Estimates the parameters of the Sample Selection Model with Skew-Normal Distribution
HeckmanSK(
selection,
outcome,
data = sys.frame(sys.parent()),
lambda,
start = NULL
)Selection equation.
Primary Regression Equation.
Database.
Initial start for asymmetry parameter.
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_infoSK: Fisher information matrix
prop_sigmaSK: 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 HeckmanSK() function fits the Sample Selection Model based on the Skew-normal distribution. For more information see Ogundimu and Hutton (2016)
Emmanuel O Ogundimu, Jane L Hutton (2016). “A Sample Selection Model with Skew-normal Distribution.” Scandinavian Journal of Statistics, 43(1), 172--190.
data("Mroz87")
attach(Mroz87)
#> The following objects are masked from MEPS2001 (pos = 3):
#>
#> age, educ
#> The following objects are masked from MEPS2001 (pos = 4):
#>
#> age, educ
#> The following objects are masked from MEPS2001 (pos = 5):
#>
#> age, educ
#> The following objects are masked from MEPS2001 (pos = 6):
#>
#> age, educ
selectEq <- lfp ~ huswage + kids5 + mtr + fatheduc + educ + city
outcomeEq <- log(wage) ~ educ+city
HeckmanSK(selectEq, outcomeEq, data = Mroz87, lambda = -1.5)
#> $coefficients
#> (Intercept) huswage kids5 mtr fatheduc educ
#> 2.91663399 -0.09441332 -0.38394348 -5.13419159 -0.01560548 0.09497407
#> city (Intercept) educ city sigma rho
#> -0.04294888 1.10265601 0.07462093 0.11951262 0.96402168 -0.79176540
#> lambda
#> -1.58721959
#>
#> $value
#> [1] -874.6076
#>
#> $loglik
#> [1] 874.6076
#>
#> $counts
#> gradient
#> 24
#>
#> $hessian
#> XS(Intercept) XShuswage XSkids5 XSmtr XSfatheduc
#> XS(Intercept) -761.77574 -5697.8421 -174.90832 -518.26756 -6631.4515
#> XShuswage -5697.84214 -54422.3225 -1333.97862 -3704.51609 -51488.3973
#> XSkids5 -174.90832 -1333.9786 -233.90702 -120.46979 -1668.4691
#> XSmtr -518.26756 -3704.5161 -120.46979 -357.15300 -4464.9524
#> XSfatheduc -6631.45155 -51488.3973 -1668.46915 -4464.95244 -67198.5411
#> XSeduc -9260.18381 -71515.3530 -2284.77789 -6250.15361 -83189.7675
#> XScity -486.77999 -4141.8544 -107.87602 -323.37060 -4444.6434
#> XO(Intercept) -382.28475 -2819.8358 -72.27350 -258.60589 -3357.3094
#> XOeduc -4694.37576 -35737.0251 -969.75186 -3151.07486 -42433.1353
#> XOcity -242.68166 -2039.8719 -46.11674 -159.98226 -2255.1997
#> sigma 277.36072 1967.0547 58.75192 192.72719 2449.6704
#> rho 292.76673 1745.7145 -31.67112 196.12375 2831.9040
#> 51.74583 391.4511 10.60955 34.92137 447.1092
#> XSeduc XScity XO(Intercept) XOeduc XOcity
#> XS(Intercept) -9260.1838 -486.77999 -382.28475 -4694.3758 -242.68166
#> XShuswage -71515.3530 -4141.85437 -2819.83579 -35737.0251 -2039.87191
#> XSkids5 -2284.7779 -107.87602 -72.27350 -969.7519 -46.11674
#> XSmtr -6250.1536 -323.37060 -258.60589 -3151.0749 -159.98226
#> XSfatheduc -83189.7675 -4444.64340 -3357.30943 -42433.1353 -2255.19966
#> XSeduc -116458.0927 -6066.00884 -4694.37753 -59709.0045 -3059.12322
#> XScity -6066.0088 -486.77999 -242.68166 -3059.1222 -242.68166
#> XO(Intercept) -4694.3775 -242.68166 -1088.86718 -13745.8008 -694.14923
#> XOeduc -59709.0045 -3059.12216 -13745.80081 -179515.0804 -8967.53326
#> XOcity -3059.1232 -242.68166 -694.14923 -8967.5333 -694.14923
#> sigma 3308.4967 174.48097 831.20519 10269.1431 526.05208
#> rho 3793.9617 176.32225 -380.92460 -4459.1313 -253.76078
#> 634.4798 33.12212 -14.90175 -235.9640 -15.25712
#> sigma rho
#> XS(Intercept) 277.36072 292.76673 51.74583
#> XShuswage 1967.05468 1745.71451 391.45105
#> XSkids5 58.75192 -31.67112 10.60955
#> XSmtr 192.72719 196.12375 34.92137
#> XSfatheduc 2449.67038 2831.90396 447.10915
#> XSeduc 3308.49673 3793.96166 634.47977
#> XScity 174.48097 176.32225 33.12212
#> XO(Intercept) 831.20519 -380.92460 -14.90175
#> XOeduc 10269.14306 -4459.13132 -235.96401
#> XOcity 526.05208 -253.76078 -15.25712
#> sigma -1554.50584 -136.12327 -66.88583
#> rho -136.12327 -1085.90377 -86.96368
#> -66.88583 -86.96368 -25.84460
#>
#> $fisher_infoSK
#> XS(Intercept) XShuswage XSkids5 XSmtr
#> XS(Intercept) 0.5061297229 -8.326701e-03 -4.011100e-03 -0.5370902267
#> XShuswage -0.0083267014 2.709059e-04 2.743346e-04 0.0097742363
#> XSkids5 -0.0040110996 2.743346e-04 7.225470e-03 0.0060220196
#> XSmtr -0.5370902267 9.774236e-03 6.022020e-03 0.6309175200
#> XSfatheduc -0.0003429192 -1.267632e-06 -8.050383e-05 0.0003487119
#> XSeduc -0.0046992423 -5.474413e-05 -4.439382e-04 0.0010798064
#> XScity -0.0008805195 -2.612733e-04 2.981502e-04 -0.0004364041
#> XO(Intercept) -0.0590692526 1.185193e-03 5.863147e-03 0.0482304740
#> XOeduc 0.0029627430 -4.714870e-05 -2.337244e-04 -0.0019002557
#> XOcity -0.0020414493 6.423417e-05 1.887134e-04 0.0030483704
#> sigma -0.0126676273 3.348246e-04 1.542273e-03 0.0147800159
#> rho 0.0178839595 -5.468719e-04 -2.747504e-03 -0.0206816802
#> 0.0182775613 -2.667198e-04 -7.864052e-04 -0.0212784754
#> XSfatheduc XSeduc XScity XO(Intercept)
#> XS(Intercept) -3.429192e-04 -4.699242e-03 -8.805195e-04 -0.0590692526
#> XShuswage -1.267632e-06 -5.474413e-05 -2.612733e-04 0.0011851934
#> XSkids5 -8.050383e-05 -4.439382e-04 2.981502e-04 0.0058631469
#> XSmtr 3.487119e-04 1.079806e-03 -4.364041e-04 0.0482304740
#> XSfatheduc 1.324545e-04 -7.721167e-05 -7.500725e-05 -0.0001610668
#> XSeduc -7.721167e-05 4.486120e-04 -1.006711e-04 0.0007570517
#> XScity -7.500725e-05 -1.006711e-04 7.830044e-03 0.0006403469
#> XO(Intercept) -1.610668e-04 7.570517e-04 6.403469e-04 0.0542898258
#> XOeduc 1.038411e-05 -9.219724e-05 7.180994e-05 -0.0033538995
#> XOcity -1.476012e-05 6.043411e-05 -2.509809e-03 -0.0002456014
#> sigma -7.952192e-06 -1.996982e-04 -4.474209e-05 0.0062873272
#> rho 6.551474e-05 2.855431e-04 -5.316432e-07 -0.0089209228
#> -1.609581e-04 5.129935e-04 6.526070e-04 -0.0029111309
#> XOeduc XOcity sigma rho
#> XS(Intercept) 2.962743e-03 -2.041449e-03 -1.266763e-02 1.788396e-02
#> XShuswage -4.714870e-05 6.423417e-05 3.348246e-04 -5.468719e-04
#> XSkids5 -2.337244e-04 1.887134e-04 1.542273e-03 -2.747504e-03
#> XSmtr -1.900256e-03 3.048370e-03 1.478002e-02 -2.068168e-02
#> XSfatheduc 1.038411e-05 -1.476012e-05 -7.952192e-06 6.551474e-05
#> XSeduc -9.219724e-05 6.043411e-05 -1.996982e-04 2.855431e-04
#> XScity 7.180994e-05 -2.509809e-03 -4.474209e-05 -5.316432e-07
#> XO(Intercept) -3.353899e-03 -2.456014e-04 6.287327e-03 -8.920923e-03
#> XOeduc 2.448577e-04 -1.889875e-04 -2.045384e-04 3.721174e-04
#> XOcity -1.889875e-04 5.034548e-03 3.553576e-04 -3.573576e-04
#> sigma -2.045384e-04 3.553576e-04 2.866223e-03 -2.260600e-03
#> rho 3.721174e-04 -3.573576e-04 -2.260600e-03 4.368764e-03
#> -3.504491e-04 -1.728474e-03 -6.563844e-03 -2.990192e-04
#>
#> XS(Intercept) 0.0182775613
#> XShuswage -0.0002667198
#> XSkids5 -0.0007864052
#> XSmtr -0.0212784754
#> XSfatheduc -0.0001609581
#> XSeduc 0.0005129935
#> XScity 0.0006526070
#> XO(Intercept) -0.0029111309
#> XOeduc -0.0003504491
#> XOcity -0.0017284737
#> sigma -0.0065638440
#> rho -0.0002990192
#> 0.0767113669
#>
#> $prop_sigmaSK
#> XS(Intercept) XShuswage XSkids5 XSmtr XSfatheduc
#> 0.71142795 0.01645922 0.08500276 0.79430317 0.01150889
#> XSeduc XScity XO(Intercept) XOeduc XOcity
#> 0.02118046 0.08848754 0.23300177 0.01564793 0.07095455
#> sigma rho
#> 0.05353712 0.06609663 0.27696817
#>
#> $level
#> [1] "0" "1"
#>
#> $nObs
#> [1] 753
#>
#> $nParam
#> [1] 13
#>
#> $N0
#> [1] 325
#>
#> $N1
#> [1] 428
#>
#> $NXS
#> [1] 7
#>
#> $NXO
#> [1] 3
#>
#> $df
#> [1] 740
#>
#> $aic
#> [1] 1775.215
#>
#> $bic
#> [1] 1835.328
#>
#> $initial.value
#> XS(Intercept) XShuswage XSkids5 XSmtr XSfatheduc
#> 3.373565235 -0.116721911 -0.549776930 -5.328591099 -0.004906663
#> XSeduc XScity XO(Intercept) XOeduc XOcity
#> 0.122317681 -0.030769825 0.641598010 0.067208950 0.100413738
#> sigma rho
#> 0.851409314 -0.709828606 -1.500000000
#>
#> attr(,"class")
#> [1] "HeckmanSK" "list"