nls2
Description of the Object Created by nls2
|
---|
GENERAL DESCRIPTION:
Objects of class "nls2" are returned by functions `nls2',
`renls2' and `rexnls2' to represent the result of
fitting a nonlinear regression model.
This entry describes the components of the nls2 objects.
Refer to the `nls2 Reference Manual' for statistical explanations.
To make reading easier, five types of components are distinguished,
according to what they contain:
- the state of the estimation process ,
- the estimation context,
- the statistical results,
- some extra results,
- the intermediate results.
In case of alternated estimation, the following components
are included
in lists called "step1", "step2" or "step3",
according to the step they describe.
- message
-
a brief description of how the estimation process terminated.
- code
-
a numerical conventional transcription of the component `message':
0 if no error occurs during execution.
See the paragraph `DETAILS' for the other possible values.
- call
-
an image of the call that produced the object, with all of the arguments explicitly named.
- model
-
a copy of the input "model" argument in which
missing components are replaced by their default values.
- response.name,X.names
-
the name of the response and the names of the independent variables.
- is.odes
-
TRUE if the model is described by an ordinary differential equations system.
- replications
-
the number of replications
of each observation.
- data.stat
-
statistics on the data;
a list with the following components:
"Y1": the sum of the response values on the replications weighted by the
number of replications
"Y2": the sum of
the squared values of the response on the replications weighted by the
number of replications
"S2":
the intra-replications variance.
- nb.steps
-
if the regression and the variance parameters have been estimated alternatively,
the number of steps that have been executed.
Otherwise, "nb.steps" is equal to 1 or, in case of no estimation, equal to 0.
- stat.ctx
-
a copy of the input context argument in which
wrong components are corrected and
missing ones are replaced by their default values.
- integ.ctx
-
a copy of the input integration context argument in which
missing components are replaced by their default values.
THE STATISTICAL RESULTS:
In case of alternated estimation, all the following components
are included
in lists called "step1", "step2" or "step3",
according to the step they describe.
- nb.iters
-
the number of iterations that have been executed.
- stop.crit,stat.crit,lambda,sigma2
-
the stopping criterion,
the fitting criterion,
the value of the Gauss-Marquardt parameter and
the estimated value of square sigma, respectively.
- theta
-
the estimated values of the regression parameters.
- beta
-
the estimated values
of the parameters that appear in the variance function only.
- response
-
the fitted values of the response.
- variance
-
the fitted values of the variance function described in the model-file.
- Z
-
the exhaustive statistics.
- B,D,Eta
-
the elements of the estimating equation.
- d.resp
-
the fitted values of the derivatives of the response with respect to the
regression parameters.
- d.theta.vari,d.beta.vari
-
when there is a variance function,
the fitted values of the derivatives of the variance with respect to the parameters
of the regression function and, if any, to the parameters that appear in the
variance function only.
- FOdes
-
when the model is described by a differential equations system,
the fitted values of the system.
- d.FOdes
-
when the model is described by a differential equations system,
the fitted values of its derivatives
with respect to the parameters.
- stat.crit.type,stat.crit.code
-
descriptions of the type of
the statistical criterion.
- method
-
description of the estimation method.
- nh
-
the number of the sufficient statistics Z.
- effic,W.type
-
indicators of the efficiency
of the estimator and of the shape of the matrix W, respectively.
SOME OTHER RESULTS:
In case of alternated estimation, all the following components
are included
in lists called "step1", "step2" or "step3",
according to the step they describe.
They are calculated by `renls2' and `rexnls2' only when requested.
- loglik
-
calculated when the family of the model is
"gaussian",
the value of "-2*log(likelihood)" divided by the total number of
observations.
- log[<family>]
-
the value of the log(likelihood) calculated according to
the family of the model.
Here <family> denotes the effective value of the current family.
- norm
-
the norm of the estimating equation
- residuals,s.residuals
-
the residuals and the standardized residuals.
When the family is multinomial,
the standardized residuals are equal to
the residuals divided by the square-root of
the estimated variance of the observations
(the formula is the same as for the binomial family).
Otherwise, the standardized residuals are equal to
the residuals divided by the square-root of
the estimated
variance described in the model-file.
- rss.unweighted,rss
-
the sum of the squared
residuals
and standardized residuals respectively.
- deviance
-
calculated when the family of the model
is not "gaussian", the value of the deviance.
- dev.residuals
-
calculated when the family of the model
neither "gaussian" nor "multinomial",
the deviance residuals.
- mu3,mu4
-
the moments of order 3 and 4
- as.var
-
the asymptotic variance
- correlation
-
the correlation matrix
- B.varZ.B
-
the product:
"transposed B * variance of Z * B"
divided by the number of observations, replications included if any.
(See the `nls2 Reference Manual').
- W
-
the product:
"transposed B * D"
divided by the number of observations, replications included if any.
This matrix is calculated for the active parameters.
(See the `nls2 Reference Manual').
"iters.sv" is
a list that contains the intermediate results calculated throughout
the iterative process, when requested.
Its possible components are:
"nb.iters.sv": the number of iterations that have been saved.
"iter": the indexes of the saved iterations.
"direction": the direction.
"omega": the optimal step.
"stop.crit", "stat.crit", "lambda", "sigma2", "theta", "beta", "response", "variance",
"B", "D", "Eta", "d.resp", "d.theta.vari", "d.beta.vari", "FOdes":
same meaning as above.
In case of alternated estimation, "iters.sv" is
included in the lists "step1", "step2", "step3".
The possible values of the component `code' and
the corresponding values of the component `message' are:
0, "No errors during execution".
200, "The estimation process has not been run: see the warnings."
156, "The regression function could not be calculated at the starting values of the parameters".
157, "The variance function could not be calculated at the starting values of the parameters".
21, "Convergence has not been reached".
22, "The maximum number of iterations has been reached".
23, "An error has occurred when calculating the direction".
61, "The minimisation criterions are equal at the 3 points of calculation".
145, "One value returned by the variance function is negative or null".
158, "One value returned by the variance function is negative or null at the first iteration".
112, "Invalid trace length".
120, "Invalid input arguments: see the warnings".
150, "A numerical error has occurred".
307, "An error has occurred when calculating the integration system"
The content of the nls2 objects can be selected by using
the components with prefix .sv in the control
argument of nls2:
see nls2.control.
Objects of class `nls2' have methods for functions:
- `all.equal.nls2', `print.nls2',
- `summary.nls2', `fitted.nls2', `coef.nls2', `residuals.nls2' (extracting functions),
- `plvar.nls2', `plres.nls2', `plfit.nls2', `plit.nls2' (plotting functions),
- `confidence.nls2', `ellips.nls2', `iso.nls2' (confidence intervals and regions)
- `wald.nls2' (test).
- `calib.nls2' (calibration)
Last release: Feb 2001 -