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Temporal discounting binary choice linear model

Source: R/td_bclm.R
td_bclm.Rd

Compute a binary choice linear model for a single subject. In these models, we can recover the parameters of a discount function from the weights of a standard logistic regression. \(\beta_1\)

Usage

td_bclm(
  data,
  model = c("all", "hyperbolic.1", "hyperbolic.2", "exponential.1", "exponential.2",
    "scaled-exponential", "nonlinear-time-hyperbolic", "nonlinear-time-exponential"),
  ...
)

Arguments

data

A data frame with columns val_imm and val_del for the values of the immediate and delayed rewards, del for the delay, and imm_chosen (Boolean) for whether the immediate reward was chosen. Other columns can also be present but will be ignored.

model

A string specifying which model to use. Below is a list of these models' linear predictors and the means by which we can recover discount function parameters.
'hyperbolic.1': \(\beta_1(1 - v_D/v_I) + \beta_2 t\); \(k = \beta_2/\beta_1\)
'hyperbolic.2': \(\beta_1(\sigma^{-1}[v_I/v_D] + \log t) + \beta_2\); \(k = \exp[\beta_2/\beta_1]\)
'exponential.1': \(\beta_1 \log (v_I/v_D) + \beta_2 t\); \(k = \beta_2/\beta_1\)
'exponential.2': \(\beta_1(G^{-1}[v_I/v_D] + \log t) + \beta_2\); \(k = \exp[\beta_2/\beta_1]\)
'scaled-exponential': \(\beta_1 \log (v_I/v_D) + \beta_2 t + \beta_3\); \(k = \beta_2/\beta_1\), \(w = \exp[-\beta_3/\beta_1]\) 'nonlinear-time-hyperbolic': \(\beta_1(\sigma^{-1}[v_I/v_D]) + \beta_2\log t + \beta_3\); \(k = \exp[\beta_3/\beta_1]\), \(s = \beta_2/\beta_1\)
'nonlinear-time-hyperbolic': \(\beta_1(G^{-1}[v_I/v_D]) + \beta_2\log t + \beta_3\); \(k = \exp[\beta_3/\beta_1]\), \(s = \beta_2/\beta_1\)
where \(\sigma^{-1}[\cdot]\) is the quantile function of the standard logistic distribution \(G^{-1}[\cdot]\) is the quantile function of the standard Gumbel distribution.

...

Additional arguments passed to glm.

Value

An object of class td_bclm, nearly identical to a glm but with an additional config component.

See also

Other linear binary choice model functions: predict.td_bclm()

Examples

if (FALSE) { # \dontrun{
data("td_bc_single_ptpt")
mod <- td_bclm(td_bc_single_ptpt, model = 'hyperbolic.1')
print(coef(mod))
} # }