mixture3p {bmm}

Three-parameter mixture model by Bays et al (2009).

Description

Three-parameter mixture model by Bays et al (2009).

Usage

mixture3p(resp_error, nt_features, set_size, regex = FALSE, ...)

Arguments

resp_error

The name of the variable in the dataset containing the response error. The response error should code the response relative to the to-be-recalled target in radians. You can transform the response error in degrees to radians using the deg2rad function.

nt_features

A character vector with the names of the non-target feature values. The non_target feature values should be in radians and centered relative to the target. Alternatively, if regex=TRUE, a regular expression can be used to match the non-target feature columns in the dataset.

set_size

Name of the column containing the set size variable (if set_size varies) or a numeric value for the set_size, if the set_size is fixed.

regex

Logical. If TRUE, the nt_features argument is interpreted as a regular expression to match the non-target feature columns in the dataset.

...

used internally for testing, ignore it

Details

• Domain: Visual working memory

• Task: Continuous reproduction

• Name: Three-parameter mixture model by Bays et al (2009).

• Citation:

  • Bays, P. M., Catalao, R. F. G., & Husain, M. (2009). The precision of visual working memory is set by allocation of a shared resource. Journal of Vision, 9(10), 1-11

• Requirements:

  • The response vairable should be in radians and represent the angular error relative to the target

• The non-target features should be in radians and be centered relative to the target

• Parameters:

  • mu1: Location parameter of the von Mises distribution for memory responses (in radians). Fixed internally to 0 by default.

  • kappa: Concentration parameter of the von Mises distribution

  • thetat: Mixture weight for target responses

  • thetant: Mixture weight for non-target responses

• Fixed parameters:

  • mu1 = 0

  • mu2 = 0

  • kappa2 = -100

• Default parameter links:

  • mu1 = tan_half; kappa = log; thetat = identity; thetant = identity

• Default priors:

  • mu1:

    • main: student_t(1, 0, 1)

  • kappa:

    • main: normal(2, 1)

    • effects: normal(0, 1)

  • thetat:

    • main: logistic(0, 1)

  • thetant:

    • main: logistic(0, 1)

Value

An object of class bmmodel

Examples

# generate artificial data from the Bays et al (2009) 3-parameter mixture model
dat <- data.frame(
  y = rmixture3p(n=2000, mu = c(0,1,-1.5,2)),
  nt1_loc = 1,
  nt2_loc = -1.5,
  nt3_loc = 2
)

# define formula
ff <- bmmformula(
  kappa ~ 1,
  thetat ~ 1,
  thetant ~ 1
)

# specify the 3-parameter model with explicit column names for non-target features
model1 <- mixture3p(resp_error = "y", nt_features = paste0('nt',1:3,'_loc'), set_size = 4)

# fit the model
fit <- bmm(formula = ff,
           data = dat,
           model = model1,
           cores = 4,
           iter = 500,
           backend = 'cmdstanr')

# alternatively specify the 3-parameter model with a regular expression to match non-target features
# this is equivalent to the previous call, but more concise
model2 <- mixture3p(resp_error = "y", nt_features = "nt.*_loc", set_size = 4, regex = TRUE)

# fit the model
fit <- bmm(formula = ff,
           data = dat,
           model = model2,
           cores = 4,
           iter = 500,
           backend = 'cmdstanr')