The formula interface as used in lm and nls searches for separate
coefficients for each variable.. it will take someone more clever than I
to figure out how to get the formula interface to think of two variables
as instances of one factor.
However, R can do nonlinear optimization just fine:
##------------
# as if read in using read.csv( fname, as.is=TRUE )
dta <- data.frame( y = observed_data$y
, p1 = as.character( observed_data$p1 )
, p2 = as.character( observed_data$p2 )
, stringsAsFactors = FALSE
)
lvls <- with( dta, unique( c( p1, p2 ) ) )
dta$p1f <- factor( dta$p1, levels = lvls )
dta$p2f <- factor( dta$p2, levels = lvls )
idxvmult <- length( lvls ) + 1L
idxvoffs <- length( lvls ) + 2L
# all values in a numeric vector
# x = c( valice, vbob, ..., vmult, voffs )
calcY <- function( x ) {
vmult <- x[ idxvmult ]
voffs <- x[ idxvoffs ]
vp1 <- x[ dta$p1f ]
vp2 <- x[ dta$p2f ]
vmult * ( voffs - ( vp1 - vp2 )^2 )
}
optfcn <- function( x ) {
sum( ( dta$y - calcY( x ) ) ^ 2 )
}
oresult <- optim( par = rep( 1, idxvoffs ), optfcn)
result <- list( multiplier = oresult$par[ idxvmult ]
, offset = oresult$par[ idxvoffs ]
, values = data.frame( lvls = lvls
, values = oresult$par[ seq.int(
length( lvls ) ) ] )
)
result
#---------
I highly recommend reading the help page for optim and the CRAN Task View
on optimization [1]
[1] https://cran.r-project.org/web/views/Optimization.html
On Wed, 13 Jul 2016, stn021 wrote:
Is this what is intended?
observed_data$p1ab <- persons$ability[ match(observed_data$p1, persons$name) ]
observed_data$p2ab <- persons$ability[ match(observed_data$p2, persons$name) ]
Hello David,
thank you for your answer.
The code in my previous post was intended as an answer to the question
in an earlier post about example-data, quote:
Would you like me to make a complete example dataset with more records and
noise ?
Yes. And preferably do it with R code.
I should have re-stated this connection in the post.
The code generates a matrix 'observed_data' which is the data the
experimenter would get during the experiment.
This matrix is output in the last line. All other output is only meant
to document the generation-process.
So the only thing visible to the experimenter before analysis is
exactly that matrix 'observed_data' (usually in the form of some
written documentation which is later entered into statistical
software). Everything before that last line simulates those unknown
parameters that the experiment is supposed to reveal.
The unknown parameters are specifically
- the matrix 'persons'
- and the variable 'multiplyer'
Both are supposed to be revealed by the analyis. p1ab and p2ab would
therefore depend on the unknown parameters and could not be added to
'observed_data' before the analysis.
Sorry again for omitting the back-reference.
I would like to know:
- how to get R to use p1 and p2 as levels of the same factor
(=persons) instead of levels of two different factors.
- how to get R to multiply the numerical levels of factors during the
search for the solution. Factors cannot be multiplied before running
lm() or some other package because before the analysis their numerical
values are not known.
THX, Stefan
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