"Error in ...% *% ...: inconsistent arguments" using native function in regression

Question

I have a function Q (x | delta): R ^ n → R, for which I would like to correspond to non-linear regression of quantiles. The Q (.) Function uses some matrix operations, and it would be very difficult not to use it. The problem is that nlrq (non-linear regression of quantiles) and nls (non-linear regression) do not work when there are matrix operations in the function used in the argument of the formula.

To illustrate, consider a simpler function F (x1, x2 | a, b, c) that I can use in the formula argument for the nlrq and nls functions when I do not use matrix operations, but which do not work in the formula argument when It was recorded using matrix operations.

    library('quantreg')

    ## Generating the data
    x1<- rnorm(200)
    x2<- rnorm(200)
    y<- 1+3*sin(x1)+2*cos(x2) +rnorm(200)
    Dat<- data.frame(y,x1,x2)

    ## The function F1 without matrix operation
    F1<- function(x_1, x_2, a, b,c){a+b*sin(x_1)+c*cos(x_2)}

    ## The function F2 with matrix operation
    F2<- function(x_1, x_2, a, b,c){t(c(1,sin(x_1),cos(x_2)))%*%c(a,b,c)}

    ## Both functions work perfectly
    F1(x_1=3, x_2=2, a=1, b=3,c=2)
    F2(x_1=3, x_2=2, a=1, b=3,c=2)

    ## But only F1 can be estimated by nls and nlrq
    nls_1<-nls(y ~ F1(x_1 = x1, x_2 = x2, a = 1, b, c),
               data = Dat, start = list(b = 3, c = 2))

    nlrq_1<-nlrq(y ~ F1(x_1 = x1, x_2 = x2, a = 1, b, c),
                 data = Dat, start = list(b = 3, c = 2), tau = 0.9)

    ## When F2 is used in the formula argument an error happens
    nls_2<-nls(y ~ F2(x_1 = x1, x_2 = x2, a = 1, b, c),
               data = Dat, start = list(b = 3, c = 2))

    nlrq_2<-nlrq(y ~ F2(x_1 = x1, x_2 = x2, a = 1, b, c),
                 data = Dat, start = list(b = 3, c = 2), tau = 0.9)

Error in t(c(1, sin(x_1), cos(x_2))) %*% c(a, b, c) : non-conformable arguments. , - F2 nls nlrq, .

Dat 200x3.

.

Answer 1

F2() x_1, x_2,... c(...) ( ).
:

F1(x_1=c(3,5), x_2=c(2,4), a=1, b=3,c=2)
F2(x_1=c(3,5), x_2=c(2,4), a=1, b=3,c=2)

:

#> F1(x_1=c(3,5), x_2=c(2,4), a=1, b=3,c=2)
#[1]  0.5910664 -3.1840601
#> F2(x_1=c(3,5), x_2=c(2,4), a=1, b=3,c=2)
#error in t(c(1, sin(x_1), cos(x_2))) %*% c(a, b, c) :  ...

nls() nlrq() F2() ( F1()) (.. Dat).

F2():

# other definitions for F2()
F2 <- function(x_1, x_2, a, b,c) cbind(1,sin(x_1),cos(x_2)) %*% c(a,b,c)
F2(x_1=c(3,5), x_2=c(2,4), a=1, b=3,c=2)

F2 <- function(x_1, x_2, a, b,c) t(rbind(1,sin(x_1),cos(x_2))) %*% c(a,b,c)
F2(x_1=c(3,5), x_2=c(2,4), a=1, b=3,c=2)

F2 <- function(x_1, x_2, a, b,c) colSums(rbind(1,sin(x_1),cos(x_2)) * c(a,b,c))
F2(x_1=c(3,5), x_2=c(2,4), a=1, b=3,c=2)

F2 <- function(x_1, x_2, a, b,c) crossprod(rbind(1,sin(x_1),cos(x_2)), c(a,b,c))
F2(x_1=c(3,5), x_2=c(2,4), a=1, b=3,c=2)

F2 <- function(x_1, x_2, a, b,c) tcrossprod(c(a,b,c), cbind(1,sin(x_1),cos(x_2)))
F2(x_1=c(3,5), x_2=c(2,4), a=1, b=3,c=2)

Answer 2

. R optim, .

. . F2 , .

sumsq <- function(beta)
{
    F2 <- function(x1, x2, a, b, c)
    {
        cbind(1, sin(x1), cos(x2)) %*% c(a, b, c)
    }
    yhat <- F2(Dat$x1, Dat$x2, beta[1], beta[2], beta[3])
    sum((Dat$y - yhat)^2)
}

beta0 <- c(mean(Dat$y), 1, 1)

optim(beta0, sumsq, method="BFGS")

#initial  value 731.387431 
#final  value 220.265745 
#converged
#$par
#[1] 0.8879371 3.0211286 2.1639280
# 
#$value
#[1] 220.2657
#
#$counts
#function gradient 
#      25        7 
#
#$convergence
#[1] 0
#
#$message
#NULL

optim . par - , , value.

nls, , .

nls(y ~ F1(x_1=x1, x_2=x2, a=1, b, c),
           data=Dat, start=list(b=3, c=2))

Nonlinear regression model
  model: y ~ F1(x_1 = x1, x_2 = x2, a = 1, b, c)
   data: Dat
    b     c 
3.026 2.041 
 residual sum-of-squares: 221

Number of iterations to convergence: 1 
Achieved convergence tolerance: 7.823e-10

- , .

Answer 3

, , F2 c(). rbind(), nls(), nlrq().

Next I will show the corrected version of F2.

    ## Changing c() for rbind()
    F2<- function(x_1, x_2, a, b,c){t(rbind(1,sin(x_1),cos(x_2)))%*%rbind(a,b,c)}

    ## Now nls() and nlrq() work properly
    nls_2<-nls(y ~ F2(x_1 = x1, x_2 = x2, a = 1, b, c),
       data = Dat, start = list(b = 3, c = 2))

    nlrq_2<-nlrq(y ~ F2(x_1 = x1, x_2 = x2, a = 1, b, c),
         data = Dat, start = list(b = 3, c = 2), tau = 0.9)

Note that the ratings in nls_2 and nlrq_2 are the same as the ratings in nls_1 and nlrq_1.

Many thanks for your help.