deglmx {SPREDA}

Functions for estimating parameters in the linear/nonlinear mixed models with dynamic covariates.

Description

Functions for estimating parameters in the linear/nonlinear mixed models with dynamic covariates. Those dynamic covariates will have restricted-shape effects such as monotonic increasing, decreasing or quadratic shape.

Usage

deglmx(fixed, data, dyn.data, id, time, random = NULL, linear = TRUE, ytrend, 
splinetrend = NULL, splinetype = NULL, degree = NULL, knots = NULL, 
weights = NULL, subset = NULL, start, maxiter = 10, method = "BFGS", ...)

Arguments

fixed

Formula with fixed effect.

data

Data with id, time, response, and fixed covariates.

dyn.data

Dynamic data with id, time, dynamic covariates.

id

The name of the id which is characters or string.

time

The name of time in the data or dyn.data which is characters or string.

random

The formula for random parts which should condition on the id.

linear

The index of linear or nonlinear.

ytrend

If ytrend=1 indicates the increasing trend of the response, if ytrend=-1 indicates the decreasing trend of the response.

splinetrend

They are a vector of trends of dynamic covariate effects. Define 1 as increasing trend and -1 as decreasing trend.

splinetype

They are a vector of the spline basis type which can be chosen among "Ms", "Is", and "Cs".

degree

The degree of the spline functions.

knots

The number of knots in the spline functions.

weights

Weights of the observation.

subset

Subset of the data.

start

The initial values for covariance and variance matrix.

maxiter

The maximum number of iteration in the optimization.

method

The method of optim function with "BFGS" as default. More details in optim.

...

Other items.

Value

The returned outputs belong to class of "deglmx". list(type = type, fit = fit, dat = dat.obj, dyn.mat = cov.mat.tmp, ytrend = ytrend, dyncovnames = dyncovnames, dyn.data = dyn.data, beta.index = beta.index, call = mfun)

type

Type of the model either linear mixed or nonlinear mixed models.

fit

The fitting results in the model including estimates, residuals, loglikelihood, and so on.

dat

The modified data.

dyn.mat

The spline basis functions.

ytrend

The indication of response trend either increasing (1) or decreasing (-1).

dyncovnames

Names of dynamic covariates in the model.

dyn.data

The modified dynamic data.

beta.index

Indications of parameters in the dyanmic covariates.

call

The call function in the model.

Note

For the nonlinear model, we currently only implement one specific nonlinear relationship.

Author(s)

Yili Hong

References

Hong. Y., Y. Duan, W. Q. Meeker, D. L. Stanley, and X. Gu (2014), Statistical Methods for Degradation Data with Dynamic Covariates Information and an Application to Outdoor Weathering Data, Technometrics, DOI: 10.1080/00401706.2014.915891.

Examples

 data(Coatingenv)
 data(Coatingout)
 
 
 fit=deglmx(DAMAGE_Y~UV+RH+TEMP, data=Coatingout, dyn.data=Coatingenv, 
           id="SPEC_NUM", time="TIME", random=~TIME|SPEC_NUM, linear=TRUE, ytrend=-1,  
           splinetrend=c(-1, -1, -1), splinetype=c("Is", "Cs", "Is"), degree=c( 3, 3, 3), 
           knots=c(4, 4, 4), weights=NULL, subset=NULL,start=c(0.017,0.0013,-0.404,0.0176), 
           maxiter=10, method='BFGS')
           
 fit=deglmx(DAMAGE_Y~G/(1+exp(-log(UV+RH+TEMP)/H)), data=Coatingout, dyn.data=Coatingenv, 
           id="SPEC_NUM", time="TIME", random=~G+H|SPEC_NUM, linear=FALSE, ytrend=-1,  
           splinetrend=c(1, 1, 1), splinetype=c("Is", "Cs", "Is"), degree=c( 3, 3, 3), 
           knots=c(4, 4, 4), weights=NULL, subset=NULL, start=c(0.1, 0.1, -0.5, 0.01), 
           maxiter=4)