assist (version 3.1.9)

snm: Fit a Semi-parametric Nonlinear Mixed-effects Model

Description

This generic function fits a semi-paramteric nonlinear mixed-effects model in the formulation described in Ke and Wang (2001). Current version only allows linear dependence on non-parametric functions.

Usage

snm(formula, func, data=list(), fixed, random=fixed, 
groups, start, spar="v", verbose=FALSE, method="REML", control=NULL, 
correlation=NULL, weights=NULL)

Value

an object of class snm is returned, representing a semi-parametric nonlinear mixed effects model fit. Generic functions such as print, summary, predict and intervals have methods to show the results of the fit.

Arguments

formula

a formula object, with the response on the left of a ~ operator, and an expression of variables, parameters and non-parametric functions on the right.

func

a list of spline formulae each specifying the spline components necessary to estimate each non-parametric function. On the left of a \(\mbox{\textasciitilde}\) operator of each component is the unknow function symbol(s) as well as its arguments, while the right side is a list of two components nb, an optional one-side formula for representing the null space's bases, and a required rk structure. nb and rk are similar to formula and rk in ssr. A missing nb denotes an empty null space.

fixed

a two-sided formula specifying models for the fixed effects. The syntax of fixed in nlme is adopted.

start

a numeric vector, the same length as the number of fixed effects, supplying starting values for the fixed effects.

spar

a character string specifying a method for choosing the smoothing parameter. "v", "m" and "u" represent GCV, GML and UBR respectively. Default is "v" for GCV.

data

An optional data frame containing the variables appearing in formula , random, rk, correlation, weights. By default, the variables are taken from the environment from which snm is called.

random

an optional random effects structure specifying models for the random effects. The same syntax of random in nlme is assumed.

groups

an optional one-sided formula of the form ~g1 (single level) or ~g1/.../gQ (multiple levels of nesting), specifying the partitions of the data over which the random effects vary. g1,...,gQ must evaluate to factors in data. See nlme for details.

verbose

an optional logical numerical value. If TRUE, information on the evolution of the iterative algorithm is printed. Default is FALSE.

method

a character string. If 'REML' the model is fit by maximizing the restricted log-likelihood. If 'ML' the log-likelihood is maximized. Default is 'REML.

control

a list of parameters to control the performance of the algorithm.

correlation

an optional corStruct object describing the within-group correlation structure. See the documentation of corClasses for a description of the available corStruct classes. Default is NULL, corresponding to no within-in group correlations.

weights

an optional varFunc object or one-sided formula describing the within-group heteroscedasticity structure. If given as a formula, it is used as the argument to varFixed, corresponding to fixed variance weights. See the documentation on varClasses for a description of the available varFunc classes. Defaults to NULL, corresponding to homoscesdatic within-group errors.

Author

Chunlei Ke and Yuedong Wang .

References

Ke, C. and Wang, Y. (2001). Semi-parametric Nonlinear Mixed Effects Models and Their Applications. JASA 96:1272-1298.

Pinheiro, J.C. and Bates, D. M. (2000). Mixed-Effects Models in S and S-PLUS. Springer.

See Also

predict.snm, intervals.snm, snm.control, print.snm,summary.snm

Examples

if (FALSE) {
data(CO2)

options(contrasts=rep("contr.treatment", 2))	
co2.fit1 <- nlme(uptake~exp(a1)*(1-exp(-exp(a2)*(conc-a3))), 
                 fixed=list(a1+a2~Type*Treatment,a3~1), 
                 random=a1~1, groups=~Plant, 
                 start=c(log(30),0,0,0,log(0.01),0,0,0,50),
                 data=CO2)

M <- model.matrix(~Type*Treatment, data=CO2)[,-1]
co2.fit2 <- snm(uptake~exp(a1)*f(exp(a2)*(conc-a3)),
                func=f(u)~list(~I(1-exp(-u))-1,lspline(u, type="exp")),
                fixed=list(a1~M-1,a3~1,a2~Type*Treatment),
                random=list(a1~1), group=~Plant, verbose=TRUE,
                start=co2.fit1$coe$fixed[c(2:4,9,5:8)], data=CO2)
}