glba (version 0.2.1)

lba: Specify and fit lba models.

Description

Specification of lba models with explanatory variables on the parameters. Models are fitted using full information maximum likelihood.

Usage

lba(rt, response, data, weights, 
sddr = ~1, 
sp = ~1, 
bound = ~1, 
nond = ~1, 
drift = ~1, 
scaling = "sum", 
loglink = c(FALSE, FALSE, FALSE, FALSE), 
sdstart=0.1,
startpars, 
fixed = NULL,
method = "L-BFGS-B",
hessian = FALSE,
lower = -Inf,
upper = Inf,
fit=TRUE,
debug=FALSE) 
# S3 method for lba
logLik(object, ...)
# S3 method for lba
print(x, ...)
# S3 method for lba
summary(object, ...)
tablba(object)

Arguments

rt

The name of the response time variable in data.frame 'data'.

response

The name of the response time variable in data.frame 'data'.

data

Data.frame containing the variables.

weights

Optional case weights.

sddr

The model for the standard deviation of the drift rate, see Details.

sp

The model for the start point parameter, see Details.

bound

The model for the boundary parameter, see Details.

nond

The model for the non-decision time, see Details.

drift

The model for the drift rate parameter, see Details.

scaling

Options for making the model identifiable; options are "sum" or "fixedSD".

loglink

Wheter parameters (sddr, sp, nond, and bound) should be fitted using a log link function (to avoid boundary estimation issues).

sdstart

Starting value of the standard deviation of the drift rates in case argument scaling uses option "fixedSD".

startpars

Vector of starting values for the parameters. This is currently a required argument as no automatic starting values are available.

fixed

Logical; when startpars is given 'fixed' can be used to specify whether parameters should remain fixed during estimation; sometimes required for more stable estimation.

method

Optimization method; passed to optim.

hessian

Logical; indicating whether the estimated hessian at the minimum; passed to optim.

lower, upper

lower and upper boundaries for the parameters; only applicable with optimization method 'L-BFGS-B' is used.

fit

Logical; indicating whehter the model should be fit, ie, its parameters optimized or not. Default is TRUE.

debug

Logical, default is FALSE; prints out detailed information on submodels, parameters et cetera during optimization.

object

a (fitted) lba model.

x

a (fitted) lba model.

...

not currently in use.

Value

The lba function returns a list with the following components:

pars

The values of fitted parameters.

logl

The optimized log likelihood

convergence

Convergence information from optim

hessian

Only included if hessian was set to TRUE

ses

Only included if hessian was set to TRUE and the hessian is non-singular

fixed

Vector of logical's indicating whether parameters were fixed

model

List of 5 sub-models of the LBA model, see Details above.

npar

The number of parameters of the model

freepars

The number of freely estimated parameters of the model

nobs

The number of observations, used in computing the BIC

call

The (matched) call to the lba function

Function tablba returns a data.frame with columns:

value

The estimated (or fixed) parameter value

se

The standard error of the parameter computed from the Hessian

z

The z-ratio of value and se

p

The p-value associated with z

Details

The 5 sub-models of the LBA model can be specified using a formula. Eg, nond=~diff, specifies a model in which the nondecision time is modeled as function of difficulty; diff may be a factor or numerical variable.

Identification of the model is attained by having the drift rates for alternatives in response sum to unity or by having a fixed standard deviation of the drift rates. These options are specified by scaling="sum" or scaling="fixedSD", respectively. In the latter case, the value of the fixed standard deviation is assumed to be the first value of startpars.

If hessian is set to TRUE, optim is used to get the Hessian at the maximum likelihood estimates of the parameters. This is used in turn to compute standard errors. The summary function pretty prints a table of parameter estimates, standard errors, z- and p-values. The summary function also prints the separate sub-model specifications and the parameter estimates. The print function prints basic information and a (named) vector of parameter estimates.

References

LBA models as in Brown and Heathcote, Cognitive science, 2008.

Examples

# NOT RUN {
data(bh08)

# reduce the data set for faster runtimes
bh1 <- bh08[c(1:300,1001:1300,2001:2300),]

# remove extreme RTs
bh1 <- bh1[bh1$rt>.180&bh1$rt<2,]

# starting values based on the quantile parameter 
# estimates from Brown and Heathcote, 2008:
# pars <- c(.25,.3,.1,.2,.9,.75,.6)

# fit the model with starting values
pars <- c(.25,.3,.1,.2,.9,.75,.6)
m1 <- lba(rt=rt,response=acc,drift=~diff-1,data=bh1,
	startpars=pars)

m1

summary(m1)

# }
# NOT RUN {
	# use random starting values instead
	set.seed(2)
	m1 <- lba(rt=rt,response=acc,drift=~diff-1,data=bh08,
	startpars=pars, hessian=TRUE)

	summary(m1)
	
	# get the parameters
	pp <- m1$pars
	# simulate some data from the model for the three conditions
	set.seed(1)
	dt1 <- rlba(1000, b=pp[3]+pp[2], A=pp[2], vs=c(pp[5],1-pp[5]), 
		s=pp[1], t0=pp[4], truncdrifts=TRUE)
	dt2 <- rlba(1000, b=pp[3]+pp[2], A=pp[2], vs=c(pp[6],1-pp[6]), 
		s=pp[1], t0=pp[4], truncdrifts=TRUE)
	dt3 <- rlba(1000, b=pp[3]+pp[2], A=pp[2], vs=c(pp[7],1-pp[7]), 
		s=pp[1], t0=pp[4], truncdrifts=TRUE)
	dt <- rbind(dt1,dt2,dt3)
	dt$diff <- gl(3,1000)
	dt$resp <- ifelse(dt$resp==2,0,1)
	
	# remove extreme RTs
	dt <- dt[dt$rt>.180&dt$rt<2,]
	
	# refit the model with the simualted data
	m1rf <- lba(rt=rt,response=resp,drift=~diff-1,data=dt,startpars=pp)
	
	data(numpp1)
	
	set.seed(9)
	m2 <- lba(rt=rt,response=acc,drift=~diff+block,data=numpp1,
	startpars=c(0.25,runif(4),0,0), scaling="fixedSD", 
		sdstart=0.25, hessian=TRUE) 
	tablba(m2) 
	
	
# }
# NOT RUN {
# }