GeneralOaxaca {GeneralOaxaca}

General Blinder-Oaxaca Decomposition

Description

Blinder-Oaxaca decomposition for generalized linear model. It provide the twofold and threefold decomposition describe in Bauer and Sinning (2008), as the characteristic, coefficient and interaction part of the observed difference on the dependent variable between the two groups. Bootstrapped standard errors are calculated (e.g., Efron, 1979).

Usage

GeneralOaxaca(formula, family = stats::gaussian, data,
groupInd, groupRef = "A", B = 1000, control = list())

Arguments

formula

an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted.

family

a description of the error distribution and link function to be used in the model. (See family for details of family functions.)

data

an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula).

groupInd

is an indicator variable that is TRUE (or equal to 1) when an observation belongs to Group A, and FALSE (or equal to 0) when it belongs to Group B

groupRef

Group of reference for the decomposition, by default Group A.

B

number of bootstrap replications for the calculation of standard errors

control

a list of parameters for controlling the fitting process.

Details

The twofold and threefold decomposition contains the characteristic and coefficient part (also the interaction for the threefold) of the decomposition, with their proportion with respect to the observed difference between groups. It also give the z value, p value and 95% confidence intervals computed using the bootstrapped standard errors. The regoutput are the results of the generalized linear model applied to data in each group (A and B). See glm for more details about the outputs.

Value

GeneralOaxaca returns the following results:

regoutput

List of two elements (names GroupA and GroupB) with the standard generalized linear model output in each group.

twofold

the twofold decomposition with the respect groupInd.

threefold

the threefold decomposition with the respect groupInd.

n

the size of each respective group.

summaryStat

descriptive statistic of the independent variable in each group.

Note

The function can perform the Blinder-Oaxaca decomposition for any generalized linear model supported by the glm function.

Author(s)

Aurelien Nicosia and Simon Baillargeon-Ladouceur

References

T. Bauer and M. Sinning. An extension of the Blinder-Oaxaca decomposition to nonlinear models (2008). Advances in Statistical Analysis, Springer-Verlag.

B. Efron. Bootstrap Methods: Another Look at the Jackknife (1979). Annals of Statistics, 7(1), 1-26.

Examples

data("chicago")
chicago$real.wage=exp(chicago$ln.real.wage)
formula=ln.real.wage~ age + female + LTHS + some.college + college + 
advanced.degree

# exemple with gamma distribution
BO_A <- GeneralOaxaca(formula,  family= Gamma, data=chicago, 
groupInd=chicago$foreign.born,B=100)
BO_A$twofold 
BO_A$regoutput$GroupA 
BO_A$threefold