Distribution functions for the two-parameter mixture model (mixture2p)

Density, distribution, and random generation functions for the two-parameter mixture model with the location of mu, precision of memory representations kappa and probability of recalling items from memory p_mem.

Usage

dmixture2p(
  x,
  mu = 0,
  kappa = 5,
  p_mem = 0.6,
  tau = 0,
  K = 3,
  set_size = NULL,
  version = "simple",
  vp_nodes = 81L,
  log = FALSE
)

pmixture2p(q, mu = 0, kappa = 7, p_mem = 0.8)

qmixture2p(p, mu = 0, kappa = 5, p_mem = 0.6)

rmixture2p(
  n,
  mu = 0,
  kappa = 5,
  p_mem = 0.6,
  tau = 0,
  K = 3,
  set_size = NULL,
  version = "simple"
)

Arguments

x

Vector of observed responses

mu

Vector of locations

kappa

Vector of precision values. With tau > 0 this is the concentration of the average trial, whose Fisher information J(kappa) is the mean of J.

p_mem

Vector of probabilities for memory recall, i.e. thetat of mixture2p() on its native scale. Used by the "simple" version; the other versions derive it from K and set_size, and warn if p_mem is given.

tau

Vector of scales for trial-to-trial variability in precision. The Fisher information J of a memory representation is drawn from gamma(mean = J(kappa), scale = tau). tau = 0, the default, is constant precision.

K

Vector of memory capacities. Used by the "slot" and "slot_averaging" versions; "simple" ignores it and warns if it is given.

set_size

Vector of set sizes. Required by the "slot" and "slot_averaging" versions, which stop without it; "simple" ignores it and warns if it is given.

version

A character string selecting the storage model: "simple", "slot" or "slot_averaging". See mixture2p().

vp_nodes

Number of quadrature nodes used when tau > 0; must be an odd number of at least 41. See mixture2p(). The random generation function needs no nodes: it draws J from its gamma distribution and then the response, which is exact.

log

Logical; if TRUE, values are returned on the log scale. Pass it by name: in bmm 1.4 it was the fifth argument, which is now tau. Until bmm 1.6.0 a logical value in that position is still read as log, with a warning.

q

Vector of quantiles

p

Vector of probability

n

Number of observations to generate data for

Value

dmixture2p gives the density of the two-parameter mixture model, pmixture2p gives the cumulative distribution function of the two-parameter mixture model, qmixture2p gives the quantile function of the two-parameter mixture model, and rmixture2p gives the random generation function for the two-parameter mixture model.

References

Zhang, W., & Luck, S. J. (2008). Discrete fixed-resolution representations in visual working memory. Nature, 453(7192), 233-235.

van den Berg, R., Shin, H., Chou, W.-C., George, R., & Ma, W. J. (2012). Variability in encoding precision accounts for visual short-term memory limitations. PNAS, 109(22), 8780-8785.

Examples

# generate random samples from the mixture2p model and overlay the density
r <- rmixture2p(10000, mu = 0, kappa = 4, p_mem = 0.8)
x <- seq(-pi, pi, length.out = 10000)
d <- dmixture2p(x, mu = 0, kappa = 4, p_mem = 0.8)
hist(r, breaks = 60, freq = FALSE)
lines(x, d, type = "l", col = "red")