finterp: 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 or response, then the key words, times will use the response times from the data object as a covariate, individuals will use the index for individuals as a factor covariate, and nesting the index for nesting as a factor covariate. The latter two only work for W&R notation.

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, ...)
# S3 method for default
finterp(.z, .envir=parent.frame(), .formula=FALSE, .vector=TRUE,
	.args=NULL, .start=1, .name=NULL, .expand=TRUE, .intercept=TRUE,
	.old=NULL, .response=FALSE, ...)

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.

Arguments

.z: A model formula beginning with ~, either in Wilkinson and Rogers notation or containing unknown parameters. If it contains unknown parameters, it can have several lines so that, for example, local variables can be assigned temporary values. In this case, enclose the formula in curly brackets.
.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, unless certain parameter names are specified in .args. Always TRUE if .envir is a data object.
.args: If .vector is TRUE, names of parameters that are to be function arguments and not included in the vector.
.start: The starting index value of the parameter vector in the function returned when .vector is TRUE.
.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.
.intercept: If W&R notation is supplied and .intercept=F, a model function without intercept is returned.
.old: The name of an existing object of class formulafn which has common parameters with the one being created, or a list of such objects. Only used if .vector=TRUE. The value of .start should ensure that there is no conflict in indexing the vector.
.response: If TRUE, any response variable can be used in the function. If FALSE, checks are made that the response is not also used as a covariate.
...: Arguments passed to other functions.

Author

J.K. Lindsey

Examples

Run this code

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))
# parameters common to two functions
fn2b <- finterp(~c0+c1*exp(b0+b1*x1+b2*x2), .old=fn2a, .start=4)
fn2b
# function returned also depends on values of another function
fn2c <- finterp(~fn2+c1*exp(b0+b1*x1+b2*x2), .old=fn2a,
	.start=4, .args="fn2")
fn2c
args(fn2c)
fn2c(rep(0.2,4),fn2(rep(2,3)))
#
# compartment model
times <- 1:20
# exp() parameters to ensure that they are positive
fn3 <- finterp(~exp(absorption-volume)/(exp(absorption)-
	exp(elimination))*(exp(-exp(elimination)*times)-
	exp(-exp(absorption)*times)))
fn3
fn3(log(c(0.3,3,0.2)))
# a more efficient way
# (note that parameters do not appear in the same order)
form <- ~{
	ka <- exp(absorption)
	ke <- exp(elimination)
	ka*exp(-volume)/(ka-ke)*(exp(-ke*times)-exp(-ka*times))}
fn3a <- finterp(form)
fn3a(log(c(0.3,0.2,3)))
#
# 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=FALSE)
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=FALSE)
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+c*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+c*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+c*z2+e*times
print(fn8 <- finterp(form8, .envir=reps))
fn8(2:5)
#
# with a variable not in the data object
form9 <- ~a+b*z1+c*z2+e*z3
print(fn9 <- finterp(form9, .envir=reps))
fn9(2:5)
# z3 assumed to be an unknown parameter:
fn9(2:6)
#
# multiline formula
form10 <- ~{
	tmp <- exp(b)
	a+tmp*z1+c*z2+d*times}
print(fn10 <- finterp(form10, .envir=reps))
fn10(2:5)