Linear mixed model with serial correlation and measurement error

SerialCorrelation: exponential, Gaussian or discrete AR(1) serial correlation. LmmSerialCovariance: marginal covariance of one subject (random intercept, serial process and measurement error). LmmSerialLoglik: profile log-likelihood (ML or REML) with the fixed effects and total scale profiled out. LmmSerialFit: Nelder-Mead fit of the Diggle (1988) model, as nlme::lme with a random intercept and corExp or corGaus with a nugget. Identical to the Python arm morie.fn.serlmm.

Usage

SerialCorrelation(u, phi, kind = "exponential")

LmmSerialCovariance(times, sigma_b2, tau2, phi, nu2, kind = "exponential")

LmmSerialLoglik(
  y,
  X,
  subject,
  times,
  sigma_b2,
  tau2,
  phi,
  nu2,
  kind = "exponential",
  reml = FALSE
)

LmmSerialFit(
  y,
  X,
  subject,
  times,
  kind = "exponential",
  reml = FALSE,
  start = NULL
)

Arguments

u

Time lags.

phi

Correlation parameter.

kind

"exponential", "gaussian" or "ar1".

times

Observation times.

sigma_b2

Random-intercept variance.

tau2

Serial process variance.

nu2

Measurement-error variance.

y

Response.

X

Design matrix including the intercept.

subject

Subject identifiers (rows grouped in any order).

reml

Use restricted maximum likelihood.

start

Starting values of the square-root variance ratio, log phi and the nugget parameter r with share r^2 / (1 + r^2).

Value

A vector, matrix or list.

References

Diggle, P. J. (1988). An approach to the analysis of repeated measurements. Biometrics 44, 959-971.

Diggle, P. J., Heagerty, P., Liang, K.-Y. and Zeger, S. L. (2002). Analysis of Longitudinal Data, 2nd edn. Oxford University Press.

Examples

SerialCorrelation(0:2, 0.5)
#> [1] 1.0000000 0.6065307 0.3678794
LmmSerialCovariance(c(0, 1), 1, 2, 0.5, 0.25)
#>          [,1]     [,2]
#> [1,] 3.250000 2.213061
#> [2,] 2.213061 3.250000