finterp {rmutil}R Documentation

Formula interpreter

Description

finterp translates a model formula into a function of the unknown parameters or of a vector of them. Such language formulae can either be in Wilkinson and Rogers notation or be expressions containing both known (existing) covariates and unknown (not existing) parameters. In the latter, factor variables cannot be used and parameters must be scalars.

The covariates in the formula are sought in the environment or in the data object provided. If the data object has class, repeated, times will use the response times as a covariate, individuals will use the index for individuals as a factor covariate, and nesting the index for nesting as a factor covariate.

Note that, in parameter displays, formulae in Wilkinson and Rogers notation use variable names whereas those with unknowns use the names of these parameters, as given in the formulae, and that the meaning of operators (*, /, :, etc.) is different in the two cases.

Usage

finterp(z, envir=sys.frame(sys.parent()), formula=FALSE,
        vector=TRUE, start=1, name=NULL, expand=TRUE)

Arguments

z A model formula beginning with ~, either in Wilkinson and Rogers notation or containing unknown parameters.
envir The environment in which the formula is to be interpreted or a data object of class, repeated, tccov, or tvcov.
formula If TRUE and the formula is in Wilkinson and Rogers notation, just returns the formula.
vector If FALSE and the formula contains unknown parameters, the function returned has them as separate arguments, if TRUE, it has one argument, the unknowns as a vector. Always true if envir is a data object.
start The starting index value of the parameter vector in the function returned.
name Character string giving the name of the data object specified by envir. Ignored unless the latter is such an object and only necessary when finterp is called within other functions.
expand If TRUE, expand functions with only time-constant covariates to return one value per observation instead of one value per individual. Ignored unless envir is an object of class, repeated.

Value

A function, of class formulafn, of the unknown parameters or of a vector of them is returned. Its attributes give the formula supplied, the model function produced, the covariate names, the parameter names, and the range of values of the index of the parameter vector. If formula is TRUE and a Wilkinson and Rogers formula was supplied, it is simply returned instead of creating a function.

Author(s)

J.K. Lindsey

See Also

fnenvir

Examples

x1 <- rpois(20,2)
x2 <- rnorm(20)
#
# Wilkinson and Rogers formula with three parameters
fn1 <- finterp(~x1+x2)
fn1
fn1(rep(2,3))
# the same formula with unknowns
fn2 <- finterp(~b0+b1*x1+b2*x2)
fn2
fn2(rep(2,3))
#
# nonlinear formulae with unknowns
# log link
fn2a <- finterp(~exp(b0+b1*x1+b2*x2))
fn2a
fn2a(rep(0.2,3))
# compartment model
times <- 1:20
# exp() parameters to ensure that they are positive
fn3 <- finterp(~exp(volume)*exp(absorption)/(exp(absorption)-
        exp(elimination))*(exp(-exp(elimination)*times)-
        exp(-exp(absorption)*times)))
fn3
fn3(log(c(3,0.3,0.2)))
#
# Poisson density
y <- rpois(20,5)
fn4 <- finterp(~mu^y*exp(-mu)/gamma(y+1))
fn4
fn4(5)
dpois(y,5)
#
# Poisson likelihood
# mean parameter
fn5 <- finterp(~-y*log(mu)+mu+lgamma(y+1),vector=F)
fn5
likefn1 <- function(p) sum(fn5(mu=p))
nlm(likefn1,p=1)
mean(y)
# canonical parameter
fn5a <- finterp(~-y*theta+exp(theta)+lgamma(y+1),vector=F)
fn5a
likefn1a <- function(p) sum(fn5a(theta=p))
nlm(likefn1a,p=1)
#
# likelihood for Poisson log linear regression
y <- rpois(20,fn2a(c(0.2,1,0.4)))
nlm(likefn1,p=1)
mean(y)
likefn2 <- function(p) sum(fn5(mu=fn2a(p)))
nlm(likefn2,p=c(1,0,0))
# or
likefn2a <- function(p) sum(fn5a(theta=fn2(p)))
nlm(likefn2a,p=c(1,0,0))
#
# likelihood for Poisson nonlinear regression
y <- rpois(20,fn3(log(c(3,0.3,0.2))))
nlm(likefn1,p=1)
mean(y)
likefn3 <- function(p) sum(fn5(mu=fn3(p)))
nlm(likefn3,p=log(c(1,0.4,0.1)))
#
# envir as data objects
y <- matrix(rnorm(20),ncol=5)
y[3,3] <- y[2,2] <- NA
x1 <- 1:4
x2 <- c("a","b","c","d")
resp <- restovec(y)
xx <- tcctomat(x1)
xx2 <- tcctomat(data.frame(x1,x2))
z1 <- matrix(rnorm(20),ncol=5)
z2 <- matrix(rnorm(20),ncol=5)
z3 <- matrix(rnorm(20),ncol=5)
zz <- tvctomat(z1)
zz <- tvctomat(z2,old=zz)
reps <- rmna(resp, ccov=xx, tvcov=zz)
reps2 <- rmna(resp, ccov=xx2, tvcov=zz)
rm(y, x1, x2 , z1, z2)
#
# repeated objects
#
# time-constant covariates
# Wilkinson and Rogers notation
form1 <- ~x1
print(fn1 <- finterp(form1, envir=reps))
fn1(2:3)
print(fn1a <- finterp(form1, envir=xx))
fn1a(2:3)
form1b <- ~x1+x2
print(fn1b <- finterp(form1b, envir=reps2))
fn1b(2:6)
print(fn1c <- finterp(form1b, envir=xx2))
fn1c(2:6)
# with unknown parameters
form2 <- ~a+b*x1
print(fn2 <- finterp(form2, envir=reps))
fn2(2:3)
print(fn2a <- finterp(form2, envir=xx))
fn2a(2:3)
#
# time-varying covariates
# Wilkinson and Rogers notation
form3 <- ~z1+z2
print(fn3 <- finterp(form3, envir=reps))
fn3(2:4)
print(fn3a <- finterp(form3, envir=zz))
fn3a(2:4)
# with unknown parameters
form4 <- ~a+b*z1+d*z2
print(fn4 <- finterp(form4, envir=reps))
fn4(2:4)
print(fn4a <- finterp(form4, envir=zz))
fn4a(2:4)
#
# note: lengths of x1 and z2 differ
# Wilkinson and Rogers notation
form5 <- ~x1+z2
print(fn5 <- finterp(form5, envir=reps))
fn5(2:4)
# with unknown parameters
form6 <- ~a+b*x1+d*z2
print(fn6 <- finterp(form6, envir=reps))
fn6(2:4)
#
# with times
# Wilkinson and Rogers notation
form7 <- ~x1+z2+times
print(fn7 <- finterp(form7, envir=reps))
fn7(2:5)
form7a <- ~x1+x2+z2+times
print(fn7a <- finterp(form7a, envir=reps2))
fn7a(2:8)
# with unknown parameters
form8 <- ~a+b*x1+d*z2+e*times
print(fn8 <- finterp(form8, envir=reps))
fn8(2:5)
#
# with a variable not in the data object
form9 <- ~a+b*z1+d*z2+e*z3
print(fn9 <- finterp(form9, envir=reps))
fn9(2:5)
# z3 assumed to be an unknown parameter:
fn9(2:6)

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