

   FFoorrmmuullaa iinntteerrpprreetteerr

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

   AArrgguummeennttss::

          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 parame-
             ters, 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.

   DDeessccrriippttiioonn::

        `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) param-
        eters. In the latter, factor variables cannot be used
        and parameters must be scalars.

        The covariates in the formula are sought in the envi-
        ronment 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 opera-
        tors (*, /, :, etc.) is different in the two cases.

   VVaalluuee::

        A function, of class formulafn, of the unknown parame-
        ters 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.

   AAuutthhoorr((ss))::

        J.K. Lindsey

   SSeeee AAllssoo::

        `fnenvir'

   EExxaammpplleess::

        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)

