Formal lack-Of-Fit test of a nonlinear model against a one-way ANOVA model
Tests the nonlinear model against a more general one-way ANOVA model and from a likelihood ratio test. P-values are derived from the F- and χ^2 distribution, respectively.
LOF.test(object)
object |
an object of class 'replist', 'pcrfit' or 'nls', which was fit with replicate response values. |
The one-way ANOVA model is constructed from the data component of the nonlinear model by factorizing each of the predictor values.
Hence, the nonlinear model becomes a submodel of the one-way ANOVA model and we test both models with the null hypothesis that the ANOVA model
can be simplified to the nonlinear model (Lack-of-fit test). This is done by two approaches:
1) an F-test (Bates & Watts, 1988).
2) a likelihood ratio test (Huet et al, 2004).
P-values are derived from an F-distribution (1) and a χ^2 distribution (2).
A list with the following components:
pF |
the p-value from the F-test against the one-way ANOVA model. |
pLR |
the p-value from the likelihood ratio test against the one-way ANOVA model. |
Andrej-Nikolai Spiess
Nonlinear Regression Analysis and its Applications.
Bates DM & Watts DG.
John Wiley & Sons (1988), New York.
Statistical Tools for Nonlinear Regression: A Practical Guide with S-PLUS and R Examples.
Huet S, Bouvier A, Poursat MA & Jolivet E.
Springer Verlag (2004), New York, 2nd Ed.
## Example with a 'replist' ## no lack-of-fit. ml1 <- modlist(reps, fluo = 2:5, model = l5) rl1 <- replist(ml1, group = c(1, 1, 1, 1)) LOF.test(rl1) ## Example with a 'nls' fit ## => there is a lack-of-fit. DNase1 <- subset(DNase, Run == 1) fm1DNase1 <- nls(density ~ SSlogis(log(conc), Asym, xmid, scal), DNase1) LOF.test(fm1DNase1)
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