R: Difference in G-Squared Statistic Based CIs (Non-Robust)

diff_Gsq_nr {cta}

R Documentation

Difference in `G`-Squared Statistic Based CIs (Non-Robust)

Description

Constructs confidence intervals (CIs), based on the difference in G^2 statistic, for estimands in contingency tables subject to equality constraints.

These confidence intervals are also referred to as likelihood ratio confidence intervals or profile likelihood confidence intervals.

The program may stop because of a non-convergence issue.

Usage

diff_Gsq_nr(y, strata, fixed.strata, h0.fct, h0.fct.deriv, S0.fct,
            S0.fct.deriv, max.mph.iter, step, change.step.after,
            y.eps, iter.orig, norm.diff.conv, norm.score.conv,
            max.score.diff.iter, S.space.H0, tol.psi, tol,
            max.iter, cut.off, delta)

Arguments

`y`	Observed table counts in the contingency table(s), in vector form.
`strata`	Vector of the same length as `y` that gives the stratum membership identifier.
`fixed.strata`	The object that gives information on which stratum (strata) has (have) fixed sample sizes.
`h0.fct`	The constraint function `h_{0}(\cdot)` with respect to `m`, where `m = E(Y)`, the vector of expected table counts.
`h0.fct.deriv`	The R function object that computes analytic derivative of the transpose of the constraint function `h_{0}(\cdot)` with respect to `m`. If `h0.fct.deriv` is not specified or `h0.fct.deriv = NULL`, numerical derivatives will be used.
`S0.fct`	The estimand function `S_{0}(\cdot)` with respect to `m`.
`S0.fct.deriv`	The R function object that computes analytic derivative of the estimand function `S_{0}(\cdot)` with respect to `m`. If `S0.fct.deriv` is not specified or `S0.fct.deriv = NULL`, numerical derivatives will be used.
`max.mph.iter`, `step`, `change.step.after`, `y.eps`, `iter.orig`, `norm.diff.conv`, `norm.score.conv`, `max.score.diff.iter`	The parameters used in `mph.fit`.
`S.space.H0`	Restricted estimand space of `S(\cdot)` under `H_{0}`, i.e. subject to the imposed equality constraints along with sampling constraints.
`tol.psi`, `tol`, `max.iter`	The parameters used in the three stopping criteria in solving for the roots to the test-inversion equation.
`cut.off`	`qchisq(cc, 1)`. i.e. The chi-square cutoff, with `1` df, based on the significance level `1-cc`.
`delta`	The constant `\delta` that is in expressions of the moving critical values within each sliding quadratic step.

Value

Provided that diff_Gsq_nr does not stop, it returns a 1-by-2 matrix which displays two endpoints of the confidence interval based on the difference in G^2 statistic.

Author(s)

Qiansheng Zhu

References

Zhu, Q. (2020) "On improved confidence intervals for parameters of discrete distributions." PhD dissertation, University of Iowa.

Difference in G-Squared Statistic Based CIs (Non-Robust)