LBA: The Linear Ballistic Accumulator (LBA)
In rtdists: Response Time Distributions
Description
Usage
Arguments
Details
Value
Note
References
Examples
Description
Density, distribution function, quantile function, and random generation for
the LBA model with the following parameters: A (upper value of
starting point), b (response threshold), t0 (non-decision
time), and driftrate (v). All functions are available with different
distributions underlying the drift rate: Normal (norm), Gamma
(gamma), Frechet (frechet), and log normal (lnorm). The
functions return their values conditional on the accumulator given in the
response argument winning.
Usage
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dLBA(rt, response, A, b, t0, ..., st0 = 0, distribution = c("norm",
"gamma", "frechet", "lnorm"), args.dist = list(), silent = FALSE)
pLBA(rt, response, A, b, t0, ..., st0 = 0, distribution = c("norm",
"gamma", "frechet", "lnorm"), args.dist = list(), silent = FALSE)
qLBA(p, response, A, b, t0, ..., st0 = 0, distribution = c("norm",
"gamma", "frechet", "lnorm"), args.dist = list(), silent = FALSE,
interval = c(0, 10), scale_p = FALSE, scale_max = Inf)
rLBA(n, A, b, t0, ..., st0 = 0, distribution = c("norm", "gamma",
"frechet", "lnorm"), args.dist = list(), silent = FALSE)
Arguments
rt
vector of RTs. Or for convenience also a data.frame with
columns rt and response (such as returned from rLBA or
rdiffusion). See examples.
response
integer vector of winning accumulators/responses
corresponding to the vector of RTs/p (i.e., used for specifying the
response for a given RT/probability). Will be recycled if necessary. Cannot
contain values larger than the number of accumulators. First
response/accumulator must receive value 1, second 2, and so forth. For
conmvenience, response is converted via as.numeric thereby
allowing factors to be passed as well (such as returned from
rdiffusion). Ignored if rt or p is a
data.frame.
A
start point interval or evidence in accumulator before beginning of
decision process. Start point varies from trial to trial in the interval
[0, A] (uniform distribution). Average amount of evidence before
evidence accumulation across trials is A/2.
b
response threshold. (b - A/2) is a measure of
"response caution".
t0
non-decision time or response time constant (in seconds). Lower
bound for the duration of all non-decisional processes (encoding and
response execution).
...
two named drift rate parameters depending on
distribution (e.g., mean_v and sd_v for
distribution=="norm"). The parameters can either be given as a
numeric vector or a list. If a numeric vector is passed each element of the
vector corresponds to one accumulator. If a list is passed each list
element corresponds to one accumulator allowing again trialwise driftrates.
The shorter parameter will be recycled as necessary (and also the elements
of the list to match the length of rt). See details.
st0
variability of non-decision time, such that t0 is uniformly
distributed between t0 and t0 + st0. Default is 0. Can
be trialwise, and will be recycled to length of rt.
distribution
character specifying the distribution of the drift rate.
Possible values are c("norm", "gamma", "frechet", "lnorm"), default
is "norm".
args.dist
list of optional further arguments to the distribution
functions (i.e., posdrift or robust for
distribution=="norm", see single-LBA).
silent
logical. Should the number of accumulators used be suppressed?
Default is FALSE which prints the number of accumulators.
p
vector of probabilities. Or for convenience also a data.frame
with columns p and response. See examples.
interval
a vector containing the end-points of the interval to be
searched for the desired quantiles (i.e., RTs) in qLBA. Default is
c(0, 10).
scale_p
logical. Should entered probabilities automatically be scaled
by maximally predicted probability? Default is FALSE. Convenience
argument for obtaining predicted quantiles. Can be slow as the maximally
predicted probability is calculated individually for each p.
scale_max
numerical scalar. Value at which maximally predicted RT
should be calculated if scale_p is TRUE.
n
desired number of observations (scalar integer).
Details
For convenience, all functions (with the exception of rdiffusion)
allow that the first argument is a data.frame containing the
information of the first and second argument in two columns (i.e.,
rt/p and response). Other columns will be ignored. This
allows, for example, to pass the data.frame generated by rLBA
directly to pLBA. See examples.
Parameters
The following arguments are allowed as ...
drift rate parameters:
-
mean_v,sd_v mean and standard
deviation of normal distribution for drift rate (norm). See
Normal
-
shape_v,rate_v,scale_v shape, rate, and
scale of gamma (gamma) and scale and shape of Frechet (frechet)
distributions for drift rate. See GammaDist or
frechet. For Gamma, scale = 1/shape and shape = 1/scale.
-
meanlog_v,sdlog_v mean and standard deviation of lognormal
distribution on the log scale for drift rate (lnorm). See
Lognormal.
As described above, the accumulator parameters can either be given as a
numeric vector or a list. If a numeric vector is passed each element of the
vector corresponds to one accumulator. If a list is passed each list element
corresponds to one accumulator allowing trialwise driftrates. The shorter
parameter will be recycled as necessary (and also the elements of the list to
match the length of rt).
The other LBA parameters (i.e., A, b, and t0, with the
exception of st0) can either be a single numeric vector (which will be
recycled to reach length(rt) or length(n) for trialwise
parameters) or a list of such vectors in which each list
element corresponds to the parameters for this accumulator (i.e., the list
needs to be of the same length as there are accumulators). Each list will
also be recycled to reach length(rt) for trialwise parameters per
accumulator.
To make the difference between both paragraphs clear: Whereas for the
accumulators both a single vector or a list corresponds to different
accumulators, only the latter is true for the other parameters. For those
(i.e., A, b, and t0) a single vector always corresponds
to trialwise values and a list must be used for accumulator wise values.
st0 can only vary trialwise (via a vector). And it should be noted
that st0 not equal to zero will considerably slow done everything.
Quantile Function
Due to the bivariate nature of the LBA,
single accumulators only return defective CDFs that do not reach 1. Only the
sum of all accumulators reaches 1. Therefore, qLBA can only return
quantiles/RTs for any accumulator up to the maximal probability of that
accumulator's CDF. This can be obtained by evaluating the CDF at Inf.
As a conveniece for the user, if scale_p = TRUE in the call to
qLBA the desired probabilities are automatically scaled by the maximal
probability for the corresponding response. Note that this can be slow as the
maximal probability is calculated separately for each desired probability.
See examples.
Also note that quantiles (i.e., predicted RTs) are obtained by numerically
minimizing the absolute difference between desired probability and the value
returned from pLBA using optimize. If the difference
between the desired probability and probability corresponding to the returned
quantile is above a certain threshold (currently 0.0001) no quantile is
returned but NA. This can be either because the desired quantile is
above the maximal probability for this accumulator or because the limits for
the numerical integration are too small (default is c(0, 10)).
RNG
For random number generation at least one of the
distribution parameters (i.e., mean_v, sd_v, shape_v,
scale_v, rate_v, meanlog_v, and sdlog_v) should
be of length > 1 to receive RTs from multiple responses. Shorter vectors are
recycled as necessary.
Note that for random number generation from a
normal distribution for the driftrate the number of returned samples may be
less than the number of requested samples if posdrifts==FALSE.
Value
dLBA returns the density (PDF), pLBA returns the
distribution function (CDF), qLBA returns the quantile/RT,
rLBA return random response times and responses (in a
data.frame).
The length of the result is determined by n for rLBA, equal
to the length of rt for dLBA and pLBA, and equal to
the length of p for qLBA.
The distribution parameters (as well as response) are recycled to
the length of the result. In other words, the functions are completely
vectorized for all parameters and even the response.
Note
These are the top-level functions intended for end-users. To obtain the
density and cumulative density the race functions are called for each
response time with the corresponding winning accumulator as first
accumulator (see LBA-race).
References
Brown, S. D., & Heathcote, A. (2008). The simplest complete model of choice
response time: Linear ballistic accumulation. Cognitive Psychology,
57(3), 153-178. doi:10.1016/j.cogpsych.2007.12.002
Donkin, C., Averell, L., Brown, S., & Heathcote, A. (2009). Getting more from
accuracy and response time data: Methods for fitting the linear ballistic
accumulator. Behavior Research Methods, 41(4), 1095-1110.
doi:10.3758/BRM.41.4.1095
Heathcote, A., & Love, J. (2012). Linear deterministic accumulator models of
simple choice. Frontiers in Psychology, 3, 292.
doi:10.3389/fpsyg.2012.00292
Examples
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## generate random LBA data:
rt1 <- rLBA(500, A=0.5, b=1, t0 = 0.5, mean_v=c(2.4, 1.6), sd_v=c(1,1.2))
head(rt1)
prop.table(table(rt1$response))
# original parameters have 'high' log-likelihood:
sum(log(dLBA(rt1$rt, rt1$response, A=0.5, b=1, t0 = 0.5, mean_v=c(2.4, 1.6), sd_v=c(1,1.2))))
# data can also be passed as data.frame (same is true for pLBA):
sum(log(dLBA(rt1, A=0.5, b=1, t0 = 0.5, mean_v=c(2.4, 1.6), sd_v=c(1,1.2))))
objective_fun <- function(par, rt, response, distribution = "norm") {
# simple parameters
spar <- par[!grepl("[12]$", names(par))]
# distribution parameters:
dist_par_names <- unique(sub("[12]$", "", grep("[12]$" ,names(par), value = TRUE)))
dist_par <- vector("list", length = length(dist_par_names))
names(dist_par) <- dist_par_names
for (i in dist_par_names) dist_par[[i]] <- as.list(unname(par[grep(i, names(par))]))
dist_par$sd_v <- c(1, dist_par$sd_v) # fix first sd to 1
# get summed log-likelihood:
d <- do.call(dLBA, args = c(rt=list(rt), response=list(response), spar, dist_par,
distribution=distribution, silent=TRUE))
if (any(d < 0e-10)) return(1e6)
else return(-sum(log(d)))
}
# gives same value as manual calculation above:
objective_fun(c(A=0.5, b=1, t0=0.5, mean_v1=2.4, mean_v2=1.6, sd_v2=1.2),
rt=rt1$rt, response=rt1$response)
## Not run:
# can we recover the parameters?
# should be run several times with different random values of init_par
init_par <- runif(6)
init_par[2] <- sum(init_par[1:2]) # ensures b is larger than A
init_par[3] <- runif(1, 0, min(rt1$rt)) #ensures t0 is mot too large
names(init_par) <- c("A", "b", "t0", "mean_v1", "mean_v2", "sd_v2")
nlminb(objective_fun, start = init_par, rt=rt1$rt, response=rt1$response, lower = 0)
## End(Not run)
# plot cdf (2 accumulators):
curve(pLBA(x, response = 1, A=0.5, b=1, t0 = 0.5, mean_v=c(2.4, 1.6), sd_v=c(1,1.2)),
xlim = c(0, 2), ylim = c(0,1),
ylab = "cumulative probability", xlab = "response time",
main = "Defective CDFs of LBA")
curve(pLBA(x, response = 2, A=0.5, b=1, t0 = 0.5, mean_v=c(2.4, 1.6), sd_v=c(1,1.2)),
add=TRUE, lty = 2)
legend("topleft", legend=c("1", "2"), title="Response", lty=1:2)
# plot cdf (3 accumulators):
curve(pLBA(x, response = 1, A=0.5, b=1, t0 = 0.5, mean_v=c(2.4, 1.6, 1.0), sd_v=c(1,1.2, 2.0)),
xlim = c(0, 2), ylim = c(0,1),
ylab = "cumulative probability", xlab = "response time",
main = "Defective CDFs of LBA")
curve(pLBA(x, response = 2, A=0.5, b=1, t0 = 0.5, mean_v=c(2.4, 1.6, 1.0), sd_v=c(1,1.2, 2.0)),
add=TRUE, lty = 2)
curve(pLBA(x, response = 3, A=0.5, b=1, t0 = 0.5, mean_v=c(2.4, 1.6, 1.0), sd_v=c(1,1.2, 2.0)),
add=TRUE, lty = 3)
legend("topleft", legend=c("1", "2", "3"), title="Response", lty=1:2)
## qLBA can only return values up to maximal predicted probability:
(max_p <- pLBA(Inf, response = 1, A=0.5, b=1, t0 = 0.5, mean_v=c(2.4, 1.6), sd_v=c(1,1.2)))
# [1] 0.6604696
qLBA(0.66, response = 1, A=0.5, b=1, t0 = 0.5, mean_v=c(2.4, 1.6), sd_v=c(1,1.2))
# 2.559532
qLBA(0.67, response = 1, A=0.5, b=1, t0 = 0.5, mean_v=c(2.4, 1.6), sd_v=c(1,1.2))
# NA
# to get predicted quantiles, scale required quantiles by maximally predicted response rate:
qs <- c(.1, .3, .5, .7, .9)
qLBA(qs*max_p, response = 1, A=0.5, b=1, t0 = 0.5, mean_v=c(2.4, 1.6), sd_v=c(1,1.2))
# or set scale_p to TRUE which scales automatically by maximum p
# (but can be slow as it calculates max_p for each probability separately)
qLBA(qs, response = 1, A=0.5, b=1, t0 = 0.5, mean_v=c(2.4, 1.6), sd_v=c(1,1.2), scale_p=TRUE)
# qLBA also accepts a data.frame as first argument:
t <- data.frame(p = rep(c(0.05, 0.1, 0.66), 2), response = rep(1:2, each = 3))
# p response
# 1 0.05 1
# 2 0.10 1
# 3 0.66 1
# 4 0.05 2
# 5 0.10 2
# 6 0.66 2
qLBA(t, A=0.5, b=1, t0 = 0.5, mean_v=c(2.4, 1.6), sd_v=c(1,1.2))
## LBA and diffusion can be used interchangeably:
rt1 <- rLBA(500, A=0.5, b=1, t0 = 0.5, mean_v=c(2.4, 1.6), sd_v=c(1,1.2))
rt2 <- rdiffusion(500, a=1, v=2, t0=0.5)
# data can also be passed as data.frame (same is true for pLBA):
sum(log(dLBA(rt1, A=0.5, b=1, t0 = 0.5, mean_v=c(2.4, 1.6), sd_v=c(1,1.2))))
sum(log(dLBA(rt2, A=0.5, b=1, t0 = 0.5, mean_v=c(2.4, 1.6), sd_v=c(1,1.2))))
sum(log(ddiffusion(rt1, a=1, v=2, t0=0.5)))
sum(log(ddiffusion(rt2, a=1, v=2, t0=0.5)))
### trial wise parameters work as expected (only since package version 0.9):
x1 <- dLBA(rt=c(1,1), response=c(1,2), A=1,b=list(c(1,3),c(2,4)),
t0=0.1, mean_v=c(3,3), sd_v=c(1,1),distribution="norm")
x2a <- dLBA(rt=c(1), response=c(1), A=1,b=list(c(1),c(2)),
t0=0.1,mean_v=c(3,3),sd_v=c(1,1),distribution="norm")
x2b <- dLBA(rt=c(1), response=c(2), A=1,b=list(c(3),c(4)),
t0=0.1,mean_v=c(3,3),sd_v=c(1,1),distribution="norm")
all(x1 == c(x2a, x2b)) ## should be TRUE
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Description Usage Arguments Details Value Note References Examples
Description
Density, distribution function, quantile function, and random generation for
the LBA model with the following parameters: A (upper value of
starting point), b (response threshold), t0 (non-decision
time), and driftrate (v). All functions are available with different
distributions underlying the drift rate: Normal (norm), Gamma
(gamma), Frechet (frechet), and log normal (lnorm). The
functions return their values conditional on the accumulator given in the
response argument winning.
Usage
1 2 3 4 5 6 7 8 9 10 11 12 | dLBA(rt, response, A, b, t0, ..., st0 = 0, distribution = c("norm",
"gamma", "frechet", "lnorm"), args.dist = list(), silent = FALSE)
pLBA(rt, response, A, b, t0, ..., st0 = 0, distribution = c("norm",
"gamma", "frechet", "lnorm"), args.dist = list(), silent = FALSE)
qLBA(p, response, A, b, t0, ..., st0 = 0, distribution = c("norm",
"gamma", "frechet", "lnorm"), args.dist = list(), silent = FALSE,
interval = c(0, 10), scale_p = FALSE, scale_max = Inf)
rLBA(n, A, b, t0, ..., st0 = 0, distribution = c("norm", "gamma",
"frechet", "lnorm"), args.dist = list(), silent = FALSE)
|
Arguments
rt |
vector of RTs. Or for convenience also a |
response |
integer vector of winning accumulators/responses
corresponding to the vector of RTs/p (i.e., used for specifying the
response for a given RT/probability). Will be recycled if necessary. Cannot
contain values larger than the number of accumulators. First
response/accumulator must receive value 1, second 2, and so forth. For
conmvenience, |
A |
start point interval or evidence in accumulator before beginning of
decision process. Start point varies from trial to trial in the interval
[0, |
b |
response threshold. ( |
t0 |
non-decision time or response time constant (in seconds). Lower bound for the duration of all non-decisional processes (encoding and response execution). |
... |
two named drift rate parameters depending on
|
st0 |
variability of non-decision time, such that |
distribution |
character specifying the distribution of the drift rate.
Possible values are |
args.dist |
list of optional further arguments to the distribution
functions (i.e., |
silent |
logical. Should the number of accumulators used be suppressed?
Default is |
p |
vector of probabilities. Or for convenience also a |
interval |
a vector containing the end-points of the interval to be
searched for the desired quantiles (i.e., RTs) in |
scale_p |
logical. Should entered probabilities automatically be scaled
by maximally predicted probability? Default is |
scale_max |
numerical scalar. Value at which maximally predicted RT
should be calculated if |
n |
desired number of observations (scalar integer). |
Details
For convenience, all functions (with the exception of rdiffusion)
allow that the first argument is a data.frame containing the
information of the first and second argument in two columns (i.e.,
rt/p and response). Other columns will be ignored. This
allows, for example, to pass the data.frame generated by rLBA
directly to pLBA. See examples.
Parameters
The following arguments are allowed as ...
drift rate parameters:
-
mean_v,sd_vmean and standard deviation of normal distribution for drift rate (norm). SeeNormal -
shape_v,rate_v,scale_vshape, rate, and scale of gamma (gamma) and scale and shape of Frechet (frechet) distributions for drift rate. SeeGammaDistorfrechet. For Gamma, scale = 1/shape and shape = 1/scale. -
meanlog_v,sdlog_vmean and standard deviation of lognormal distribution on the log scale for drift rate (lnorm). SeeLognormal.
As described above, the accumulator parameters can either be given as a
numeric vector or a list. If a numeric vector is passed each element of the
vector corresponds to one accumulator. If a list is passed each list element
corresponds to one accumulator allowing trialwise driftrates. The shorter
parameter will be recycled as necessary (and also the elements of the list to
match the length of rt).
The other LBA parameters (i.e., A, b, and t0, with the
exception of st0) can either be a single numeric vector (which will be
recycled to reach length(rt) or length(n) for trialwise
parameters) or a list of such vectors in which each list
element corresponds to the parameters for this accumulator (i.e., the list
needs to be of the same length as there are accumulators). Each list will
also be recycled to reach length(rt) for trialwise parameters per
accumulator.
To make the difference between both paragraphs clear: Whereas for the
accumulators both a single vector or a list corresponds to different
accumulators, only the latter is true for the other parameters. For those
(i.e., A, b, and t0) a single vector always corresponds
to trialwise values and a list must be used for accumulator wise values.
st0 can only vary trialwise (via a vector). And it should be noted
that st0 not equal to zero will considerably slow done everything.
Quantile Function
Due to the bivariate nature of the LBA,
single accumulators only return defective CDFs that do not reach 1. Only the
sum of all accumulators reaches 1. Therefore, qLBA can only return
quantiles/RTs for any accumulator up to the maximal probability of that
accumulator's CDF. This can be obtained by evaluating the CDF at Inf.
As a conveniece for the user, if scale_p = TRUE in the call to
qLBA the desired probabilities are automatically scaled by the maximal
probability for the corresponding response. Note that this can be slow as the
maximal probability is calculated separately for each desired probability.
See examples.
Also note that quantiles (i.e., predicted RTs) are obtained by numerically
minimizing the absolute difference between desired probability and the value
returned from pLBA using optimize. If the difference
between the desired probability and probability corresponding to the returned
quantile is above a certain threshold (currently 0.0001) no quantile is
returned but NA. This can be either because the desired quantile is
above the maximal probability for this accumulator or because the limits for
the numerical integration are too small (default is c(0, 10)).
RNG
For random number generation at least one of the
distribution parameters (i.e., mean_v, sd_v, shape_v,
scale_v, rate_v, meanlog_v, and sdlog_v) should
be of length > 1 to receive RTs from multiple responses. Shorter vectors are
recycled as necessary.
Note that for random number generation from a
normal distribution for the driftrate the number of returned samples may be
less than the number of requested samples if posdrifts==FALSE.
Value
dLBA returns the density (PDF), pLBA returns the
distribution function (CDF), qLBA returns the quantile/RT,
rLBA return random response times and responses (in a
data.frame).
The length of the result is determined by n for rLBA, equal
to the length of rt for dLBA and pLBA, and equal to
the length of p for qLBA.
The distribution parameters (as well as response) are recycled to
the length of the result. In other words, the functions are completely
vectorized for all parameters and even the response.
Note
These are the top-level functions intended for end-users. To obtain the
density and cumulative density the race functions are called for each
response time with the corresponding winning accumulator as first
accumulator (see LBA-race).
References
Brown, S. D., & Heathcote, A. (2008). The simplest complete model of choice response time: Linear ballistic accumulation. Cognitive Psychology, 57(3), 153-178. doi:10.1016/j.cogpsych.2007.12.002
Donkin, C., Averell, L., Brown, S., & Heathcote, A. (2009). Getting more from accuracy and response time data: Methods for fitting the linear ballistic accumulator. Behavior Research Methods, 41(4), 1095-1110. doi:10.3758/BRM.41.4.1095
Heathcote, A., & Love, J. (2012). Linear deterministic accumulator models of simple choice. Frontiers in Psychology, 3, 292. doi:10.3389/fpsyg.2012.00292
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 | ## generate random LBA data:
rt1 <- rLBA(500, A=0.5, b=1, t0 = 0.5, mean_v=c(2.4, 1.6), sd_v=c(1,1.2))
head(rt1)
prop.table(table(rt1$response))
# original parameters have 'high' log-likelihood:
sum(log(dLBA(rt1$rt, rt1$response, A=0.5, b=1, t0 = 0.5, mean_v=c(2.4, 1.6), sd_v=c(1,1.2))))
# data can also be passed as data.frame (same is true for pLBA):
sum(log(dLBA(rt1, A=0.5, b=1, t0 = 0.5, mean_v=c(2.4, 1.6), sd_v=c(1,1.2))))
objective_fun <- function(par, rt, response, distribution = "norm") {
# simple parameters
spar <- par[!grepl("[12]$", names(par))]
# distribution parameters:
dist_par_names <- unique(sub("[12]$", "", grep("[12]$" ,names(par), value = TRUE)))
dist_par <- vector("list", length = length(dist_par_names))
names(dist_par) <- dist_par_names
for (i in dist_par_names) dist_par[[i]] <- as.list(unname(par[grep(i, names(par))]))
dist_par$sd_v <- c(1, dist_par$sd_v) # fix first sd to 1
# get summed log-likelihood:
d <- do.call(dLBA, args = c(rt=list(rt), response=list(response), spar, dist_par,
distribution=distribution, silent=TRUE))
if (any(d < 0e-10)) return(1e6)
else return(-sum(log(d)))
}
# gives same value as manual calculation above:
objective_fun(c(A=0.5, b=1, t0=0.5, mean_v1=2.4, mean_v2=1.6, sd_v2=1.2),
rt=rt1$rt, response=rt1$response)
## Not run:
# can we recover the parameters?
# should be run several times with different random values of init_par
init_par <- runif(6)
init_par[2] <- sum(init_par[1:2]) # ensures b is larger than A
init_par[3] <- runif(1, 0, min(rt1$rt)) #ensures t0 is mot too large
names(init_par) <- c("A", "b", "t0", "mean_v1", "mean_v2", "sd_v2")
nlminb(objective_fun, start = init_par, rt=rt1$rt, response=rt1$response, lower = 0)
## End(Not run)
# plot cdf (2 accumulators):
curve(pLBA(x, response = 1, A=0.5, b=1, t0 = 0.5, mean_v=c(2.4, 1.6), sd_v=c(1,1.2)),
xlim = c(0, 2), ylim = c(0,1),
ylab = "cumulative probability", xlab = "response time",
main = "Defective CDFs of LBA")
curve(pLBA(x, response = 2, A=0.5, b=1, t0 = 0.5, mean_v=c(2.4, 1.6), sd_v=c(1,1.2)),
add=TRUE, lty = 2)
legend("topleft", legend=c("1", "2"), title="Response", lty=1:2)
# plot cdf (3 accumulators):
curve(pLBA(x, response = 1, A=0.5, b=1, t0 = 0.5, mean_v=c(2.4, 1.6, 1.0), sd_v=c(1,1.2, 2.0)),
xlim = c(0, 2), ylim = c(0,1),
ylab = "cumulative probability", xlab = "response time",
main = "Defective CDFs of LBA")
curve(pLBA(x, response = 2, A=0.5, b=1, t0 = 0.5, mean_v=c(2.4, 1.6, 1.0), sd_v=c(1,1.2, 2.0)),
add=TRUE, lty = 2)
curve(pLBA(x, response = 3, A=0.5, b=1, t0 = 0.5, mean_v=c(2.4, 1.6, 1.0), sd_v=c(1,1.2, 2.0)),
add=TRUE, lty = 3)
legend("topleft", legend=c("1", "2", "3"), title="Response", lty=1:2)
## qLBA can only return values up to maximal predicted probability:
(max_p <- pLBA(Inf, response = 1, A=0.5, b=1, t0 = 0.5, mean_v=c(2.4, 1.6), sd_v=c(1,1.2)))
# [1] 0.6604696
qLBA(0.66, response = 1, A=0.5, b=1, t0 = 0.5, mean_v=c(2.4, 1.6), sd_v=c(1,1.2))
# 2.559532
qLBA(0.67, response = 1, A=0.5, b=1, t0 = 0.5, mean_v=c(2.4, 1.6), sd_v=c(1,1.2))
# NA
# to get predicted quantiles, scale required quantiles by maximally predicted response rate:
qs <- c(.1, .3, .5, .7, .9)
qLBA(qs*max_p, response = 1, A=0.5, b=1, t0 = 0.5, mean_v=c(2.4, 1.6), sd_v=c(1,1.2))
# or set scale_p to TRUE which scales automatically by maximum p
# (but can be slow as it calculates max_p for each probability separately)
qLBA(qs, response = 1, A=0.5, b=1, t0 = 0.5, mean_v=c(2.4, 1.6), sd_v=c(1,1.2), scale_p=TRUE)
# qLBA also accepts a data.frame as first argument:
t <- data.frame(p = rep(c(0.05, 0.1, 0.66), 2), response = rep(1:2, each = 3))
# p response
# 1 0.05 1
# 2 0.10 1
# 3 0.66 1
# 4 0.05 2
# 5 0.10 2
# 6 0.66 2
qLBA(t, A=0.5, b=1, t0 = 0.5, mean_v=c(2.4, 1.6), sd_v=c(1,1.2))
## LBA and diffusion can be used interchangeably:
rt1 <- rLBA(500, A=0.5, b=1, t0 = 0.5, mean_v=c(2.4, 1.6), sd_v=c(1,1.2))
rt2 <- rdiffusion(500, a=1, v=2, t0=0.5)
# data can also be passed as data.frame (same is true for pLBA):
sum(log(dLBA(rt1, A=0.5, b=1, t0 = 0.5, mean_v=c(2.4, 1.6), sd_v=c(1,1.2))))
sum(log(dLBA(rt2, A=0.5, b=1, t0 = 0.5, mean_v=c(2.4, 1.6), sd_v=c(1,1.2))))
sum(log(ddiffusion(rt1, a=1, v=2, t0=0.5)))
sum(log(ddiffusion(rt2, a=1, v=2, t0=0.5)))
### trial wise parameters work as expected (only since package version 0.9):
x1 <- dLBA(rt=c(1,1), response=c(1,2), A=1,b=list(c(1,3),c(2,4)),
t0=0.1, mean_v=c(3,3), sd_v=c(1,1),distribution="norm")
x2a <- dLBA(rt=c(1), response=c(1), A=1,b=list(c(1),c(2)),
t0=0.1,mean_v=c(3,3),sd_v=c(1,1),distribution="norm")
x2b <- dLBA(rt=c(1), response=c(2), A=1,b=list(c(3),c(4)),
t0=0.1,mean_v=c(3,3),sd_v=c(1,1),distribution="norm")
all(x1 == c(x2a, x2b)) ## should be TRUE
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