Description Usage Arguments Details Value Author(s) References Examples
Obtains the maximum likelihood estimates of the parameters for linear mixed effects models with random intercept and a stationary or non-stationary stochastic process component, under multivariate normal response distribution
1 2 |
formula |
a typical |
data |
a data frame from which the variables are to be extracted |
id |
a numerical vector for subject identification |
process |
a character string for the stochastic process: |
timeVar |
a numerical vector for the time variable |
init |
a numerical vector of initial values for the variance parameters to
start the Fisher-Scoring or Nelder-Mead algorithms;
if the user does not provide their own values |
tol |
a numerical value for the maximum tolerance to assess the convergence |
maxiter |
a numerical value for the number of iterations for the Fisher-Scoring or Nelder-Mead algorithms |
silent |
a character string, if set to |
For "process"
, "sgp-powered-power-method"
is a general form for stationary process
with powered correlation function. "power"
is the shapre parameter and
corresponds to "c"
in
exp(-|t-s|^c/φ),
where t and s are two time points and φ is the scale parameter,
and "method"
might be "fs"
for Fisher-Scoring or "nm"
for Nelder-Mead.
Some examples are: "sgp-powered-1-fs"
for stationary process with exponential correlation
function with Fisher-Scoring algorithm and
"sgp-powered-2-nm"
for stationary process with Gaussian correlation
function with Nelder-Mead algorithm. Similarly, "sgp-matern-kappa"
is a general form for
stationary process with Matern correlation
function. "kappa"
is the shape parameter and corresponds to κ in
≤ft\{ 2^{κ-1} Γ ≤ft( κ \right) \right \}^{-1} ≤ft(|t - s|/ν \right)^{κ} K_{κ} ≤ft(|t - s|/ν \right),
t and s are two time points and ν is the scale parameter.
An example is "sgp-matern-0.5"
for
stationary process with exponential correlation function. Nelder-Mead algorithm is automatically specified
for the choice of Matern, i.e. Fisher-Scoring is not available.
"init"
assumes the following:
- 3 element vectors for "process = bm"
and "process = ibm"
, with initials for the
variances of random intercept, stochastic process and measurement error, respectively
- 4 element vector for "process = iou"
, with initials for the variance of
random intercept variance, (two) parameters of the stochastic process, variance of measurement error
- 3 element vector for "process = sgp-powered-power-fs"
, with initials for
log of the fraction of the variance of random intercept and variance of the process,
log(φ) and log of the fraction of the variance of measurement error and
variance of the process.
- NULL
for any of the specification of "process"
, in which case lmenssp
finds the initals internally using the lme
function of the nlme package.
Returns the results as lists
Ozgur Asar, Peter J. Diggle
Diggle PJ (1988) An approach to the analysis of repeated measurements. Biometrics, 44, 959-971.
Diggle PJ, Sousa I, Asar O (2015) Real time monitoring of progression towards renal failure in primary care patients. Biostatistics, 16(3), 522-536.
Taylor JMG, Cumberland WG, Sy JP (1994) A Stochastic Model for Analysis of Longitudinal AIDS Data. Journal of the American Statistical Association, 89, 727-736.
1 2 3 4 5 6 7 8 9 10 11 | # loading the data set and subsetting it for the first 20 patients
# for the sake illustration of the usage of the functions
data(data.sim.ibm)
data.sim.ibm.short <- data.sim.ibm[data.sim.ibm$id <= 20, ]
# fitting the model with integrated Brownian motion
fit.ibm <- lmenssp(log.egfr ~ sex + bage + fu + pwl, data = data.sim.ibm.short,
id = data.sim.ibm.short$id, process = "ibm", timeVar = data.sim.ibm.short$fu,
silent = FALSE)
fit.ibm
|
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