R: Model Comparison Statistics

f.psi {cta}

R Documentation

Model Comparison Statistics

Description

Computes one of the model comparison statistics.

The model comparison statistics include:

"diff.Gsq": The difference in G^2 statistic,

G^{2}(\psi) - G^2 = G^{2}(y; H_{0}(\psi)) - G^{2}(y; H_{0});
"diff.Xsq": The difference in X^2 statistic,

X^{2}(\psi) - X^2 = X^{2}(y; H_{0}(\psi)) - X^{2}(y; H_{0});
"diff.PD": The difference in power-divergence statistic, with index parameter \lambda,

PD_{\lambda}(\psi) - PD_{\lambda} = PD_{\lambda}(y; H_{0}(\psi)) - PD_{\lambda}(y; H_{0});
"nested.Gsq": The nested G^2 statistic,

G^{2}(y; H_{0}(\psi) | H_{0});
"nested.Xsq": The nested X^2 statistic,

X^{2}(y; H_{0}(\psi) | H_{0});
"nested.PD": The nested power-divergence statistic, with index parameter \lambda,

PD_{\lambda}(y; H_{0}(\psi) | H_{0}).

Usage

f.psi(y, strata, fixed.strata, h0.fct, h0.fct.deriv = NULL,
      S0.fct, S0.fct.deriv = NULL, method_specific, psi,
      max.mph.iter, step, change.step.after, y.eps, iter.orig,
      norm.diff.conv, norm.score.conv, max.score.diff.iter,
      pdlambda = NULL, Gsq_H0, Xsq_H0, PD_H0, cons.MLE.m_H0)

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.
`method_specific`	A character string that indicates which model comparison statistic to compute. It can be one of `"diff.Xsq"`, `"nested.Xsq"`, `"diff.Gsq"`, `"nested.Gsq"`, `"diff.PD"`, or `"nested.PD"`.
`psi`	The real number `\psi` in the model comparison statistic.
`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`.
`pdlambda`	The index parameter `\lambda` in the power-divergence statistic.
`Gsq_H0`	The `G^2` statistic for testing `H_{0}` vs. not `H_{0}`, i.e. `G^{2}(y; H_{0})`.
`Xsq_H0`	The `X^2` statistic for testing `H_{0}` vs. not `H_{0}`, i.e. `X^{2}(y; H_{0})`.
`PD_H0`	The power-divergence statistic for testing `H_{0}` vs. not `H_{0}`, i.e. `PD_{\lambda}(y; H_{0})`.
`cons.MLE.m_H0`	Constrained MLE of `m = E(Y)` subject to `H_{0}`.

Value

f.psi returns a numeric value, which is the computed model comparison statistic.

Note

Among the four inputs: Gsq_H0, Xsq_H0, PD_H0, and cons.MLE.m_H0, only one of them needs to be specified.

Author(s)

Qiansheng Zhu

References

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