Creating a function with a variable number of variables in the body - r

Question

I'm trying to create a function that has set arguments, and in the body of the function it has a set formula but a random number of variables in the formula, determined only when the data is received. How do I write the function body so that it can adjust itself for an unknown number of variables?
Here's the backstory: I'm using the nls.lm package to optimize a function for a set of parameters in the function. nls.lm requires a function that returns a vector of residuals. This function is pretty simple: observed-predicted values. However, I also need to create a function to actually get the predicted values. This is where it gets tricky, since the predicted value formula contains the parameters that need to be regressed and optimized.
This is my general formula I am trying to perform non-linear regression on:
Y=A+(B-A)/(1+(10^(X-C-N))
Where A and B are global parameters shared across the entire data set and N is some constant. C can be anywhere from 1 to 8 parameters that need to be determined individually depending on the data set associated with each parameter.
Right now my working function contains the formula and 8 parameters to be estimated.
getPredictors<- function(params, xvalues) {
(params$B) + ((params$A-params$B)/(1+(10^(xvalues-
params$1*Indicator[1,]-params$2*Indicator[2,]-
params$3*Indicator[3,]-params$4*Indicator[4,]-
params$5*Indicator[5,]-params$6*Indicator[6,]-
params$7*Indicator[7,]-params$8*Indicator[8,]-
constant))))
}
params is a list of parameters with an initial value. Indicator is a table where each row consists 1's and 0's that act as an indicator variable to correctly pair each individual parameter with its associated data points. In its simplest form, if it had only one data point per parameter, it would look like a square identity matrix.
When I pair this function with nls.lm() I am successful in my regression:
residFun<- function(p, observed, xx) {
observed - getPredictors(p,xx)
}
nls.out<- nls.lm(parameterslist, fn = residFun, observed = Yavg, xx = Xavg)
> summary(nls.out)
Parameters:
Estimate Std. Error t value Pr(>|t|)
1 -6.1279 0.1857 -32.997 <2e-16 ***
2 -6.5514 0.1863 -35.174 <2e-16 ***
3 -6.2077 0.1860 -33.380 <2e-16 ***
4 -6.4275 0.1863 -34.495 <2e-16 ***
5 -6.4805 0.1863 -34.783 <2e-16 ***
6 -6.1777 0.1859 -33.235 <2e-16 ***
7 -6.3098 0.1862 -33.882 <2e-16 ***
8 -7.7044 0.1865 -41.303 <2e-16 ***
A 549.7203 11.5413 47.631 <2e-16 ***
B 5.9515 25.4343 0.234 0.816
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 82.5 on 86 degrees of freedom
Number of iterations to termination: 7
Reason for termination: Relative error in the sum of squares is at most `ftol'.
Now, the problem comes in when the data I receive does not contain 8 parameters. I can't just substitute 0 for these values since I am certain the degrees of freedom change with less parameters. Therefore I will need some way to create a getPredictors function on the fly, depending on the data I receive.
I've tried a couple things. I've tried combining all the parameters into a list of strings like so: (It's still 8 parameters, for comparison reasons, but it can be anywhere from 1-7 parameters.)
for (i in 1:length(data$subjects)){
paramsandindics[i]<-c(paste0("params$",i,"*","Indicator[",i,",]"))
}
combined<-paste0(paramsandindics, collapse="-")
> combined
[1] "params$1*Indicator[1,]-params$2*Indicator[2,]-
params$3*Indicator[3,]-params$4*Indicator[4,]-
params$5*Indicator[5,]-params$6*Indicator[6,]-
params$7*Indicator[7,]-params$8*Indicator[8,]"
Which appears to get me what I need. So I try dropping it into a new equation
getPredictors2<- function(params, xvalues) {
(params$B) + ((params$A-params$B)/
(1+(10^(xvalues-parse(text=combined)-constant))))
}
But I get an error "non-numeric argument to binary operator". Makes sense, it's probably trying to subtract a character string which won't work. So I switch to:
getPredictors2<- function(params, xvalues) {
(params$B) + ((params$A-params$B)/
(1+(10^(xvalues-eval(parse(text=combined))-constant))))
}
Which immediately evaluates the whole thing, producing only 1 parameter, which breaks my regression.
Ultimately I'd like a function that is written to accept a variable or dynamic number of variables to be filled in in the body of the function. These variables need to be written as-is and not evaluated immediately because the Levenberg-Marquardt algorithm, which is employed in the nls.lm (part of the minpack.lm package) requires an equation in addition to initial parameter guesses and residuals to minimize.
A simple example should suffice. I'm sorry if none of my stuff is reproducible- the data set is quite specific and too large to properly upload.
Sorry if this is long winded. This is my first time trying any of this (coding, nonlinear regression, stackoverflow) so I am a little lost. I'm not sure I am even asking the right question. Thank you for your time and consideration.
EDIT
I've included a smaller sample involving 2 parameters as an example. I hope it can help.
Subjects<-c("K1","K2")
#Xvalues
Xvals<-c(-11, -10, -9, -11, -10, -9)
#YValues, Observed
Yobs<-c(467,330,220,567,345,210)
#Indicator matrix for individual parameters
Indicators<-matrix(nrow = 2, ncol = 6)
Indicators[1,]<-c(1,1,1,0,0,0)
Indicators[2,]<-c(0,0,0,1,1,1)
#Setting up the parameters and functions needed for nls.lm
parameternames<-c("K1","K2","A","B")
#Starting values that nls.lm will iterate on
startingestimates<-c(-7,-7,0,500)
C<-.45
parameterlist<-as.list(setNames(startingestimates, parameternames))
getPredictors<- function(params, xx){
(params$A) + ((params$B-params$A)/
(1+(10^(xx-params$K1*Indicators[1,]-params$K2*Indicators[2,]-C))))}
residFunc<- function(p, observed, xx) {
observed - getPredictors(p,xx)
}
nls.output<- nls.lm(parameterlist, fn = residFunc, observed = Yobs, xx = Xvals)
#Latest attempt at creating a dynamic getPredictor function
combinationtext<-c()
combination<-c()
for (i in 1:length(Subjects)){
combinationtext[i]<-c(paste0("params$K",i,"*","Indicators[",i,",]"))
}
combination<-paste0(combinationtext, collapse="-")
getPredictorsDynamic<-function(params, xx){
(params$A) + ((params$B-params$A)/
(1+(10^(xx-(parse(text=combination))-C))))}
residFunc2<- function(p, observed, xx) {
observed - getPredictorsDynamic(p,xx)
}
nls.output2<-nls.lm(parameterlist, fn = residFunc2, observed = Yobs, xx = Xvals)
#Does not work