SITAR is a method of growth curve analysis, based on nlme, that summarises a set of growth curves with a mean growth curve as a regression spline, plus a set of up to four fixed and random effects (a, b, c and d) defining how individual growth curves differ from the mean curve.
sitar(
x,
y,
id,
data,
df,
knots,
fixed = NULL,
random = "a + b + c",
pdDiag = FALSE,
a.formula = ~1,
b.formula = ~1,
c.formula = ~1,
d.formula = ~1,
bounds = 0.04,
start,
xoffset = "mean",
bstart = xoffset,
returndata = FALSE,
verbose = FALSE,
correlation = NULL,
weights = NULL,
subset = NULL,
method = "ML",
na.action = na.fail,
control = nlmeControl(msMaxIter = 100, returnObject = TRUE),
keep.data = TRUE
)# S3 method for sitar
update(object, ..., evaluate = TRUE)
An object inheriting from class sitar
representing the
nonlinear mixed-effects model fit, with all the components returned by
nlme
(see nlmeObject
for a full description) plus the
following components:
the function returning the predicted value of y
.
copy of data
(if keep.data
true).
data frame of mean a-b-c-d values for unique combinations
of covariates (excluding x
).
the internal sitar
call that produced the object.
the value of xoffset
.
the lm
object providing starting values for the B-spline curve.
Generic functions such as print
, plot
, anova
and
summary
have methods to show the results of the fit. The functions
residuals
, coef
, fitted
, fixed.effects
,
random.effects
, predict
, getData
, getGroups
,
getCovariate
and getVarCov
can be used to extract some of its
components.
vector of ages.
vector of measurements.
factor of subject identifiers.
data frame containing variables x
, y
and
id
.
degrees of freedom for cubic regression spline (0 or more, see Details).
vector of values for knots (default df
quantiles of
x
distribution).
character string specifying a, b, c, d fixed effects (default
random
or the subset of "a + b + c + d" within random
).
character string specifying a, b, c, d random effects (default
"a+b+c"
). Alternatively nlme
formula e.g.
"list(id = pdDiag(a + b + c ~ 1))"
.
logical which if TRUE fits a diagonal random effects covariance matrix, or if FALSE (default) a general covariance matrix.
formula for fixed effect a (default ~ 1
).
formula for fixed effect b (default ~ 1
).
formula for fixed effect c (default ~ 1
).
formula for fixed effect d (default ~ 1
).
span of x
for regression spline, or fractional
extension of range (default 0.04).
optional numeric vector of initial estimates for the fixed
effects, or list of initial estimates for the fixed and random effects (see
nlme
).
optional value of offset for x
(either "mean"
(default), "apv" or value).
optional starting value for fixed effect b
(either
"mean", "apv" or value (default xoffset
)).
logical which if TRUE causes the model matrix to be
returned, or if FALSE (default) the fitted model. Setting returndata TRUE is
useful in conjunction with subset
and subsample
for
simulation purposes.
optional logical value to print information on the evolution
of the iterative algorithm (see nlme
).
optional corStruct
object describing the
within-group correlation structure (see nlme
).
optional varFunc
object or one-sided formula
describing the within-group heteroscedasticity structure (see
nlme
).
optional expression indicating the subset of the rows of data
that should be used in the fit (see nlme
).
character string, either "REML" or "ML" (default) (see
nlme
).
function for when the data contain NAs (see
nlme
).
list of control values for the estimation algorithm (see
nlme
) (default nlmeControl(returnObject = TRUE)).
logical to control saving data
as part of the model
object (default TRUE).
object of class sitar
.
further parameters for update
consisting of any of the
above sitar
parameters.
logical to control evaluation. If TRUE (default) the
expanded update
call is passed to sitar
for evaluation, while
if FALSE the expanded call itself is returned.
Tim Cole tim.cole@ucl.ac.uk
The SITAR model usually has up to three random effects (a, b and c), termed
size, timing and intensity respectively. df
sets the degrees of freedom
for the mean spline curve, taking values from 1 (i.e. linear) upwards. In
addition there is a random effect for the slope, d, which is fitted when
df = 0
, and combined with a, it provides the classic random intercept random
slope model, which is similar to the 1 df spline model. In addition d can be
fitted, along with a, b and c, to extend
SITAR to model variability in the adult slope of the growth curve.
xoffset
allows the origin of x
to be varied, while
bstart
specifies the starting value for b
, both of which can
affect the model fit and particularly b
. The values of bstart
,
knots
and bounds
are offset by xoffset
for fitting
purposes, and similarly for fixed effect b
.
The formulae a.formula
, b.formula
, c.formula
and d.formula
allow for cov.names and
can include functions and interactions. make.names
is used to
ensure that the names of the corresponding model terms are valid. The
modified not the original names need to be specified in predict.sitar
.
update
updates the model by taking the object
call, adding any
new parameters and replacing changed ones. Where feasible the fixed and
random effects of the model being updated are suitably modified and passed
via the start
argument.
data(heights)
## fit simple model
(m1 <- sitar(x=age, y=height, id=id, data=heights, df=5))
## relate random effects to age at menarche (with censored values +ve)
## both a (size) and b (timing) are positively associated with age at menarche
(m2 <- update(m1, a.formula = ~abs(men), b.formula = ~abs(men), c.formula = ~abs(men)))
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