Fits a logspline density using splines to approximate the log-density
using
the 1997 knot addition and deletion algorithm (logspline).
The 1992 algorithm is available using the oldlogspline function.
logspline(x, lbound, ubound, maxknots = 0, knots, nknots = 0, penalty,
silent = TRUE, mind = -1, error.action = 2)Object of the class logspline, that is intended as input for
plot.logspline (summary plots),
summary.logspline (fitting summary),
dlogspline (densities),
plogspline (probabilities),
qlogspline (quantiles),
rlogspline (random numbers from the fitted distribution).
The object has the following members:
the command that was executed.
the number of knots in the model that was selected.
coefficients of the polynomial part of the spline. The first coefficient is the constant term and the second is the linear term.
coefficients of the knots part of the spline.
The k-th element is the coefficient
of \((x-t(k))^3_+\) (where \(x^3_+\) means the positive part of the third power
of \(x\),
and \(t(k)\) means knot k).
vector of the locations of the knots in the logspline model.
the largest number of knots minus one considered during fitting
(i.e. with maxknots = 6 the maximum number of knots is 5).
the penalty that was used.
first element: 0 - lbound was \(-\inf\) 1 it was something else; second
element: lbound, if specified; third element: 0 - ubound was \(\inf\),
1 it was something else; fourth element: ubound, if specified.
the sample size.
matrix with 3 columns. Column one: number of knots; column two: model fitted during addition (1) or deletion (2); column 3: log-likelihood.
range of the input data.
minimum distance in order statistics between knots required during fitting (the actual minimum distance may be much larger).
data vector. The data needs to be uncensored. oldlogspline
can deal with right- left- and interval-censored data.
lower/upper bound for the support of the density. For example, if there
is a priori knowledge that the density equals zero to the left of 0,
and has a discontinuity at 0,
the user could specify lbound = 0. However, if the density is
essentially zero near 0, one does not need to specify lbound.
the maximum number of knots. The routine stops adding knots when this number of knots is reached. The method has an automatic rule for selecting maxknots if this parameter is not specified.
ordered vector of values (that should cover the complete range of the
observations), which forces the method to start with these knots.
Overrules knots.
If knots is not specified, a default knot-placement rule is employed.
forces the method to start with nknots knots.
The method has an automatic rule
for selecting nknots if this parameter is not specified.
the parameter to be used in the AIC criterion. The method chooses
the number of knots that minimizes
-2 * loglikelihood + penalty * (number of knots - 1).
The default
is to use a penalty parameter of penalty = log(samplesize) as in BIC. The effect of
this parameter is summarized in summary.logspline.
should diagnostic output be printed?
minimum distance, in order statistics, between knots.
how should logspline deal with non-convergence problems? Very-very rarely
in some extreme situations
logspline has convergence problems. The only two situations that I am aware of are when
there is effectively a sharp bound, but this bound was not specified, or when the data is severly
rounded. logspline can deal with this in three ways. If error.action is 2, the same
data is rerun with the slightly more stable, but less flexible oldlogspline. The object is translated
in a logspline object using oldlogspline.to.logspline, so this is almost
invisible to the user. It is particularly useful when you run simulation studies, as he code can
seemlessly continue. Only the lbound and ubound options are passed on to
oldlogspline, other options revert to the default. If error.action is 1, a warning is printed,
and logspline returns nothing (but does not crash). This is useful if you run a
simulation, but do not like to revert to oldlogspline. If error.action is 0, the
code crashes using the stop function.
Charles Kooperberg clk@fredhutch.org.
Charles Kooperberg and Charles J. Stone. Logspline density estimation for censored data (1992). Journal of Computational and Graphical Statistics, 1, 301--328.
Charles J. Stone, Mark Hansen, Charles Kooperberg, and Young K. Truong. The use of polynomial splines and their tensor products in extended linear modeling (with discussion) (1997). Annals of Statistics, 25, 1371--1470.
plot.logspline,
summary.logspline,
dlogspline,
plogspline,
qlogspline,
rlogspline,
oldlogspline,
oldlogspline.to.logspline.
y <- rnorm(100)
fit <- logspline(y)
plot(fit)
#
# as (4 == length(-2, -1, 0, 1, 2) -1), this forces these initial knots,
# and does no knot selection
fit <- logspline(y, knots = c(-2, -1, 0, 1, 2), maxknots = 4, penalty = 0)
#
# the following example give one of the rare examples where logspline
# crashes, and this shows the use of error.action = 2.
#
set.seed(118)
zz <- rnorm(300)
zz[151:300] <- zz[151:300]+5
zz <- round(zz)
fit <- logspline(zz)
#
# you could rerun this with
# fit <- logspline(zz, error.action=0)
# or
# fit <- logspline(zz, error.action=1)
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