pulest {unknown} | R Documentation |

This function accomplishes the third step of the algorithm in Yang, Liu and Wang (2004). It estimates all parameters in the model.

pulest(x, y, data, baseline=list(nb=~x, rk=cubic(x)), puloc, start, type = c("dblexp", "user"), params=list(infrate="common", decrate="mixed", amplitude="mixed"), pulse.usr=list(shape, parlist, devlist), weights = NULL, correlation = NULL, control=pul.control(IDF=1))

`x` |
a vector of observation time points. |

`y` |
a vector of hormone concentrations. |

`data` |
a data frame containing the variables occurring in the x
and y arguments. If this option is not specified, the variables
should be on the search list. Missing values are not allowed. |

`baseline` |
a list specifies the model space for the baseline function.
nb is a one-sided formula specifying the basis of the null
space. rk is an expression specifying the reproducing kernel of the
orthogonal complementary space to the null space. The default options
of nb and rk correspond to the cubic spline.
If baseline=0, the baseline function is fixed at its
initial input. |

`start` |
a list of initial values. It includes two components:
fixed, a vector of starting values for the common
and fixed parameters specified in the argument params or
in the component parlist of the argument pulse.usr (note
that the order is very important: the initial values for common
parameters appear before those for fixed parameters); Inif,
initial baseline estimates evaluated at x. |

`type` |
a character string specifies a predefined type of the
pulse shape functions. If type="dblexp", a double exponential function
will be used as the pulse shape function. If type="user", the user can
input the shape function and parameters in the argument
pulse.usr. |

`params` |
when type="dblexp", params is a list of
three components, infrate, decrate and amplitude,
which correspondingly specifies models to be assumed for the pulse
infussion rate, pulse decay rate and pulse amplitude parameters. Current
possible options are “common” for infrate; “common”,
“fixed” and “mixed” for pulse decrate; “common”,
“fixed”, “mixed” and “random” for amplitude.
Here “common” means that a common parameter is assumed in all pulses;
“fixed” means that different deterministic parameters are assumed for
all pulses; “random” means that the parameters are assumed to be from a
normal distribution with mean 0; “mixed” means that the paramters
are assumed to be from a normal distribution with a unknown constant mean.
Current program assumes that all random parameters are independent. |

`pulse.usr` |
when type="user", pulse.usr is a
list of three components, shape, parlist,
and devlist, which correspondingly specify the pulse shape,
pulse parameters, and first derivatives of the pulse
shape function with respect to the parameters.
shape is a formula. parlist is a list of character
vectors with four components: common, random,
fixed, and p.
The component common specifies fixed parameters used
in the pulse formula which are common for all pulses; the
component random specifies random parameters in the
pulse formula; and the component fixed specifies
fixed parameters which are different for each pulse.
Current program assumes that all random parameters are independent.
The fourth component p is used to specify the
parameter name of the pulse locations.
devlist is a list of the derivatives in the order of
the common, random parameters and fixed parameters.
For each type of parameters, the order should be consistent
with the order of the parameters supplied in textt{palist}. |

`weights` |
an optional varFunc object or one-sided formula describing
the heteroscedasticity structure. See the documentation on
varClasses in the nlme package for a description of the available
varFunc classes. Defaults to NULL, corresponding to homoscesdatic errors. |

`correlation` |
an optional corStruct object describing the
correlation structure. See the documentation of corClasses
in the nlme package for a description of the available corStruct
classes. Defaults to NULL, corresponding to no correlations. |

`control` |
a list of control values for the estimation algorithm to
replace the default values returned by the function `pulest.control` . |

`pulest`

estimates all parameters using the
double-penalized log-likelihood and the approximate profile-likelihood
(Yang, Liu and Wang, 2004).

a list which contains

`tbl` |
a summary matrix of the fit with columns corresponding to the number of pulses (NP), BIC, RIC, AIC, GCV, total degrees of freedom (DF), degrees of freedom of the baseline function (df(base)), smoothing parameters in log10 scale (nlaht), and residual sum of squares (RSS). |

`coef` |
estimated parameters. |

`Var` |
Covariance matrix of the estimated parameters. |

`baseFitted` |
estimates of the baseline function. |

`nlmeFitted` |
estimates of the hormone secretion with baseline subtracted. |

`nlmeObj` |
nlme object of the `nlme` function if it is used. |

`gnlsObj` |
gnls object of the `gnls` function if it is used. |

`callxObj` |
object returned from the inside function NLMEcallx or GNLScallx. |

`nlme` |
whether nlme is used in the fitting. |

Yu-Chieh Yang, Anna Liu, Yuedong Wang

Pinheiro, J. and Bates, D. M. (2000), *Mixed-effects Models in
S and S-plus*, Springer, New York.

Yang, Y. (2002), *Detecting Change Points and Hormone Pulses
Using Partial Spline Models*, Ph.D. Thesis, University of
California-Santa Barbara, Dept. of Statistics and Applied Probability.

Yang, Y. and Liu, A. and Wang, Y., (2004), *Detecting
Pulsatile Hormone Secretions Using Nonlinear Mixed Effects
Partial Spline Models*.
Available at www.pstat.ucsb.edu/faculty/yuedong/research.

Wang, Y. and Ke, C. (2002), *ASSIST: A Suite of S-plus
functions Implementing Spline smoothing Techniques*. Available at
cran.us.r-project.org/src/contrib/PACKAGES.html.
Manual for the ASSIST package is available at
www.pstat.ucsb.edu/faculty/yuedong/software.

`baseini`

,
`nlme`

, `pul.control`

,
`puldec`

,
`ssr`

,
`summary.pulest`

fit.cmm <- pulest(time, conc, data=acth, type=c("dblexp"), puloc=pl5, start=list(fixed=fix.ini, Inif=bl1), params=list(infrate="common", decrate="mixed", amplitude="mixed"), control =list(pul=list(IDF=1)))