gamlss (version 4.3-4)

lms: A function to fit LMS curves for centile estimation

Description

This function is design to help the user to easily construct growth curve centile estimation. It is applicable when only "one" explanatory variable is available (usually age).

Usage

lms(y, x, families = LMS, data = NULL, k = 2, 
        cent = 100 * pnorm((-4:4) * 2/3), 
        calibration = TRUE, trans.x = FALSE, 
        fix.power = NULL, lim.trans = c(0, 1.5), 
        prof = FALSE, step = 0.1, legend = FALSE, 
        mu.df = NULL, sigma.df = NULL, nu.df = NULL, 
        tau.df = NULL, c.crit = 0.01, 
        method.pb = c("ML", "GAIC"), ...)

Arguments

y

The response variable

x

The unique explanatory variable

families

a list of gamlss.families with default LMS=c("BCCGo", "BCPEo", "BCTo")

data

the data frame

k

the penalty to be used in the GAIC

cent

a vector with elements the % centile values for which the centile curves have to be evaluated

calibration

whether calibration is required with default TRUE

trans.x

whether to check for transformation in x with default FALSE

fix.power

if set it fix the power of the transformation for x

lim.trans

the limits for the search of the power parameter for x

prof

whether to use the profile GAIC of the power tranformation

step

if code{prof=TRUE} is used this determine the step for the profile GAIC

legend

whether a legend is required in the plot with default FALSE

mu.df

mu effective degrees of freedom if required otherwise are estimated

sigma.df

sigma effective degrees of freedom if required otherwise are estimated

nu.df

nu effective degrees of freedom if required otherwise are estimated

tau.df

tau effective degrees of freedom if required otherwise are estimated

c.crit

the convergence critetion to be pass to gamlss()

method.pb

the method used in the pb() for estimating the smoothing parameters. The default is local maximum likelihood "ML". "GAIC" is also permitted where k is taken from the k argument of the fun

...

extra argument which can be passed to gamlss()

Value

• It returns a gamlss fitted object

Details

This function should be used if the construction of the centile curves involves only one explanatory variable.

The model assumes that the response variable has a flexible distribution i.e. $y ~ D(\mu, \sigma, \nu, \tau)$ where the parameters of the distribution are smooth functions of the explanatory variable i.e. $g(\mu)= s(x)$, where $g()$ is a link function and $s()$ is a smooth function. Occasionally a power transformation in the x-axis helps the construction of the centile curves. That is, in this case the parameters are modelled by $x^p$ rather than just x, i.e.$g(\mu)= s(x^p)$. The function lms() uses P-splines (pb()) as a smoother.

If a transformation is needed for x the function lms() starts by finding an optimum value for p using the simple model $NO(\mu=s(x^p))$. (Note that this value of p is not the optimum for the final chosen model but it works well in practice.)

After fitting a Normal error model for staring values the function proceeds by fitting several "appropriate" distributions for the response variable. The set of gamlss.family distributions to fit is specified by the argument families. The default families arguments is LMS=c("BCCGo", "BCPEo", "BCTo") that is the LMS class of distributions, Cole and Green (1992). Note that this class is only appropriate when y is positive (with no zeros). If the response variable contains negative values and zeros then use the argument families=theSHASH where theSHASH <- c("NO", "SHASHo") or add any other list of distributions which you may think is appropriate. Justification of using the specific centile (0.38 2.27 9.1211220 25.25, 50, 74.75, 90.88, 97.72, 99.62) is given in Cole (1994).

References

Cole, T. J. (1994) Do growth chart centiles need a face lift? BMJ, 308--641.

Cole, T. J. and Green, P. J. (1992) Smoothing reference centile curves: the LMS method and penalized likelihood, Statist. Med. 11, 1305--1319

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion), Appl. Statist., 54, part 3, pp 507-554.

Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2006) Instructions on how to use the GAMLSS package in R. Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.org/).

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R. Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, http://www.jstatsoft.org/v23/i07.

See Also

gamlss, centiles, calibration

Examples

data(abdom)
m1 <- lms(y,x , data=abdom, n.cyc=30)
m2 <- lms(y,x ,data=abdom, method.pb="GAIC", k=log(610))
# this example takes time
data(db)
m1 <- lms(y=head, x=age, data=db, trans.x=TRUE)