maple.dr.group: Maximum approximate profile likelihood estimate of the...

In mable: Maximum Approximate Bernstein/Beta Likelihood Estimation

Maximum approximate profile likelihood estimate of the density ratio model for grouped data with given regression coefficients

Description

Select optimal degree of Bernstein polynomial model for grouped data with a given regression coefficients.

Usage

maple.dr.group(
  t,
  n0,
  n1,
  M,
  regr,
  ...,
  interval = c(0, 1),
  alpha = NULL,
  vb = 0,
  controls = mable.ctrl(),
  progress = TRUE,
  message = TRUE
)

Arguments

t	cutpoints of class intervals
n0, n1	frequencies of two sample data grouped by the classes specified by t. coden0:"Control", n1: "Case".
M	a positive integer or a vector (m0, m1).
regr	regressor vector function r(x)=(1,r_1(x),...,r_d(x)) which returns n x (d+1) matrix, n=length(x)
...	additional arguments to be passed to regr
interval	a vector (a,b) containing the endpoints of supporting/truncation interval of x and y.
alpha	a given regression coefficient, missing value is imputed by logistic regression
vb	code for vanishing boundary constraints, -1: f0(a)=0 only, 1: f0(b)=0 only, 2: both, 0: none (default).
controls	Object of class mable.ctrl() specifying iteration limit and the convergence criterion for EM and Newton iterations. Default is mable.ctrl. See Details.
progress	logical: should a text progressbar be displayed
message	logical: should warning messages be displayed

Details

Suppose that n0("control") and n1("case") are frequencies of independent samples grouped by the classes t from f0 and f1 which satisfy f1(x)=f0(x)exp[alpha0+alpha'r(x)] with r(x)=(r1(x),...,r_d(x)). Maximum approximate Bernstein/Beta likelihood estimates of f0 and f1 are calculated with a given regression coefficients which are efficient estimates provided by other semiparametric methods such as logistic regression. If support is (a,b) then replace r(x) by r[a+(b-a)x]. For a fixed m, using the Bernstein polynomial model for baseline f_0, MABLEs of f_0 and parameters alpha can be estimated by EM algorithm and Newton iteration. If estimated lower bound m_b for m based on n1 is smaller that that based on n0, then switch n0 and n1 and use f_1 as baseline. If M=m or m0=m1=m, then m is a preselected degree. If m0<m1 it specifies the set of consective candidate model degrees m0:m1 for searching an optimal degree by the change-point method, where m1-m0>3.

Value

A list with components

• m the given or a selected degree by method of change-point

• p the estimated vector of mixture proportions p = (p_0, \ldots, p_m) with the given or selected degree m

• alpha the given regression coefficients

• mloglik the maximum log-likelihood at degree m

• interval support/truncation interval (a,b)

• baseline ="control" if f_0 is used as baseline, or ="case" if f_1 is used as baseline.

• M the vector (m0, m1), where m1, if greater than m0, is the largest candidate when the search stoped

• lk log-likelihoods evaluated at m \in \{m_0, \ldots, m_1\}

• lr likelihood ratios for change-points evaluated at m \in \{m_0+1, \ldots, m_1\}

• pval the p-values of the change-point tests for choosing optimal model degree

• chpts the change-points chosen with the given candidate model degrees

Author(s)

Zhong Guan <[e-mail]>

References

Guan, Z., Application of Bernstein Polynomial Model to Density and ROC Estimation in a Semiparametric Density Ratio Model

mable documentation built on Aug. 24, 2023, 5:10 p.m.