Jackknifing in Nonlinear Regression

Fox, T. Colcott; Hinkley, D. V.; Larntz, Kinley

doi:10.2307/1268380

Cited by 73 publications

(42 citation statements)

References 13 publications

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“…Comparisons between diets are also given in terms of pg C cell-', using values from the literature (PM = 274, TR = 157 and PT = 6.8; Saunders 1991, Ianora & Poulet 1993. Curve fitting analysis and statistics were performed for each algal concentration, using the SYSTAT and Sigm.a plot programs (Wllkinson et al 1992, Fox & Shotton 1995.…”

Section: Methodsmentioning

confidence: 99%

Is hatching success of copepod eggs diatom density-dependent?

Chaudron¹,

Poulet²,

Laabir³

et al. 1996

Mar. Ecol. Prog. Ser.

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Two species of diatoms, Phaeodactylurn tncornutum and Thalassiosira rotula, were fed to Calanus helgolandjcus females at concentrations varying between 10 and 106 cells ml-l. Their effects on the fecundity and hatching success of eggs were compared with those of the dinoflagellate diet Prorocentrum minl~nurn at 104 cells ml-' used as a control. Specific maximum fecundity was never reached with the diatom diets. The paradox is that fecundity and inhibition of hatching were diatom densitydependent, but varied in opposite directions in relation to concentration. At high diatom concentrations (ca 210' cells ml-l) fecundity increased, whereas hatchlng was totally inhibited. At low concentrations (ca ~1 0 % e l l s ml-'), resembling in situ conditions, fecundity was depressed while hatching success values were generally below 70% or showed high amplitude variations. Inhibition of hatching was proportional to fecal pellet production rate, reflecting the causal relation between ingestion, duration of feeding and accumulation of the inhibitor. The inhibitory mechanism was best fitted by a logistic function of time, the parameters of which were significantly modified for diatom concentrations >103 cells ml-' These results suggest that ingestion of diatoms might be considered as one of the causes limiting C. helgolandicus population recruitment in nature, since both fecundity and hatching can be significantly lowered at low and high diatom concentrations, respectively.

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Section: Methodsmentioning

confidence: 99%

Is hatching success of copepod eggs diatom density-dependent?

Chaudron¹,

Poulet²,

Laabir³

et al. 1996

Mar. Ecol. Prog. Ser.

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“…Since the initial description of the jackknife by Quenouille (1956), this method has been recognized as a powerful means of eliminating the biases in parameters estimated using least squares methods (Miller, 1974;Hinkley, 1977;Fox et al, 1980). The biggest advantage of this technique, aside from its applicability to both linear and nonlinear models, is that jackknife estimation does not require a normal error distribution or homoscedastic errors for its approximate validity (Fox et aI., 1980).…”

Section: Bias In Parameters Determined Using Npe Methodsmentioning

confidence: 99%

“…In the extreme case, each group contains one data pair. Next, n regressions are done to obtain n "pseudovalues" (Hinkley, 1977;Fox et al, 1980) of the parameters. The pseudo values for each parameter are defined as…”

Section: Bias In Parameters Determined Using Npe Methodsmentioning

confidence: 99%

Determining Microbial Kinetic Parameters Using Nonlinear Regression Analysis

Robinson

1985

Advances in Microbial Ecology

200

147

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“…Jackknife is implemented via the function nlsJack(). By using a leave-oneout procedure, it produces jackknife parameter estimates together with confidence intervals (Quenouille 1956;Fox, Hinkley, and Larntz 1980;Seber and Wild 1989). It can also be used to assess the influence of each observation on each parameter estimate.…”

Section: Resampling Techniquesmentioning

confidence: 99%

A Toolbox for Nonlinear Regression inR: The Packagenlstools

Baty¹,

Ritz²,

Charles³

et al. 2015

J. Stat. Soft.

612

367

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Nonlinear regression models are applied in a broad variety of scientific fields. Various R functions are already dedicated to fitting such models, among which the function nls() has a prominent position. Unlike linear regression fitting of nonlinear models relies on non-trivial assumptions and therefore users are required to carefully ensure and validate the entire modeling. Parameter estimation is carried out using some variant of the leastsquares criterion involving an iterative process that ideally leads to the determination of the optimal parameter estimates. Therefore, users need to have a clear understanding of the model and its parameterization in the context of the application and data considered, an a priori idea about plausible values for parameter estimates, knowledge of model diagnostics procedures available for checking crucial assumptions, and, finally, an understanding of the limitations in the validity of the underlying hypotheses of the fitted model and its implication for the precision of parameter estimates. Current nonlinear regression modules lack dedicated diagnostic functionality. So there is a need to provide users with an extended toolbox of functions enabling a careful evaluation of nonlinear regression fits. To this end, we introduce a unified diagnostic framework with the R package nlstools. In this paper, the various features of the package are presented and exemplified using a worked example from pulmonary medicine.

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Jackknifing in Nonlinear Regression

Abstract: The standard jackknife and two linear jackknife methods based on a single fit are compared in the context of non-linear regression fitting. Emphasis is on determination of confidence regions for parameters, where we find that the standard jackknife may be inferior.

Cited by 73 publications

References 13 publications

Is hatching success of copepod eggs diatom density-dependent?

Is hatching success of copepod eggs diatom density-dependent?

Determining Microbial Kinetic Parameters Using Nonlinear Regression Analysis

A Toolbox for Nonlinear Regression inR: The Packagenlstools

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