kalcount {repeated}

Repeated Measurements Models for Counts with Frailty or Serial Dependence

Description

kalcount is designed to handle repeated measurements models with time-varying covariates. The distributions have two extra parameters as compared to the functions specified by intensity and are generally longer tailed than those distributions. Dependence among observations on a unit can be through gamma or power variance family frailties (a type of random effect), with or without autoregression, or serial dependence over time.

Usage

kalcount(
  response = NULL,
  times = NULL,
  origin = 0,
  intensity = "exponential",
  depend = "independence",
  update = "Markov",
  mu = NULL,
  shape = NULL,
  density = FALSE,
  ccov = NULL,
  tvcov = NULL,
  preg = NULL,
  ptvc = NULL,
  pbirth = NULL,
  pintercept = NULL,
  pshape = NULL,
  pinitial = 1,
  pdepend = NULL,
  pfamily = NULL,
  envir = parent.frame(),
  print.level = 0,
  ndigit = 10,
  gradtol = 1e-05,
  steptol = 1e-05,
  fscale = 1,
  iterlim = 100,
  typsize = abs(p),
  stepmax = 10 * sqrt(p %*% p)
)

Arguments

response

A list of two column matrices with counts and corresponding times for each individual, one matrix or dataframe of counts, or an object of class, response (created by restovec) or repeated (created by rmna or lvna). If the repeated data object contains more than one response variable, give that object in envir and give the name of the response variable to be used here.

times

When response is a matrix, a vector of possibly unequally spaced times when they are the same for all individuals or a matrix of times. Not necessary if equally spaced. Ignored if response has class, response or repeated.

origin

If the time origin is to be before the start of observations, a positive constant to be added to all times.

intensity

The form of function to be put in the Pareto distribution. Choices are exponential, Weibull, gamma, log normal, log logistic, log Cauchy, log Student, and gen(eralized) logistic.

depend

Type of dependence. Choices are independence, frailty, and serial.

update

Type of for serial dependence. Choices are Markov, serial, event, cumulated, count, and kalman. With frailty dependence, weighting by length of observation time may be specified by setting update to time.

mu

A regression function for the location parameter or a formula beginning with ~, specifying either a linear regression function in the Wilkinson and Rogers notation (a log link is assumed) or a general function with named unknown parameters. Give the initial estimates in preg if there are no time-varying covariates and in ptvc if there are.

shape

A regression function for the shape parameter or a formula beginning with ~, specifying either a linear regression function in the Wilkinson and Rogers notation or a general function with named unknown parameters. It must yield one value per observation.

density

If TRUE, the density of the function specified in intensity is used instead of the intensity.

ccov

A vector or matrix containing time-constant baseline covariates with one row per individual, a model formula using vectors of the same size, or an object of class, tccov (created by tcctomat). If response has class, repeated, the covariates must be supplied as a Wilkinson and Rogers formula unless none are to be used or mu is given.

tvcov

A list of matrices with time-varying covariate values, observed in the time periods in response, for each individual (one column per variable), one matrix or dataframe of such covariate values, or an object of class, tvcov (created by tvctomat). If response has class, repeated, the covariates must be supplied as a Wilkinson and Rogers formula unless none are to be used or mu is given.

preg

Initial parameter estimates for the regression model: intercept plus one for each covariate in ccov. If mu is a formula or function, the parameter estimates must be given here only if there are no time-varying covariates. If mu is a formula with unknown parameters, their estimates must be supplied either in their order of appearance in the expression or in a named list.

ptvc

Initial parameter estimates for the coefficients of the time-varying covariates, as many as in tvcov. If mu is a formula or function, the parameter estimates must be given here if there are time-varying covariates present.

pbirth

If supplied, this is the initial estimate for the coefficient of the birth model.

pintercept

The initial estimate of the intercept for the generalized logistic intensity.

pshape

An initial estimate for the shape parameter of the intensity function (except exponential intensity). If shape is a function or formula, the corresponding initial estimates. If shape is a formula with unknown parameters, their estimates must be supplied either in their order of appearance in the expression or in a named list.

pinitial

An initial estimate for the initial parameter. With frailty dependence, this is the frailty parameter.

pdepend

An initial estimate for the serial dependence parameter. For frailty dependence, if a value is given here, an autoregression is fitted as well as the frailty.

pfamily

An optional initial estimate for the second parameter of a two-parameter power variance family mixture instead of the default gamma mixture. This yields a gamma mixture as family -> 0, an inverse Gauss mixture for family = 0.5, and a compound distribution of a Poisson-distributed number of gamma distributions for -1 < family < 0.

envir

Environment in which model formulae are to be interpreted or a data object of class, repeated, tccov, or tvcov; the name of the response variable should be given in response. If response has class repeated, it is used as the environment.

print.level

Arguments for nlm.

ndigit

Arguments for nlm.

gradtol

Arguments for nlm.

steptol

Arguments for nlm.

fscale

Arguments for nlm.

iterlim

Arguments for nlm.

typsize

Arguments for nlm.

stepmax

Arguments for nlm.

Details

By default, a gamma mixture of the distribution specified in intensity is used, as the conditional distribution in the serial dependence models, and as a symmetric multivariate (random effect) model for frailty dependence.

Unless specified otherwise, the time origin is taken to be zero. The given times are the ends of the periods in which the counts occurred.

Here, the variance, with exponential intensity, is a quadratic function of the mean, whereas, for nbkal, it is proportional to the mean function.

If the counts on a unit are clustered, not longitudinal, use the failty dependence with the default exponential intensity, yielding a multivariate negative binomial distribution.

Nonlinear regression models can be supplied as formulae where parameters are unknowns in which case factor variables cannot be used and parameters must be scalars. (See finterp.)

Marginal and individual profiles can be plotted using mprofile and iprofile and residuals with plot.residuals.

Value

A list of classes kalcount and recursive is returned.

Author(s)

J.K. Lindsey

Examples

treat <- c(0,0,1,1)
tr <- tcctomat(treat)
dose <- 
  matrix(c(9,13,16,7,12,6,9,10,11,9,10,10,7,9,9,9,8,10,15,4),
         ncol=5,byrow=TRUE)
dd <- tvctomat(dose)
y <- restovec(structure(c(6, 4, 0, 0, 3, 6, 1, 1, 1, 5, 0, 0, 0, 4, 0, 1, 0, 
                          13, 0, 3), dim = 4:5))
reps <- rmna(y, ccov=tr, tvcov=dd)
kalcount(y, intensity="log normal", dep="independence", 
        preg=0.3, pshape=0.1)
kalcount(y, intensity="log normal", dep="frailty", pinitial=0.1,
         preg=1, psh=0.1)
kalcount(y, intensity="log normal", dep="serial", pinitial=0.1,
         preg=1, pdep=0.75, psh=0.1)
# random effect and autoregression (commented out: AR difficult to estimate)
#kalcount(y, intensity="log normal", dep="frailty", pinitial=0.1,
#         pdep=0.5, preg=1, psh=0.1)
# add time-constant variable
kalcount(y, intensity="log normal", pinitial=1, psh=1,
         preg=c(0.8,0.11), ccov=treat)
# or
kalcount(y, intensity="log normal", mu=~b0+b1*treat,
         pinitial=1, psh=.1, preg=c(0.4,-0.04), envir=reps)
# add time-varying variable
kalcount(y, intensity="log normal", pinitial=1, psh=1,
         preg=c(-1,2), ccov=treat, ptvc=0, tvc=dose)
# or equivalently, from the environment
dosev <- as.vector(t(dose))
kalcount(y, intensity="log normal", mu=~b0+b1*rep(treat,rep(5,4))+b2*dosev,
         pinitial=1, psh=1, ptvc=c(-1,2,0))
# or from the reps data object
kalcount(y, intensity="log normal", mu=~b0+b1*treat+b2*dose,
        pinitial=1, psh=1, ptvc=c(-1,2,0), envir=reps)
# try power variance family
kalcount(y, intensity="log normal", mu=~b0+b1*treat+b2*dose,
         pinitial=1, psh=1, ptvc=c(-1,2,0.1), envir=reps,
         pfamily=0.8)