mb can be used to calculate the (worst-case and IV) Manski's bounds and confidence interval covering the true effect of interest
with a fixed probability.mb(treat, outc, IV = NULL, Model, B = 100, sig.lev = 0.05)Model = "B" or prevalence when Model = "BSS". When an IV is employed
the function returns IV Manski bounds.
For comparison, it also returns the estimated effect assuming random assignment (i.e., the treatment received or selection relies
on the assumption of ignorable observed and unobserved selection). Note that this is different from
what provided by AT or est.prev when naive = FALSE as observed confounders are accounted for
and the assumption here is of ignorable unobserved selection.
A confidence interval covering the true ATE/prevalence with a fixed probability is also provided. This is based on the approach
described in Imbens and Manski (2004). NOTE that this interval is typically very close (if not identical) to the lower
and upper bounds.
The ATE can be at most 1 (or 100 in percentage) and the worst-case Manski's bounds have width 1. This means that
0 is always included within the possibilites of these bounds. Nevertheless, this may be useful to check whether
the effect from a bivariate recursive model is included within the possibilites of the bounds.
When estimating the prevalance the worst-case Manski's bounds have width equal to the non-response probability,
which provides a measure of the uncertainty about the prevalence caused by non-response. Again, this may be useful to check whether
the prevalence from a bivariate non-random sample selection model is included within the possibilites of the bounds.
See SemiParBIVProbit for some examples.SemiParBIVProbit## see examples for SemiParBIVProbitRun the code above in your browser using DataLab