Fits a sample selection model based on the Skew-Normal distribution using Maximum Likelihood Estimation (MLE). This model allows for asymmetry in the distribution of the outcome variable's error term, addressing potential skewness.
Usage
HeckmanSK(
selection,
outcome,
data = sys.frame(sys.parent()),
lambda,
start = NULL
)Value
A list containing:
coefficients: Named vector of estimated model parameters.value: The (negative) log-likelihood at convergence.loglik: The maximum log-likelihood.counts: Number of gradient evaluations.hessian: Hessian matrix at the optimum.fisher_infoSK: Approximate Fisher information matrix.prop_sigmaSK: Standard errors for the estimates.level: Levels of the selection variable.nObs: Number of observations.nParam: Number of model parameters.N0: Number of censored (unobserved) observations.N1: Number of observed (uncensored) observations.NXS: Number of covariates in the selection equation.NXO: Number of covariates in the outcome equation.df: Degrees of freedom (observations minus parameters).aic: Akaike Information Criterion.bic: Bayesian Information Criterion.initial.value: Initial parameter values used.
Details
The function implements MLE for a sample selection model where the outcome equation's errors follow a Skew-Normal distribution, as proposed in Ogundimu and Hutton (2016) . The optimization is performed via the BFGS algorithm.
The results include estimates for:
Selection equation coefficients.
Outcome equation coefficients.
Standard deviation of the error term (
sigma).Correlation between the selection and outcome errors (
rho).Skewness parameter (
lambda).Robust standard errors from the Fisher information matrix.
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
selectEq <- lfp ~ huswage + kids5 + mtr + fatheduc + educ + city
outcomeEq <- log(wage) ~ educ + city
HeckmanSK(selectEq, outcomeEq, data = Mroz87, lambda = -1.5)
#> Start not provided using default start values.
#> $coefficients
#> (Intercept) huswage kids5 mtr fatheduc educ
#> 2.91662397 -0.09441349 -0.38395436 -5.13417100 -0.01560489 0.09497449
#> city (Intercept) educ city sigma rho
#> -0.04295576 1.10262877 0.07462305 0.11951616 0.96402482 -0.79175493
#> lambda
#> -1.58728652
#>
#> $value
#> [1] -874.6076
#>
#> $loglik
#> [1] -874.6076
#>
#> $counts
#> gradient
#> 47
#>
#> $hessian
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] -761.7616 -5697.7338 -174.90498 -518.25799 -6631.3240 -9260.0083
#> [2,] -5697.7338 -54421.2862 -1333.95430 -3704.44564 -51487.4053 -71513.9632
#> [3,] -174.9050 -1333.9543 -233.90244 -120.46746 -1668.4387 -2284.7332
#> [4,] -518.2580 -3704.4456 -120.46746 -357.14648 -4464.8672 -6250.0362
#> [5,] -6631.3240 -51487.4053 -1668.43866 -4464.86724 -67197.2067 -83188.1359
#> [6,] -9260.0083 -71513.9632 -2284.73322 -6250.03625 -83188.1359 -116455.8347
#> [7,] -486.7713 -4141.7774 -107.87398 -323.36488 -4444.5593 -6065.8973
#> [8,] -382.2667 -2819.7008 -72.26997 -258.59364 -3357.1481 -4694.1549
#> [9,] -4694.1532 -35735.3046 -969.70450 -3150.92533 -42431.0844 -59706.1578
#> [10,] -242.6706 -2039.7765 -46.11459 -159.97496 -2255.0939 -3058.9824
#> [11,] 277.3505 1966.9865 58.74978 192.71995 2449.5816 3308.3822
#> [12,] 292.7946 1745.9666 -31.66055 196.14271 2832.1353 3794.3060
#> [13,] 51.7407 391.4114 10.60834 34.91793 447.0649 634.4167
#> [,7] [,8] [,9] [,10] [,11] [,12]
#> [1,] -486.77126 -382.26666 -4694.1532 -242.67057 277.35053 292.79463
#> [2,] -4141.77742 -2819.70084 -35735.3046 -2039.77647 1966.98655 1745.96663
#> [3,] -107.87398 -72.26997 -969.7045 -46.11459 58.74978 -31.66055
#> [4,] -323.36488 -258.59364 -3150.9253 -159.97496 192.71995 196.14271
#> [5,] -4444.55930 -3357.14807 -42431.0844 -2255.09394 2449.58162 2832.13532
#> [6,] -6065.89726 -4694.15492 -59706.1578 -3058.98238 3308.38218 3794.30602
#> [7,] -486.77126 -242.67057 -3058.9813 -242.67057 174.47566 176.34120
#> [8,] -242.67057 -1088.85633 -13745.6740 -694.14240 831.19533 -380.90115
#> [9,] -3058.98133 -13745.67400 -179513.5549 -8967.45099 10269.04817 -4458.84151
#> [10,] -242.67057 -694.14240 -8967.4510 -694.14240 526.04741 -253.74429
#> [11,] 174.47566 831.19533 10269.0482 526.04741 -1554.48298 -136.09970
#> [12,] 176.34120 -380.90115 -4458.8415 -253.74429 -136.09970 -1085.77412
#> [13,] 33.11873 -14.90048 -235.9433 -15.25629 -66.88540 -86.95696
#> [,13]
#> [1,] 51.74070
#> [2,] 391.41142
#> [3,] 10.60834
#> [4,] 34.91793
#> [5,] 447.06494
#> [6,] 634.41668
#> [7,] 33.11873
#> [8,] -14.90048
#> [9,] -235.94334
#> [10,] -15.25629
#> [11,] -66.88540
#> [12,] -86.95696
#> [13,] -25.84295
#>
#> $fisher_infoSK
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.5061487579 -8.327244e-03 -4.013654e-03 -0.5371120728 -3.428459e-04
#> [2,] -0.0083272437 2.709240e-04 2.744186e-04 0.0097748699 -1.270217e-06
#> [3,] -0.0040136544 2.744186e-04 7.226075e-03 0.0060250470 -8.051846e-05
#> [4,] -0.5371120728 9.774870e-03 6.025047e-03 0.6309429661 3.486240e-04
#> [5,] -0.0003428459 -1.270217e-06 -8.051846e-05 0.0003486240 1.324573e-04
#> [6,] -0.0046989830 -5.475479e-05 -4.440042e-04 0.0010794756 -7.721135e-05
#> [7,] -0.0008806198 -2.612742e-04 2.981766e-04 -0.0004362881 -7.500774e-05
#> [8,] -0.0590758997 1.185436e-03 5.864600e-03 0.0482390049 -1.611029e-04
#> [9,] 0.0029630290 -4.715956e-05 -2.337884e-04 -0.0019006473 1.038548e-05
#> [10,] -0.0020417580 6.424387e-05 1.887737e-04 0.0030487025 -1.476144e-05
#> [11,] -0.0126689099 3.348703e-04 1.542570e-03 0.0147815261 -7.961141e-06
#> [12,] 0.0178885748 -5.470207e-04 -2.748362e-03 -0.0206870705 6.553555e-05
#> [13,] 0.0182748108 -2.666511e-04 -7.861372e-04 -0.0212752130 -1.609516e-04
#> [,6] [,7] [,8] [,9] [,10]
#> [1,] -4.698983e-03 -8.806198e-04 -0.0590758997 2.963029e-03 -2.041758e-03
#> [2,] -5.475479e-05 -2.612742e-04 0.0011854356 -4.715956e-05 6.424387e-05
#> [3,] -4.440042e-04 2.981766e-04 0.0058646000 -2.337884e-04 1.887737e-04
#> [4,] 1.079476e-03 -4.362881e-04 0.0482390049 -1.900647e-03 3.048703e-03
#> [5,] -7.721135e-05 -7.500774e-05 -0.0001611029 1.038548e-05 -1.476144e-05
#> [6,] 4.486229e-04 -1.006737e-04 0.0007568160 -9.218447e-05 6.042436e-05
#> [7,] -1.006737e-04 7.830085e-03 0.0006403754 7.180597e-05 -2.509722e-03
#> [8,] 7.568160e-04 6.403754e-04 0.0542936801 -3.354060e-03 -2.454182e-04
#> [9,] -9.218447e-05 7.180597e-05 -0.0033540598 2.448635e-04 -1.889947e-04
#> [10,] 6.042436e-05 -2.509722e-03 -0.0002454182 -1.889947e-04 5.034535e-03
#> [11,] -1.997339e-04 -4.472223e-05 0.0062881286 -2.045755e-04 3.554003e-04
#> [12,] 2.856504e-04 -5.578512e-07 -0.0089234364 3.722263e-04 -3.574583e-04
#> [13,] 5.129161e-04 6.525616e-04 -0.0029103951 -3.504477e-04 -1.728526e-03
#> [,11] [,12] [,13]
#> [1,] -1.266891e-02 1.788857e-02 0.0182748108
#> [2,] 3.348703e-04 -5.470207e-04 -0.0002666511
#> [3,] 1.542570e-03 -2.748362e-03 -0.0007861372
#> [4,] 1.478153e-02 -2.068707e-02 -0.0212752130
#> [5,] -7.961141e-06 6.553555e-05 -0.0001609516
#> [6,] -1.997339e-04 2.856504e-04 0.0005129161
#> [7,] -4.472223e-05 -5.578512e-07 0.0006525616
#> [8,] 6.288129e-03 -8.923436e-03 -0.0029103951
#> [9,] -2.045755e-04 3.722263e-04 -0.0003504477
#> [10,] 3.554003e-04 -3.574583e-04 -0.0017285264
#> [11,] 2.866391e-03 -2.261126e-03 -0.0065637206
#> [12,] -2.261126e-03 4.370226e-03 -0.0002994573
#> [13,] -6.563721e-03 -2.994573e-04 0.0767131556
#>
#> $prop_sigmaSK
#> [1] 0.71144132 0.01645977 0.08500632 0.79431918 0.01150901 0.02118072
#> [7] 0.08848777 0.23301004 0.01564811 0.07095446 0.05353869 0.06610769
#> [13] 0.27697140
#>
#> $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
#> [1] 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 -1.5
#>
#> attr(,"class")
#> [1] "HeckmanSK" "list"