carma {growth} | R Documentation |
carma
is designed to handle a polynomial within subject
design matrix with unequally spaced observations which can be at
different times for different subjects. The origin of time is taken
as the mean time of all the subjects. The within subject errors are
assumed to be independent Gaussian or have a continuous time ARMA(p,q)
Gaussian structure with the option to include measurement error.
The between subject random coefficients are assumed to have an
arbitrary covariance matrix. The fixed effect design matrix is a
polynomial of equal or higher order than the within subject design
matrix. This matrix can be augmented by covariates multiplied by
polynomial design matrices of any order up to the order of the first
partition of the design matrix. The method is based on exact maximum
likelihood using the Kalman filter to calculate the likelihood.
For clustered (non-longitudinal) data, where only random effects will
be fitted, times
are not necessary.
Marginal and individual profiles can be plotted using
mprofile
and iprofile
and
residuals with plot.residuals
.
For any ARMA of order superior to an AR(1), the (complex) roots of the characteristic equation are printed out; see Jones and Ackerson (1991) for their use in calculation of the covariance function.
carma(response=NULL, ccov=NULL, times=NULL, torder=0, interaction, arma=c(0,0,0), parma=NULL, pre=NULL, position=NULL, iopt=TRUE, resid=TRUE, transform="identity", delta=NULL, envir=parent.frame(), print.level=0, typsiz=abs(p), ndigit=10, gradtol=0.00001, steptol=0.00001, iterlim=100, fscale=1, stepmax=10*sqrt(p%*%p)) fitted.carma(z, recursive=TRUE) mprofile.carma(z, times=NULL, ccov, plotse=TRUE) residuals.carma(z, recursive=TRUE)
response |
A list of two column matrices with response values and
times for each individual, one matrix or dataframe of response
values, or an object of either 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. |
ccov |
A matrix of columns of 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 specified as a
Wilkinson and Rogers formula unless none are to be used. |
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 . |
torder |
Order of the polynomial in time to be fitted. |
interaction |
Vector indicating order of interactions of covariates with time. |
transform |
Transformation of the response variable: identity ,
exp , square , sqrt , or log . |
arma |
Vector of three values: order of AR, order of MA, binary indicator for presence of measurement error. Not required for an AR(1) if an initial estimate is supplied. If only one value is supplied, it is assumed to be the order of the AR. |
parma |
Initial estimates of ARMA parameters. For example, with
arma=c(1,0,0) , an AR(1), the parameter is
parma[1]=log(theta) , where theta is the positive,
continuous time autoregressive coefficient. The finite step
autoregression coefficient for a step of length delta is then
alpha=exp(-delta*theta)
i.e. alpha=exp(-delta*exp(parma[1])) . |
pre |
Initial estimates of random effect parameters. |
position |
Two column matrix with rows giving index positions of random effects in the covariance matrix. |
iopt |
TRUE if optimization should be performed. |
resid |
TRUE if residuals to be calculated. |
delta |
Scalar or vector giving the unit of measurement
for each response value, set to unity by default. For example, if a
response is measured to two decimals, delta=0.01 . Ignored if
response has class, response or repeated . |
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. |
others |
Arguments controlling nlm . |
z |
An object of class, carma . |
plotse |
Plot the standard errors around the marginal profile curve. |
recursive |
If TRUE, recursive residuals or fitted values are given; otherwise, marginal ones. |
A list of class carma
is returned that contains all of the
relevant information calculated, including error codes.
R.H. Jones and J.K. Lindsey
Jones, R. H. and Ackerson, L. M. (1991) Serial correlation in unequally spaced longitudinal data. Biometrika, 77, 721-731.
Jones, R.H. (1993) Longitudinal Data Analysis with Serial Correlation: A State-space Approach. Chapman and Hall
elliptic
, gar
,
gnlmix
, glmm
,
gnlmm
, iprofile
,
kalseries
, mprofile
,
plot.residuals
, potthoff
,
read.list
, restovec
,
rmna
, tcctomat
,
tvctomat
.
y <- matrix(rnorm(40),ncol=5) x1 <- gl(2,4) x2 <- gl(2,1,8) # independence with time trend carma(y, ccov=~x1, torder=2) # AR(1) carma(y, ccov=~x1, torder=2, arma=c(1,0,0), parma=-0.5) carma(y, ccov=~x1, torder=3, interact=3, arma=c(1,0,0), parma=-1) # ARMA(2,1) carma(y, ccov=~x1+x2, interact=c(2,0), torder=3,arma=c(2,1,0), parma=c(0.3,2,0.7)) # random intercept carma(y, ccov=~x1+x2, interact=c(2,0), torder=3, pre=-0.4, position=c(1,1)) # random coefficients carma(y, ccov=~x1+x2, interact=c(2,0), torder=3, pre=c(-0.4,0.1), position=rbind(c(1,1),c(2,2)))