Estimates the parameters of the Sample Selection Model with Skew-Normal Distribution

HeckmanSK(
  selection,
  outcome,
  data = sys.frame(sys.parent()),
  lambda,
  start = NULL
)

Arguments

selection

Selection equation.

outcome

Primary Regression Equation.

data

Database.

lambda

Initial start for asymmetry parameter.

start

initial values.

Value

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.

Details

The HeckmanSK() function fits the Sample Selection Model based on the Skew-normal distribution. For more information see Ogundimu and Hutton (2016)

References

Emmanuel O Ogundimu, Jane L Hutton (2016). “A Sample Selection Model with Skew-normal Distribution.” Scandinavian Journal of Statistics, 43(1), 172--190.

Examples

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"