ATE() R function from [GJRM]

Average Treatment Effect of a binary or continuous treatment variable

ATE can be used to calculate the causal average treatment effect of a binary or continuous Gaussian treatment variable, with corresponding interval obtained using posterior simulation.


ATE(x, trt, int.var = NULL, eq = NULL, joint = TRUE, n.sim = 100, 
    prob.lev = 0.05, length.out = NULL, percentage = FALSE)

Arguments

x: A fitted gjrm object as produced by the respective fitting function.
trt: Name of the treatment variable.
int.var: A vector made up of the name of the variable interacted with nm.end, and a value for it.
eq: Number of equation containing the treatment variable. This is only used for trivariate models.
joint: If FALSE then the effect is obtained from the univariate model which neglects the presence of unobserved confounders. When TRUE, the effect is obtained from the simultaneous model which accounts for observed and unobserved confounders.
n.sim: Number of simulated coefficient vectors from the posterior distribution of the estimated model parameters. It may be increased if more precision is required.
prob.lev: Overall probability of the left and right tails of the AT distribution used for interval calculations.
length.out: Length of the sequence to be used when calculating the effect that a continuous treatment has on a binary outcome.
percentage: Only for the Roy model, when TRUE it provides results in terms of percentage.

Details

ATE measures the causal average difference in outcomes under treatment (the binary predictor or treatment assumes value 1) and under control (the binary treatment assumes value 0). Posterior simulation is used to obtain a confidence/credible interval. See the references below for details.

ATE can also calculate the effect that a continuous Gaussian endogenous variable has on a binary outcome. In this case the effect will depend on the unit increment chosen (as shown by the plot produced).

Returns

res: It returns three values: lower confidence interval limit, estimated AT and upper interval limit.
prob.lev: Probability level used.
sim.ATE: It returns a vector containing simulated values of the average treatment effect. This is used to calculate intervals.
Effects: For the case of continuous/discrete endogenous variable and binary outcome, it returns a matrix made up of three columns containing the effects for each incremental value in the endogenous variable and respective intervals.

Author(s)

Maintainer: Giampiero Marra giampiero.marra@ucl.ac.uk

References

Marra G. and Radice R. (2011), Estimation of a Semiparametric Recursive Bivariate Probit in the Presence of Endogeneity. Canadian Journal of Statistics, 39(2), 259-279.

ATE function