nls2 welcome nls2 function

nls2
Description of the Object Created by nls2



GENERAL DESCRIPTION WHAT HAPPENED DURING THE ESTIMATION PROCESS THE ESTIMATION CONTEXT
THE STATISTICAL RESULTS SOME OTHER RESULTS INTERMEDIATE RESULTS
DETAILS NOTES Reference Manual


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.

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WHAT HAPPENED DURING THE ESTIMATION PROCESS:

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.

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THE ESTIMATION CONTEXT:

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.

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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.

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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').

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INTERMEDIATE RESULTS:

"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".

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DETAILS:

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"

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Notes:

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)

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Last release: Feb 2001 -