f.psi: Model Comparison Statistics

In cta: Contingency Table Analysis Based on ML Fitting of MPH Models

Description

Computes one of the model comparison statistics.

The model comparison statistics include:

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

  G^{2}(ψ) - G^2 = G^{2}(y; H_{0}(ψ)) - G^{2}(y; H_{0});

• "diff.Xsq": The difference in X^2 statistic,

  X^{2}(ψ) - X^2 = X^{2}(y; H_{0}(ψ)) - X^{2}(y; H_{0});

• "diff.PD": The difference in power-divergence statistic, with index parameter λ,

  PD_{λ}(ψ) - PD_{λ} = PD_{λ}(y; H_{0}(ψ)) - PD_{λ}(y; H_{0});

• "nested.Gsq": The nested G^2 statistic,

  G^{2}(y; H_{0}(ψ) | H_{0});

• "nested.Xsq": The nested X^2 statistic,

  X^{2}(y; H_{0}(ψ) | H_{0});

• "nested.PD": The nested power-divergence statistic, with index parameter λ,

  PD_{λ}(y; H_{0}(ψ) | 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 ψ 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 λ 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_{λ}(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.

See Also

diff_Xsq_nr, nested_Xsq_nr, diff_Gsq_nr, nested_Gsq_nr, diff_PD_nr, nested_PD_nr, diff_Xsq_robust, nested_Xsq_robust, diff_Gsq_robust, nested_Gsq_robust, diff_PD_robust, nested_PD_robust, ci.table

cta documentation built on Aug. 24, 2021, 1:06 a.m.