Select optimal degree of Bernstein polynomial model for grouped data with a given regression coefficients.
maple.dr.group(
t,
n0,
n1,
M,
regr,
...,
interval = c(0, 1),
alpha = NULL,
vb = 0,
controls = mable.ctrl(),
progress = TRUE,
message = TRUE
)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
cutpoints of class intervals
frequencies of two sample data grouped by the classes
specified by t. n0:"Control", n1: "Case".
a positive integer or a vector (m0, m1).
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
a vector (a,b) containing the endpoints of
supporting/truncation interval of x and y.
a given regression coefficient, missing value is imputed by logistic regression
code for vanishing boundary constraints, -1: f0(a)=0 only, 1: f0(b)=0 only, 2: both, 0: none (default).
Object of class mable.ctrl() specifying iteration limit
and the convergence criterion for EM and Newton iterations. Default is
mable.ctrl. See Details.
logical: should a text progressbar be displayed
logical: should warning messages be displayed
Zhong Guan <zguan@iu.edu>
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.
Guan, Z., Application of Bernstein Polynomial Model to Density and ROC Estimation in a Semiparametric Density Ratio Model