R: Formula Interpreter

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

### 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.

### 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

`FormulaMethods`, `covariates`, `fnenvir`, `formula`, `model`, `parameters`

### 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))
    # 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)

[Package rmutil version 1.1.3 Index]