Marginal effects Summary

It produces the summary table of marginal effects for GLM estimation with GEL. Only implemented for ATEgel.

# S3 method for class 'ategel'
marginal(object, ...)

Arguments

object

An object of class ategel returned by the function ATEgel

...

Other arguments for other methods

Value

It returns a matrix with the marginal effects, the standard errors based on the Delta method when the link is nonlinear, the t-ratios, and the pvalues.

References

Owen, A.B. (2001), Empirical Likelihood. Monographs on Statistics and Applied Probability 92, Chapman and Hall/CRC

Examples

## We create some artificial data with unbalanced groups and binary outcome
genDat <- function(n)
    {
        eta=c(-1, .5, -.25, -.1)
        Z <- matrix(rnorm(n*4),ncol=4)
        b <- c(27.4, 13.7, 13.7, 13.7)
        bZ <- c(Z%*%b)
        Y1 <- as.numeric(rnorm(n, mean=210+bZ)>220)
        Y0 <- as.numeric(rnorm(n, mean=200-.5*bZ)>220)
        etaZ <- c(Z%*%eta)
        pZ <- exp(etaZ)/(1+exp(etaZ))
        T <- rbinom(n, 1, pZ)
        Y <- T*Y1+(1-T)*Y0
        X1 <- exp(Z[,1]/2)
        X2 <- Z[,2]/(1+exp(Z[,1]))
        X3 <- (Z[,1]*Z[,3]/25+0.6)^3
        X4 <- (Z[,2]+Z[,4]+20)^2
        data.frame(Y=Y, cbind(X1,X2,X3,X4), T=T)
    }

dat <- genDat(200)
res <- ATEgel(Y~T, ~X1+X2+X3+X4, data=dat, type="ET", family="logit")
summary(res)
#> 
#> Call:
#> ATEgel(g = Y ~ T, balm = ~X1 + X2 + X3 + X4, family = "logit", 
#>     type = "ET", data = dat)
#> 
#> Type of GEL:  ATE with unrestricted balancing
#> Method: ET, Family: Binomial with logit link
#> (S.E. are robust to misspecification) 
#> 
#> Coefficients:
#>              Estimate  Std. Error  t value   Pr(>|t|)
#> (Intercept)  -2.11070   0.33398    -6.31979   0.00000
#> T             1.67118   0.43486     3.84307   0.00012
#> TreatProb1    0.44783   0.04411    10.15307   0.00000
#> 
#> Lambdas:
#>                   Estimate  Std. Error  t value   Pr(>|t|)
#> Lam((Intercept))  -0.00037   0.00004    -8.91556   0.00000
#> Lam(T)             0.00022   0.00005     4.53170   0.00001
#> Lam(TreatProb1)   -0.56423   1.82494    -0.30918   0.75718
#> Lam(Treat1_X1)     1.74162   0.34789     5.00627   0.00000
#> Lam(Treat1_X2)    -0.08364   0.40868    -0.20467   0.83783
#> Lam(Treat1_X3)     2.54159   3.96975     0.64024   0.52202
#> Lam(Treat1_X4)    -0.00463   0.00430    -1.07743   0.28129
#> 
#>  Over-identifying restrictions tests: degrees of freedom is 7 
#>          statistics  p-value   
#> LR test  3.9582e+01  1.5135e-06
#> LM test  3.9202e+01  1.7884e-06
#> J test   5.0203e+01  1.3178e-08
#> 
#> 
#> Convergence code for the coefficients:  0 
#> 
#> Convergence code for the lambdas:  0 

marginal(res)
#>                        Estimate Std. Error  t value     Pr(>|t|)
#> Control               0.1080609 0.03219052 3.356915 7.881728e-04
#> Treat1 versus Control 0.2837947 0.06589534 4.306748 1.656718e-05