response in a data.frame, and growth rates can be
computed using derivativesUses smooth.spline to fit a natural cubic smoothing spline or JOPS to fit a
P-spline to all the values of response stored in data.
The amount of smoothing can be controlled by tuning parameters, these being
related to the penalty. For a natural cubic smoothing spline, these are
df or lambda and, for a P-spline, it is lambda.
For a P-spline, npspline.segments also influences the smoothness of the fit.
The smoothing.method provides for direct and logarithmic
smoothing. The method of Huang (2001) for correcting the fitted spline for
estimation bias at the end-points will be applied when fitting using a
natural cubic smoothing spline if correctBoundaries is TRUE.
The derivatives of the fitted spline can also be obtained, and the
Absolute and Relative Growth Rates ( AGR and RGR) computed using them, provided
correctBoundaries is FALSE. Otherwise, growth rates can be
obtained by difference using byIndv4Times_GRsDiff.
The handling of missing values in the observations is controlled via
na.x.action and na.y.action. If there are not
at least four distinct, nonmissing x-values, a warning is issued and
all smoothed values and derivatives are set to NA.
The function probeSmoothing can be used to investgate the effect
the smoothing parameters (smoothing.method and df or
lambda) on the smooth that results.
fitSpline(data, response, response.smoothed, x,
smoothing.method = "direct",
spline.type = "NCSS", df = NULL, lambda = NULL,
npspline.segments = NULL, correctBoundaries = FALSE,
deriv = NULL, suffices.deriv = NULL, extra.rate = NULL,
na.x.action = "exclude", na.y.action = "trimx", ...)A list with two components named predictions and
fit.spline.
The predictions component is a data.frame containing x
and the fitted smooth. The names of the columns will be the value of
x and the value of response.smoothed. The number of rows in
the data.frame will be equal to the number of pairs that have neither
a missing x or response and the order of x will be the
same as the order in data. If deriv is not NULL,
columns containing the values of the derivative(s) will be added to the
data.frame; the name each of these columns will be the value of
response.smoothed with .dvf appended, where f is the
order of the derivative, or the value of response.smoothed and the
corresponding element of suffices.deriv appended. If RGR is
not NULL, the RGR is calculated as the ratio of value of the first
derivative of the fitted spline and the fitted value for the spline.
The fit.spline component is a list with components
x:the distinct x values in increasing order;
y:the fitted values, with boundary values possibly corrected, and corresponding to x;
lev:leverages, the diagonal values of the smoother matrix (NCSS only);
lambda:the value of lambda (corresponding to spar for NCSS - see smooth.spline);
df:the efective degrees of freedom;
npspline.segments:the number of equally spaced segments used for smoothing method set to PS;
uncorrected.fit:the object returned by smooth.spline for smoothing method set to NCSS or by JOPS::psNormal for PS.
A data.frame containing the column to be smoothed.
A character giving the name of the column in
data that is to be smoothed.
A character specifying the name of the column
containing the values of the smoothed response variable, corresponding
to response.
A character giving the name of the column in
data that contains the values of the predictor variable.
A character giving the smoothing method
to use. The two possibilites are (i) "direct", for directly
smoothing the observed response, and (ii) "logarithmic", for
smoothing the log-transformed response and then
back-transforming by taking the exponentional of the fitted values.
A character giving the type of spline
to use. Currently, the possibilites are (i) "NCSS", for natural
cubic smoothing splines, and (ii) "PS", for P-splines.
A numeric specifying, for natural cubic smoothing splines
(NCSS), the desired equivalent number of degrees of freedom of the
smooth (trace of the smoother matrix). Lower values result in more smoothing.
If df = NULL, the amount of smoothing can be controlled by setting
lambda. If both df and lambda are NULL, smoothing
is controlled by the default arguments for smooth.spline, and any
that you supply via the ellipsis (...) argument.
A numeric specifying the positive penalty to apply.
The amount of smoothing decreases as lamda decreases.
A numeric specifying, for P-splines (PS),
the number of equally spaced segments between min(x) and max(x),
excluding missing values, to use in constructing the B-spline basis for the
spline fitting. If npspline.segments is NULL, npspline.segments
is set to the maximum of 10 and ceiling((nrow(data)-1)/2) i.e. there will
be at least 10 segments and, for more than 22 x values, there will be
half as many segments as there are x values. The amount of smoothing
decreases as npspline.segments increases.
A logical indicating whether the fitted spline
values are to have the method of Huang (2001) applied
to them to correct for estimation bias at the end-points. Note that
spline.type must be NCSS and lambda and deriv
must be NULL for correctBoundaries to be set to TRUE.
A numeric specifying one or more orders of derivatives
that are required.
A character giving the characters to be
appended to response.method to construct the names of the derivatives.
If NULL and the derivatives are to be retained, then .dv
followed by the order of the derivative is appended to
response.method
.
A named character nominating a single growth
rate (AGR or RGR) to be computed using the first
derivative, which one being dependent on the smoothing.method.
The name of this element will used as a suffix to be appended to
the response when naming the resulting growth rate (see Examples).
If unamed, AGR or RGR will be used, as appropriate.
Note that, for the smoothing.method set to direct,
the first derivative is the AGR and so extra.rate must be set
to RGR, which is computed as the AGR / smoothed response.
For the smoothing.method set to logarithmic,
the first derivative is the RGR and so extra.rate must be set
to AGR, which is computed as the RGR * smoothed response.
Make sure that deriv includes one so that the first derivative
is available for calculating the extra.rate.
A character string that specifies the action to
be taken when values of x are NA. The possible
values are fail, exclude or omit.
For exclude and omit, predictions and derivatives
will only be obtained for nonmissing values of x.
The difference between these two codes is that for exclude
the returned data.frame will have as many rows as
data, the missing values have been incorporated.
A character string that specifies the action to
be taken when values of y, or the response, are
NA. The possible values are fail, exclude,
omit, allx, trimx, ltrimx or
rtrimx. For all options, except fail, missing
values in y will be removed before smoothing.
For exclude and omit, predictions
and derivatives will be obtained only for nonmissing values of
x that do not have missing y values. Again, the
difference between these two is that, only for exclude
will the missing values be incorporated into the
returned data.frame. For allx, predictions and
derivatives will be obtained for all nonmissing x.
For trimx, they will be obtained for all nonmissing
x between the first and last nonmissing y values
that have been ordered for x; for ltrimx and
utrimx either the lower or upper missing y
values, respectively, are trimmed.
allows for arguments to be passed to smooth.spline.
Chris Brien
Eilers, P.H.C and Marx, B.D. (2021) Practical smoothing: the joys of P-splines. Cambridge University Press, Cambridge.
Huang, C. (2001) Boundary corrected cubic smoothing splines. Journal of Statistical Computation and Simulation, 70, 107-121.
splitSplines, probeSmoothing,
byIndv4Times_GRsDiff, smooth.spline,
predict.smooth.spline, JOPS.
data(exampleData)
fit <- fitSpline(longi.dat, response="PSA", response.smoothed = "sPSA",
x="xDAP", df = 4,
deriv=c(1,2), suffices.deriv=c("AGRdv","Acc"))
fit <- fitSpline(longi.dat, response="PSA", response.smoothed = "sPSA",
x="xDAP",
spline.type = "PS", lambda = 0.1, npspline.segments = 10,
deriv=c(1,2), suffices.deriv=c("AGRdv","Acc"))
fit <- fitSpline(longi.dat, response="PSA", response.smoothed = "sPSA",
x="xDAP", df = 4,
deriv=c(1), suffices.deriv=c("AGRdv"),
extra.rate = c(RGR.dv = "RGR"))
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