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

snm {assist}

R Documentation

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=sys.parent(), fixed, random=fixed, 
groups, start, spar="v", verbose=FALSE, method="REML", control=NULL, 
correlation=NULL, weights=NULL)

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 ~ 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 'ML.
`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.

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.

Author(s)

Chunlei Ke chunlei_ke@yahoo.com and Yuedong Wang yuedong@pstat.ucsb.edu.

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.

Examples

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)

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