iso.nls2 - Confidence Regions for an nls2 Object
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DESCRIPTION
USAGE
REQUIRED-ARGUMENTS
OPTIONAL-ARGUMENTS
VALUE
CONSTRAINTS
SIDE-EFFECTS
DETAILS
SEE-ALSO
EXAMPLE
DESCRIPTION:
Return what is necessary to define
confidence regions in the space of two parameters that have been
estimated by function `nls2' when
the statistical criterion is equal to -2*log(likelihood)/n,
where n is the total number of observations.
Let p1, p2 be two active parameters and stat.crit the estimated statistical criterion.
The returned structure contains the quantities
"z(x,y)=C(x,y)-(stat.crit*n)",
x and y varying on a grid regularly spaced
around p1, p2.
"C(x,y)" is the quantity "-2*log(likelihood)" calculated at p1=x, p2=y,
the remaining parameters set to the estimated values.
The extends of the grid and the density of the points
can be different for x and y and at each side of p1, p2.
From z, confidence regions can be defined and plotted:
a confidence region is the set of points
for which z is less or equal to the
quantile of a chi-square distribution with number of degrees of freedom
equal to the number of active parameters.
USAGE:
iso.nls2(nls2.object, axis,
extends=matrix(3,nrow=2,ncol=2),
density=matrix(12,nrow=2,ncol=2),
bounds=NULL)
REQUIRED ARGUMENTS:
- nls2.object
-
an object of class `nls2' (see `nls2.object').
- axis
-
the identification of the two-dimensional space (x,y). Vector of length 2, either
character (the names of the parameters) or integer
(values from 1 to the total number of multiple parameters,
the variance parameters been numbered after the regression parameters).
OPTIONAL ARGUMENTS:
- extends
-
the extends of the grid.
A matrix of 2 columns and 2 rows:
the lower bound of x is "p1-(extends[1,1]*se1)"
where se1 is the standard error of p1,
and its upper bound is "p1+(extends[2,1]*se1)".
Similarly, the lower and upper bounds of y are
"p2-(extends[1,2]*se2)"and "p2+(extends[2,2]*se2)",
se2 being the standard error of p2.
- density
-
the density of the points along the grid.
A matrix of 2 columns and 2 rows:
density[1,1] is the number of points x at the left side
of p1
and density[2,1] is the number of points at its right.
Similarly, density[1,2] and density[2,2] are the number of points y at the
left and at the right sides of p2.
- bounds
-
The bounds of the grid.
When this argument exists, it replaces the argument `extends'.
A matrix of 2 columns and 2 rows:
bounds[1,1] is the lower bound of x
and bounds[2,1] is its upper bound.
Similarly, bounds[1,2] and bounds[2,2] are the lower and upper bounds
of y.
VALUE:
A list with
the following components:
"x": the coordinates of the points x.
Vector of length "density[1,1]+density[2,1]"
"y": the coordinates of the points y.
Vector of length "density[1,2]+density[2,2]".
"z": the values of the grid.
Matrix of dimension (length(x), length(y)).
"z[i,j]" is the value at the point (x[i],y[j]).
CONSTRAINTS:
Function `loadnls2' should have been previously called
to load into the S-session all the programs necessary
for execution and the file that describes the model must exist.
SIDE EFFECTS:
If no program has been previously loaded to calculate the model
(see `loadnls2'),
an operating-system file is created which contains the C-programs
that correspond to the formal description of the model.
If this file already exists, it is replaced.
DETAILS:
When the statistical criterion is not equal to
"-2*log(likelihood)/n" in the `nls2.object',
a warning is issued and the quantity
"-2*log(likelihood)/n" is used in the calculations instead of the statistical criterion.
This function is a method for the generic function `iso'
for class `nls2'.
It can be invoked by calling `iso' for an object of the appropriate
class, or directly by calling `iso.nls2' regardless of the
class of the object.
SEE ALSO:
EXAMPLE:
loadnls2()
iso.out_ iso(nls2.out, axis=c(1,2))
# Plot of iso-contours for different probabilities:
# The levels are the quantiles of a chi-square distribution
# with number of degrees of freedom equal to five, because
# five parameters have been estimated in the nls2.object.
X11()
contour(iso.out, levels=qchisq(c(0.50, 0.90, 0.99),5))
- Mon Sep 30 1996 -