fit.SATcurve: fit SAT curves
In matsukik/mrsat: Multiple Response Speed Accuracy Tradeoff

Description Usage Arguments Details Value See Also Examples

A function to fit curve to d primes obtained from MR-SAT experiment.

fit.SATcurve(data, par.cond, 
             fix.asym = FALSE,
             params = get.param(par.cond, auto.asym=fix.asym, data=data),
             opt = c("acp" ,"nlminb", "nlm", "optim"), 
             multi.opt = FALSE,
             rep=1, quiet=TRUE, maxit=500, strict=TRUE, trace=FALSE)

`data`	data frame contining columns named `dprime`, `lags`, and `condition` (as in the output of `get.dprime`), or character specifying the location of dat file (see `read.dat` for detail of the file format)
`par.cond`	a list specifying the configuraiton of parameters per condition. Should contain three named elements: `asym`, `rate`, and `incp`. See 'Details'.
`fix.asym`	a logical specifying whether asymptote parameters of the model should be fixed to the starting values supplied in the `params` argument.
`params`	a data frame specifying parameters, containing columns named `start`, `lower`, and `upper`. Defalt to `get.param(par.cond)`, see `get.param`. It can also be a character vector specifying the location of 'par' file (see `read.param` for detail of the file format).
`opt`	charaster or a character vector indication the optimizer to be used. If `length(opt) > 1` and `multi.opt=TRUE`, all of the specified methods will be used in the specified order. If `length(opt) > 1` and `multi.opt=FALSE`, the first element of `opt` will be used.
`multi.opt`	logical, specifying wheather to fit the data using multiple optimizer.
`rep`	numeric, representing number of times the optimazation process is repeated. If `multi.opt = TRUE`, each optimizer specified in `opt` is run as many times as `rep`.
`quiet`	logical. Default to `TRUE`. If `FALSE`, a progress bar is printed.
`maxit`	The maximun number of iteration. Defaults to `500`.
`strict`	logical. Only relevant if `method="acp"`. See 'Details' of `acp`
`trace`	logical. Only relevant if `method="acp"`. See 'Details' of `acp`

The argument par.cond specifies whether or not and how certain parameter(s) are shared across conditions (which are specified in condition column of data). The argument par.cond can take either list or matrix, as long as it meets following specification. If it is a list, then it should be a named list containing following elements: asym, rate, and incp. Each element of the list must be of same length, being equal either to length(condition) or to length(levels(condition)) (or length(unique(condition)) if condition is not a factor). If it is a matrix, then it should have asym, rate, and incp as its columns, and rows should represent different condiitons.

As an example, there are three elements in par (i.e., length(par) = 3), and there are three conditions so that the three conditions share all of λ (asymptote), β (rate) and δ (intercept). In this case, par.cond should be specified as list(asym=c(1,1,1), rate=c(1,1,1), incp=c(1,1,1)).

As another example, there are six elements in par, consisting of three λ (asymptote; one for each condition) , two β (rate; one for condition 1 and anothor for condition 2 and 3), and one δ (intercept; for all the conditions). Here, par.cond = list(asym=c(1,2,3), rate=c(1,2,2), incp=c(1,1,1))

`fit`	a list of object returned from the optimizer (if multiple optimizers were used, the one that returned the smallest RMSE), with a few additinal information
`SSE`	Sum of Squared Error of the model.
`MSE`	Mean Squared Error of the model. A object of class `logLik`.
`RMSE`	Root Mean Squared Error of the model.
`logLik`	Log likelihood of the model. A object of class `logLik`.
`R2`	R squared of the model
`adjR2`	adjusted R squared of the model
`data`	same as the argument `data`
`par.cond`	same as the argument `par.cond`
`rep.out`	If `rep>1`, the data.frame containing the parameters and fit statistics obtained from each repeated fitting of the data. If `rep=1`, `NULL`

acp, optim, nlminb, nlm

#load data
data(Auditory_demo)

#need to define the scale.list
exp1.signal <- list(noint = c(1,3), 
                obrel = c(5,8), 
                obrelsub = c(11, 14))

exp1.noise <- list(noint = c(2,4), 
               obrel = c(6, 7, 9, 10), 
               obrelsub = c(12, 13, 15, 16))


# tag bins
s01.bins <- get.bins(Auditory_demo, auditory=TRUE, window = "fixed")

#calculate dprimes
s01.dp<- get.dprime(s01.bins$bins, 
  signal.list = exp1.signal, noise.list = exp1.noise, is.index = TRUE,
  binmax=14)

# specify par.cond
my.pc <- list(asym=c(1,2,3), rate=c(1,2,2), incp=c(1,1,1))

# fit the data
s01.fit <- fit.SATcurve(s01.dp, par.cond = my.pc)

#plot the data and fitter curves
plot(s01.fit)

#to calculate AIC and BIC, do
AIC(s01.fit)
BIC(s01.fit)

#you may also calculate AIC analogue using MSE
# as suggested by Burnham and Anderson (1998)
AIC(s01.fit$MSE)