value. Minimum (or maximum) of the likelihood function calculated from the estimated coefficients.
counts: Component of the Optim function. A two-element integer vector giving the number of calls to fn and gr respectively. This excludes those calls needed to compute the Hessian, if requested, and any calls to fn to compute a finite-difference approximation to the gradient.
hessian: Component of the Optim function, with pre-defined option hessian=TRUE. A symmetric matrix giving an estimate of the Hessian at the solution found. Note that this is the Hessian of the unconstrained problem even if the box constraints are active.
fisher_infotS: Fisher information matrix
prop_sigmatS: Square root of the Fisher information matrix diagonal
level: Selection variable levels
nObs: Numeric value representing the size of the database
nParam: Numerical value representing the number of model parameters
N0: Numerical value representing the number of unobserved entries
N1: Numerical value representing the number of complete entries
NXS: Numerical value representing the number of parameters of the selection model
NXO: Numerical value representing the number of parameters of the regression model
df: Numerical value that represents the difference between the size of the response vector of the selection equation and the number of model parameters
aic: Numerical value representing Akaike's information criterion.
bic: Numerical value representing Schwarz's Bayesian Criterion
initial.value: Numerical vector that represents the input values (Initial Values) used in the parameter estimation.
The HeckmantS() function fits the Sample Selection Model based on the Student's t distribution. For more information see Marchenko and Genton (2012)
Yulia V Marchenko, Marc G Genton (2012). “A Heckman selection-t model.” Journal of the American Statistical Association, 107(497), 304--317.
data(MEPS2001)
attach(MEPS2001)
#> The following objects are masked from Mroz87:
#>
#> age, educ
#> The following objects are masked from MEPS2001 (pos = 4):
#>
#> age, age2, agefem, ambexp, blhisp, dambexp, dhospexp, educ,
#> fairpoor, female, ffs, good, hospexp, income, ins, instype,
#> instype_s1, lambexp, lnambx, totchr, vgood, year01
#> The following objects are masked from MEPS2001 (pos = 5):
#>
#> age, age2, agefem, ambexp, blhisp, dambexp, dhospexp, educ,
#> fairpoor, female, ffs, good, hospexp, income, ins, instype,
#> instype_s1, lambexp, lnambx, totchr, vgood, year01
#> The following objects are masked from MEPS2001 (pos = 6):
#>
#> age, age2, agefem, ambexp, blhisp, dambexp, dhospexp, educ,
#> fairpoor, female, ffs, good, hospexp, income, ins, instype,
#> instype_s1, lambexp, lnambx, totchr, vgood, year01
#> The following objects are masked from MEPS2001 (pos = 7):
#>
#> age, age2, agefem, ambexp, blhisp, dambexp, dhospexp, educ,
#> fairpoor, female, ffs, good, hospexp, income, ins, instype,
#> instype_s1, lambexp, lnambx, totchr, vgood, year01
selectEq <- dambexp ~ age + female + educ + blhisp + totchr + ins + income
outcomeEq <- lnambx ~ age + female + educ + blhisp + totchr + ins
HeckmantS(selectEq, outcomeEq, data = MEPS2001, df=12)
#> $coefficients
#> (Intercept) age female educ blhisp totchr
#> -0.747972299 0.098549379 0.724861923 0.064839075 -0.393568747 0.890081444
#> ins income (Intercept) age female educ
#> 0.180028786 0.002977546 5.205843434 0.206833445 0.306532774 0.017314842
#> blhisp totchr ins sigma rho df
#> -0.192966533 0.512711577 -0.052497676 1.194852538 -0.321991620 12.930320957
#>
#> $value
#> [1] -5822.076
#>
#> $loglik
#> [1] 5822.076
#>
#> $counts
#> gradient
#> 25
#>
#> $hessian
#> XS(Intercept) XSage XSfemale XSeduc
#> XS(Intercept) -1045.260400 -3974.90009 -359.382145 -13503.6213
#> XSage -3974.900088 -16386.94634 -1349.195238 -51285.6828
#> XSfemale -359.382145 -1349.19524 -359.382145 -4656.3861
#> XSeduc -13503.621338 -51285.68283 -4656.386108 -181847.3957
#> XSblhisp -430.062783 -1582.90667 -169.548343 -5232.0707
#> XStotchr -145.845489 -602.78949 -46.157957 -1834.9704
#> XSins -346.530157 -1411.30718 -103.891102 -4536.0179
#> XSincome -35001.958269 -138422.09776 -10348.425492 -473344.6507
#> XO(Intercept) -190.685144 -739.11549 -76.199025 -2506.1790
#> XOage -739.115020 -3104.45087 -287.623844 -9698.6907
#> XOfemale -76.199025 -287.62418 -76.199025 -995.5972
#> XOeduc -2506.162799 -9698.62786 -995.586110 -34285.2474
#> XOblhisp -70.736951 -266.03473 -32.914756 -874.7341
#> XOtotchr -35.548417 -148.71612 -12.320213 -450.4024
#> XOins -66.914409 -273.86663 -23.852604 -891.5231
#> sigma -30.247935 -141.09352 -27.356370 -455.2462
#> rho -84.838569 -323.60240 -16.516751 -1036.6100
#> -3.459894 -14.61434 -2.229851 -47.5671
#> XSblhisp XStotchr XSins XSincome
#> XS(Intercept) -4.300628e+02 -145.845489 -346.530157 -35001.9583
#> XSage -1.582907e+03 -602.789486 -1411.307178 -138422.0978
#> XSfemale -1.695483e+02 -46.157957 -103.891102 -10348.4255
#> XSeduc -5.232071e+03 -1834.970448 -4536.017855 -473344.6507
#> XSblhisp -4.300628e+02 -59.288185 -132.943170 -12403.5646
#> XStotchr -5.928818e+01 -166.272099 -43.194262 -4820.1821
#> XSins -1.329432e+02 -43.194262 -346.530157 -13209.0794
#> XSincome -1.240356e+04 -4820.182080 -13209.079436 -1752514.1432
#> XO(Intercept) -7.073695e+01 -35.548420 -66.914409 -6585.1940
#> XOage -2.660347e+02 -148.715832 -273.866428 -26614.2859
#> XOfemale -3.291476e+01 -12.320215 -23.852604 -2303.1325
#> XOeduc -8.747321e+02 -450.393577 -891.515861 -90404.3523
#> XOblhisp -7.073695e+01 -13.467160 -24.144987 -2086.7792
#> XOtotchr -1.346716e+01 -41.520766 -11.166676 -1209.0065
#> XOins -2.414499e+01 -11.166677 -66.914409 -2603.7106
#> sigma -7.918516e-01 -20.376659 -15.302573 -1480.3096
#> rho -4.373482e+01 2.012891 -22.489829 -2805.8010
#> -7.613901e-01 -1.594650 -1.357224 -131.8663
#> XO(Intercept) XOage XOfemale XOeduc
#> XS(Intercept) -190.685144 -739.11502 -76.199025 -2506.16280
#> XSage -739.115490 -3104.45087 -287.624181 -9698.62786
#> XSfemale -76.199025 -287.62384 -76.199025 -995.58611
#> XSeduc -2506.178996 -9698.69072 -995.597219 -34285.24739
#> XSblhisp -70.736951 -266.03467 -32.914756 -874.73208
#> XStotchr -35.548420 -148.71583 -12.320215 -450.39358
#> XSins -66.914409 -273.86643 -23.852604 -891.51586
#> XSincome -6585.193995 -26614.28595 -2303.132538 -90404.35229
#> XO(Intercept) -1795.394585 -7408.19155 -998.535041 -24387.53348
#> XOage -7408.191550 -32811.92952 -4103.238261 -100670.18992
#> XOfemale -998.535041 -4103.23826 -998.535041 -13532.30008
#> XOeduc -24387.533481 -100670.18992 -13532.300077 -342593.40479
#> XOblhisp -498.022405 -1963.47560 -294.903126 -6339.24350
#> XOtotchr -1005.590008 -4506.16855 -620.839678 -13568.40189
#> XOins -689.113680 -2935.27086 -353.798208 -9447.70462
#> sigma 37.501223 101.26251 -9.506342 375.35512
#> rho -510.021232 -1946.30659 -175.482274 -6578.36149
#> -3.263302 -14.02572 -1.940081 -46.05649
#> XOblhisp XOtotchr XOins sigma
#> XS(Intercept) -70.7369511 -35.548417 -66.914409 -30.2479348
#> XSage -266.0347342 -148.716123 -273.866632 -141.0935183
#> XSfemale -32.9147560 -12.320213 -23.852604 -27.3563697
#> XSeduc -874.7340620 -450.402400 -891.523143 -455.2461888
#> XSblhisp -70.7369511 -13.467158 -24.144987 -0.7918516
#> XStotchr -13.4671598 -41.520766 -11.166677 -20.3766593
#> XSins -24.1449869 -11.166676 -66.914409 -15.3025729
#> XSincome -2086.7791519 -1209.006464 -2603.710551 -1480.3096361
#> XO(Intercept) -498.0224047 -1005.590008 -689.113680 37.5012233
#> XOage -1963.4755989 -4506.168549 -2935.270860 101.2625080
#> XOfemale -294.9031264 -620.839678 -353.798208 -9.5063422
#> XOeduc -6339.2435005 -13568.401893 -9447.704621 375.3551179
#> XOblhisp -498.0224047 -254.226359 -173.624649 30.7049535
#> XOtotchr -254.2263587 -1757.408787 -349.662081 -35.0513770
#> XOins -173.6246495 -349.662081 -689.113680 12.7433435
#> sigma 30.7049535 -35.051377 12.743344 -3856.0428696
#> rho -209.5551923 -68.166024 -166.686242 -328.3871183
#> -0.8024373 -2.086292 -1.016658 19.8756062
#> rho
#> XS(Intercept) -84.838569 -3.4598943
#> XSage -323.602398 -14.6143372
#> XSfemale -16.516751 -2.2298513
#> XSeduc -1036.609956 -47.5671032
#> XSblhisp -43.734819 -0.7613901
#> XStotchr 2.012891 -1.5946503
#> XSins -22.489829 -1.3572235
#> XSincome -2805.801047 -131.8663089
#> XO(Intercept) -510.021232 -3.2633017
#> XOage -1946.306587 -14.0257243
#> XOfemale -175.482274 -1.9400807
#> XOeduc -6578.361490 -46.0564921
#> XOblhisp -209.555192 -0.8024373
#> XOtotchr -68.166024 -2.0862922
#> XOins -166.686242 -1.0166581
#> sigma -328.387118 19.8756062
#> rho -338.718176 1.8040460
#> 1.804046 -0.2659644
#>
#> $fisher_infotS
#> XS(Intercept) XSage XSfemale XSeduc
#> XS(Intercept) 4.313922e-02 -3.500210e-03 -1.216844e-03 -2.126610e-03
#> XSage -3.500210e-03 8.848053e-04 -1.106393e-05 3.884258e-05
#> XSfemale -1.216844e-03 -1.106393e-05 4.700278e-03 -5.218862e-05
#> XSeduc -2.126610e-03 3.884258e-05 -5.218862e-05 1.639796e-04
#> XSblhisp -4.653816e-03 1.471184e-04 -4.579127e-04 1.706177e-04
#> XStotchr -9.537949e-04 -2.578311e-04 4.708729e-04 5.855568e-05
#> XSins -7.050974e-05 -3.081996e-04 2.686799e-04 -9.475320e-06
#> XSincome 2.931276e-05 -7.887692e-06 1.434611e-05 -5.703991e-06
#> XO(Intercept) -4.159339e-03 5.109932e-04 -3.590409e-04 1.614582e-04
#> XOage 3.186456e-04 -9.671472e-05 3.174769e-05 3.119701e-06
#> XOfemale -4.148472e-05 -3.198028e-05 -3.400934e-04 2.109081e-05
#> XOeduc 2.084709e-04 -3.476959e-06 2.267254e-05 -1.503420e-05
#> XOblhisp 6.713354e-04 1.616945e-08 -4.969208e-05 -3.232422e-05
#> XOtotchr -1.543929e-04 4.731693e-06 1.083817e-04 1.111920e-05
#> XOins 3.286943e-05 1.047594e-05 -2.338154e-05 6.365650e-06
#> sigma 3.154143e-04 -2.005610e-05 -2.634153e-04 -1.718690e-05
#> rho -6.062956e-04 -1.720827e-04 3.256463e-04 6.371185e-05
#> 4.349877e-02 -6.408184e-03 -4.043335e-02 -1.884692e-03
#> XSblhisp XStotchr XSins XSincome
#> XS(Intercept) -4.653816e-03 -9.537949e-04 -7.050974e-05 2.931276e-05
#> XSage 1.471184e-04 -2.578311e-04 -3.081996e-04 -7.887692e-06
#> XSfemale -4.579127e-04 4.708729e-04 2.686799e-04 1.434611e-05
#> XSeduc 1.706177e-04 5.855568e-05 -9.475320e-06 -5.703991e-06
#> XSblhisp 4.426094e-03 -1.456496e-04 -9.580534e-06 5.654848e-06
#> XStotchr -1.456496e-04 7.612860e-03 3.498068e-04 2.733373e-06
#> XSins -9.580534e-06 3.498068e-04 4.625314e-03 -8.482626e-06
#> XSincome 5.654848e-06 2.733373e-06 -8.482626e-06 2.092589e-06
#> XO(Intercept) 8.093827e-04 -1.410652e-03 -2.948364e-04 2.034895e-06
#> XOage -3.703410e-05 9.285434e-05 4.336198e-05 -1.221543e-07
#> XOfemale -3.754290e-05 3.428463e-04 5.360484e-05 -6.493827e-07
#> XOeduc -3.100959e-05 4.596481e-05 1.238556e-05 -1.606099e-08
#> XOblhisp -5.009667e-04 -1.926896e-04 -7.706378e-05 3.696687e-07
#> XOtotchr -4.966990e-05 -5.629332e-06 3.607011e-05 -2.625975e-07
#> XOins -2.672521e-05 2.994162e-05 -4.425393e-04 -2.786759e-07
#> sigma 1.247369e-04 -4.408124e-04 -7.131725e-05 -7.243034e-07
#> rho -1.635925e-04 1.036656e-03 3.112422e-04 -2.406242e-06
#> 1.911024e-02 -5.966139e-02 -6.955095e-03 -1.542936e-04
#> XO(Intercept) XOage XOfemale XOeduc
#> XS(Intercept) -4.159339e-03 3.186456e-04 -4.148472e-05 2.084709e-04
#> XSage 5.109932e-04 -9.671472e-05 -3.198028e-05 -3.476959e-06
#> XSfemale -3.590409e-04 3.174769e-05 -3.400934e-04 2.267254e-05
#> XSeduc 1.614582e-04 3.119701e-06 2.109081e-05 -1.503420e-05
#> XSblhisp 8.093827e-04 -3.703410e-05 -3.754290e-05 -3.100959e-05
#> XStotchr -1.410652e-03 9.285434e-05 3.428463e-04 4.596481e-05
#> XSins -2.948364e-04 4.336198e-05 5.360484e-05 1.238556e-05
#> XSincome 2.034895e-06 -1.221543e-07 -6.493827e-07 -1.606099e-08
#> XO(Intercept) 4.393772e-02 -2.552845e-03 -4.989094e-03 -1.728591e-03
#> XOage -2.552845e-03 5.107889e-04 1.638307e-04 1.753710e-05
#> XOfemale -4.989094e-03 1.638307e-04 3.180826e-03 9.372247e-05
#> XOeduc -1.728591e-03 1.753710e-05 9.372247e-05 1.052740e-04
#> XOblhisp -5.727071e-04 2.524474e-05 -6.287232e-04 5.447514e-05
#> XOtotchr -2.436548e-03 -5.498951e-05 4.418245e-04 7.167563e-05
#> XOins -1.644306e-03 -6.736117e-05 4.224072e-04 1.603966e-05
#> sigma 1.309132e-03 -5.859077e-05 -2.929292e-04 -4.012826e-05
#> rho -1.519548e-02 5.738413e-04 3.542260e-03 3.912621e-04
#> -4.006095e-02 1.418476e-05 1.157226e-02 -2.627832e-05
#> XOblhisp XOtotchr XOins sigma
#> XS(Intercept) 6.713354e-04 -1.543929e-04 3.286943e-05 3.154143e-04
#> XSage 1.616945e-08 4.731693e-06 1.047594e-05 -2.005610e-05
#> XSfemale -4.969208e-05 1.083817e-04 -2.338154e-05 -2.634153e-04
#> XSeduc -3.232422e-05 1.111920e-05 6.365650e-06 -1.718690e-05
#> XSblhisp -5.009667e-04 -4.966990e-05 -2.672521e-05 1.247369e-04
#> XStotchr -1.926896e-04 -5.629332e-06 2.994162e-05 -4.408124e-04
#> XSins -7.706378e-05 3.607011e-05 -4.425393e-04 -7.131725e-05
#> XSincome 3.696687e-07 -2.625975e-07 -2.786759e-07 -7.243034e-07
#> XO(Intercept) -5.727071e-04 -2.436548e-03 -1.644306e-03 1.309132e-03
#> XOage 2.524474e-05 -5.498951e-05 -6.736117e-05 -5.859077e-05
#> XOfemale -6.287232e-04 4.418245e-04 4.224072e-04 -2.929292e-04
#> XOeduc 5.447514e-05 7.167563e-05 1.603966e-05 -4.012826e-05
#> XOblhisp 3.334561e-03 -3.046175e-04 -9.648881e-05 1.770157e-04
#> XOtotchr -3.046175e-04 1.283735e-03 2.901597e-04 -1.997668e-04
#> XOins -9.648881e-05 2.901597e-04 2.548323e-03 -6.198009e-05
#> sigma 1.770157e-04 -1.997668e-04 -6.198009e-05 5.592752e-04
#> rho -2.183412e-03 2.383726e-03 1.191633e-03 -1.089371e-03
#> -7.772549e-03 7.114243e-03 9.941469e-03 3.707844e-02
#> rho
#> XS(Intercept) -6.062956e-04 4.349877e-02
#> XSage -1.720827e-04 -6.408184e-03
#> XSfemale 3.256463e-04 -4.043335e-02
#> XSeduc 6.371185e-05 -1.884692e-03
#> XSblhisp -1.635925e-04 1.911024e-02
#> XStotchr 1.036656e-03 -5.966139e-02
#> XSins 3.112422e-04 -6.955095e-03
#> XSincome -2.406242e-06 -1.542936e-04
#> XO(Intercept) -1.519548e-02 -4.006095e-02
#> XOage 5.738413e-04 1.418476e-05
#> XOfemale 3.542260e-03 1.157226e-02
#> XOeduc 3.912621e-04 -2.627832e-05
#> XOblhisp -2.183412e-03 -7.772549e-03
#> XOtotchr 2.383726e-03 7.114243e-03
#> XOins 1.191633e-03 9.941469e-03
#> sigma -1.089371e-03 3.707844e-02
#> rho 1.490818e-02 6.271223e-02
#> 6.271223e-02 8.174046e+00
#>
#> $prop_sigmatS
#> XS(Intercept) XSage XSfemale XSeduc XSblhisp
#> 0.207699822 0.029745678 0.068558571 0.012805452 0.066528899
#> XStotchr XSins XSincome XO(Intercept) XOage
#> 0.087251702 0.068009662 0.001446579 0.209613253 0.022600639
#> XOfemale XOeduc XOblhisp XOtotchr XOins
#> 0.056398811 0.010260313 0.057745661 0.035829254 0.050480914
#> sigma rho
#> 0.023649001 0.122099068 2.859028916
#>
#> $level
#> [1] "0" "1"
#>
#> $nObs
#> [1] 3328
#>
#> $nParam
#> [1] 18
#>
#> $N0
#> [1] 526
#>
#> $N1
#> [1] 2802
#>
#> $NXS
#> [1] 8
#>
#> $NXO
#> [1] 7
#>
#> $df
#> [1] 3310
#>
#> $aic
#> [1] 11680.15
#>
#> $bic
#> [1] 11790.13
#>
#> $initial.value
#> XS(Intercept) XSage XSfemale XSeduc XSblhisp
#> -0.668643899 0.086814848 0.663505390 0.061883892 -0.365784312
#> XStotchr XSins XSincome XO(Intercept) XOage
#> 0.795747277 0.169106526 0.002677301 5.288927373 0.202466773
#> XOfemale XOeduc XOblhisp XOtotchr XOins
#> 0.292133967 0.012388871 -0.182865733 0.500633176 -0.046509658
#> sigma rho
#> 1.290541875 -0.359316986 12.000000000
#>
#> attr(,"class")
#> [1] "HeckmantS" "list"