FlexParamCurve (version 1.4-3)

extraF: Compare Two $nlsList$ Models Using Extra Sum-of-Squares F-Tests

Description

Function to compare two nested models using extra sum-of-squares F-Tests.

Usage

extraF(submodel = 1,

genmodel = 1)

Arguments

submodel

$nlsList$ model with fewer curve parameters (reduced model)

genmodel

$nlsList$ model with more curve parameters (general model)

Value

• A data.frame listing the names of the models compared, F, numerator degrees of freedom, demonimator degrees of freedom, P value and the residual sum of squares for both the general and reduced models

Details

Models must be entered in the correct order with the reduced model appearing first in the call and the more general model appearing later. These must be nested models, i.e. the general model must contain all of the curve parameters in the reduced model and more. Entering models with the same number of parameters will produce NAs in the output, but the function will produce seemingly adequate output with non-nested models. The user must check that models are nested prior to use. This function is primarily designed to be called by the model selection functions pn.modselect.step and pn.mod.compare but can be used independently. Extra sum-of-squares is obtained from: F = (SS1 - SS2)/(df1 - df2) / (SS2 / df2) where SS = sum-of-squares and df = degrees of freedom, for the more reduced model (1) and the more general model (2), respectively. If the F value is significant then the more general model provides a significant improvement over the reduced model, but if the models are not significantly different then the reduced parameter model is to be preferred. In extraF (formulated especially for nlsList models), the root mean square error (and sum of squares) is inflated to the value expected if all groups (levels) were fitted [i.e. RSE = RSE* (sqrt(n1) / sqrt(n0)), where RSE is root mean square error, n0 is the sample size (total number of data points used in fit) for the model with missing levels, and n1 is the inflated sample size (total number of data points in dataset)]. This is based on RSE changing with the square root of sample size, as discussed in the help file for pn.mod.compare. Degrees of freedom are then increased to the vaue if all individuals had been fitted successfully, i.e. total df - (# curve parameters * # levels). Thus, RSE and df are enlarged for models with missing levels so all models are compared based on the variability expected if all levels had been fitted . This allows the Fstat from extraF to be independent of missing levels in either of the two models.

References

Ritz, C. and Streibigg, J. C. (2008) $Nonlinear regression with R.$ Springer-Verlag, New York.

See Also

extraF.nls nlsList pn.modselect.step pn.mod.compare

Examples

#compare two nested nlsList models (4 vs 8 parameter models)

data(posneg.data)

   modpar(posneg.data$age, posneg.data$mass, pn.options.name = "myoptions")

   # (only first 4 group levels in data used for example's sake)

   subdata<-subset(posneg.data, as.numeric(row.names (posneg.data) ) < 53)

   richardsR2.lis <- nlsList(mass ~ SSposnegRichards(age, Asym = Asym, K = K,

     Infl = Infl, M = M, RAsym = RAsym, Rk = Rk, Ri = Ri,modno = 2, pn.options = myoptions)

                        , data = subdata)

   richardsR12.lis <- nlsList(mass ~ SSposnegRichards(age, Asym = Asym, K = K,

     Infl = Infl, M = M, modno = 12, pn.options = myoptions)

                        , data = subdata)

   extraF(richardsR12.lis, richardsR2.lis)