nlqmm: Fitting Nonlinear Quantile Mixed Models

In marco-geraci/nlqmm: Nonlinear Quantile Mixed Models

Description

nlqmm is used to fit nonlinear quantile mixed models based on the asymmetric Laplace distribution.

Usage

nlqmm(model, fixed, random, group, covariance = "pdDiag", tau = 0.5,
    data = sys.frame(sys.parent()), subset, weights, na.action = na.fail,
    control = list(), nlmeFit = NULL, start = NULL, gradHess = FALSE,
    fit = TRUE) 

Arguments

model	a nonlinear model formula, with the response on the left of a ~ operator and an expression involving parameters and covariates on the right.
fixed	a two-sided linear formula of the form f1+...+fn~x1+...+xm, or a list of two-sided formulas of the form f1~x1+...+xm, with possibly different models for different parameters. The f1,...,fn are the names of parameters included on the right hand side of model and the x1+...+xm expressions define linear models for these parameters (when the left hand side of the formula contains several parameters, they all are assumed to follow the same linear model, described by the right hand side expression). A 1 on the right hand side of the formula(s) indicates a single fixed effects for the corresponding parameter(s).
random	a two-sided linear formula of the form r1+...+rn~x1+...+xm, or a list of two-sided formulas of the form r1~x1+...+xm, with possibly different models for different parameters. The r1,...,rn are the names of parameters included on the right hand side of model and the x1+...+xm expressions define linear models for these parameters (when the left hand side of the formula contains several parameters, they all are assumed to follow the same linear model, described by the right hand side expression). A 1 on the right hand side of the formula(s) indicates a single fixed effects for the corresponding parameter(s).
group	grouping factor.
covariance	variance–covariance matrix of the random effects. Default is pdDiag (see details).
tau	the quantile(s) to be estimated.
data	an optional data frame containing the variables named in fixed, random and group. By default the variables are taken from the environment from which nlqmm is called.
subset	an optional vector specifying a subset of observations to be used in the fitting process.
weights	an optional vector specifying likelihood weights (see details).
na.action	a function that indicates what should happen when the data contain NAs. The default action (na.fail) causes nlqmm to print an error message and terminate if there are any incomplete observations.
control	list of control parameters of the fitting process. See nlqmmControl.
nlmeFit	a nlme object with the same model as specified in the nlqmm call. If provided, its predicted random effects and estimated variance-covariance matrix will be used as initial values for nlqmm.
start	an optional list of initial (crude) estimates for the fixed effects (see details and nlqmmControl). It must be a list. The current implementation does not handle model functions of class selfStart.
gradHess	logical flag. If TRUE gradient and Hessian of the log-likelihood be calculated numerically with numDeriv. See details.
fit	logical flag. If FALSE the function returns a list of arguments for fitting.

Details

The function computes an estimate on the tau-th quantile function of the response, conditional on the covariates, as specified by the formula argument, and on random effects, as specified by the random argument. The quantile predictor is assumed to be nonlinear. The function maximizes the (log)likelihood of the Laplace regression proposed by Geraci (2019) using a Laplacian approximation of the likelihood. The optimization algorithm minimizes the negative smoothed Laplace log–likelihood using optim. The available options are the Nelder-Mead and BFGS algorithms which are specified via the argument method in nlqmmControl.

Optional starting values for the fixed effects are provided via start. Parameters are named internally as b1, b2, ... See examples further below. These values are then passed on to the initialization algorithm (see nlqmmControl) which provides the initial values to the nlqmm algorithm.

Different standard types of positive–definite matrices for the random effects can be specified: pdIdent multiple of an identity; pdCompSymm compound symmetry structure (constant diagonal and constant off–diagonal elements); pdDiag diagonal; pdSymm general positive–definite matrix, with no additional structure.

Weights are assumed to be the same for all observations within the same cluster. Weights must be strictly positive. These represent likelihood weights: the larger the weight for a cluster, the more importance is given to the cluster during estimation.

If gradHess = TRUE, the gradient and Hessian of the log-likelihood are calculated at the optimum. The results are stored as attributes of logLik and can be extracted via logLik.nlqmm. If calculation fails, a warning will be printed out.

Value

nlqmm returns an object of class nlqmm.

Note

Updates/FAQ/news are published here http://marcogeraci.wordpress.com/. New versions are usually published here https://r-forge.r-project.org/R/?group_id=1396 before going on CRAN.

Author(s)

Marco Geraci

References

Chen C. (2007). A finite smoothing algorithm for quantile regression. Journal of Computational and Graphical Statistics, 16(1), 136-164.

Geraci M. (2019). Modelling and estimation of nonlinear quantile regression with clustered data. Computational Statistics and Data Analysis, 136, 30-46.

See Also

lqmm

Examples

## Not run: 

# Pharmacokinetics of Indomethacin (package datasets)

Indometh$Subject <- as.factor(as.numeric(Indometh$Subject))
tau <- c(.1,.5,.9)
nt <- length(tau)

# Provide starting values for fixed effects
ss <- list(b1 = 3, b2 = 0.5, b3 = 0.5, b4 = -1)

# Fit bi-exponential mixed models for 3 quantiles 
fit <- list()
ctrl <- nlqmmControl(method = "Nelder-Mead", initialize = "nlrq", verbose = FALSE)
for(i in 1:nt){
	fit[[i]] <- nlqmm(conc ~ A1*exp(-exp(lrc1)*time)+A2*exp(-exp(lrc2)*time),
	data = Indometh, fixed = A1 + lrc1 + A2 + lrc2 ~ 1,
	random = A1 + lrc1 + A2 ~ 1, group = Subject, tau = tau[i],
	covariance = "pdDiag", start = ss, control = ctrl, fit = TRUE)
}

## End(Not run)

## Not run: 
# Growth of soybean plants (package nlme)

data(Soybean, package = "nlme")
tau <- c(0.05, .1, .5, .9, .95)
nt <- length(tau)
ss <- c(20, -8, -3, 1.6, 5.5, 0.1, 54.8, -2, -5, -1, 8, -1, -0.6) # Pinheiro and Bates (2000, p.294)

# Fit logistic mixed models for 5 quantiles 
ctrl <- nlqmmControl(method = "BFGS", initialize = "nlrq", verbose = FALSE,
	beta = 0.2, LL_tol = 1e-05)
names(ss) <- paste0("b", 1:13)
fit <- list()
for(i in 1:nt){
	fit[[i]] <- nlqmm(weight ~ Asym/(1+exp((xmid-Time)/scal)), data = Soybean,
	fixed = list(Asym ~ Year*Variety, xmid ~ Year + Variety, scal ~ Year),
	random = Asym ~ 1, group = Plot, tau = tau[i], covariance = "pdSymm",
	start = as.list(ss), control = ctrl, fit = TRUE)
}


## End(Not run)

marco-geraci/nlqmm documentation built on April 16, 2020, 12:37 a.m.