How to pass loop results as initial parameters for nlslm model?

I am running a nonlinear regression model that needs initial values to start, but the number of variables I want to include may be too large to manually type all the values - therefore I was wondering if there's an alternative to that.

set.seed(12345)
y = rnorm(100, 1000,150)
x1 = rnorm(100,10000,251)
x2 = rnorm(100, 3000,654)
x3 = rnorm(100, 25000,100)
x4 = rnorm(100, 200000,589)
x5 = rnorm(100, 31657,296)

adstock <- function(x,rate=0){
  return(as.numeric(stats::filter(x=log(x+1),filter=rate,method="recursive")))
}

library(minpack.lm)

nlsLM(y~b0  
      + b1 * adstock(x1, r1)
      + b2 * adstock(x2, r2)
      + b3 * adstock(x3, r3)
      + b4 * adstock(x4, r4)
      + b5 * adstock(x5, r5)
      
      , algorithm = "LM"

# this is where I need to paste the results from the loop 
      , start = c(b0=1,b1=1,b2=1,b3=1,b4=1,b5=1
                  ,r1=0.1,r2=0.1,r3=0.1,r4=0.1,r5=0.1
                  )
# end
      
      , control = list(maxiter = 200)
)

My idea was to use a loop to pass the values to the model, but I can't make it work (the following code should be for b_i coefficients)

test_start <- NULL

for(i in 1:(5+1)) {
  test_start[i] = paste0("b",i-1,"=",1)
}

cat(test_start)

This is the result, which is not exactly what the model expects:

b0=1 b1=1 b2=1 b3=1 b4=1 b5=1

How can I pass the results of the loop to the model? Also, how can I add r_i start coefficients to b_i start coefficients in the loop? Any help would be very appreciated.

PS: at the moment I am interested to assign to each b0,b1,...,b5 the same value (in this case, 1) and to each r1,r2,...,r5 the same value (in this case, 0.1)

Solution

Define the data as DF and the formula as fo and then grep out the b and r variables. The line defining v creates a vector with their names and the line defining st a named vector with value 1 for the b's and 0.1 for the r's.

DF <- data.frame(y, x1, x2, x3, x4, x5)

n <- ncol(DF) - 1
rhs <- c("b0", sprintf("b%d * adstock(x%d, r%d)", 1:n, 1:n, 1:n))
fo <- reformulate(rhs, "y")

v <- grep("[br]", all.vars(fo), value = TRUE)
st <- setNames(grepl("b", v) + 0.1 * grepl("r", v), v)
st

nlsLM(fo, DF, start = st, algorithm = "LM", control = list(maxiter = 200))

Regarding the comment try defining rhs like this. In the first line take whatever subset of labs you want, e.g. labs <- labels(...)[1:9] or change the formula in the first line, e.g. labs <- labels(terms(y ~ .*(1 + x1), data = DF))

labs <- labels(terms(y ~ .^2, data = DF))
labs <- sub(":", "*", labs)
n <- length(labs)
rhs <- c("b0", sprintf("b%d * adstock(%s, r%d)", 1:n, labs, 1:n))