Simulate within-subject demand data for TICKET-011 Phase 2 parity tests — .simulate_within_subject

Generates long-format demand data where each subject is observed at every price under every level of an in-subject condition factor. Used by the Phase 2 parity tests to confirm that fit_demand_tmb() matches fit_demand_mixed() on factor-expanded random-effects specifications (pdDiag(Q0+alpha~condition), pdSymm(Q0+alpha~condition) etc.).

Usage

.simulate_within_subject_demand(
  n_subjects = 30,
  n_conditions = 3,
  prices = c(0.1, 0.5, 1, 2, 5, 10, 20),
  log_q0_pop = log(20),
  log_alpha_pop = log(0.005),
  delta_q0 = NULL,
  delta_alpha = NULL,
  sigma_b = 0.3,
  sigma_d = 0.3,
  rho_bd = 0,
  sigma_e = 0.1,
  seed = NULL
)

Arguments

n_subjects: Integer; number of subjects.
n_conditions: Integer; number of within-subject condition levels (named "C1", "C2", ...).
prices: Numeric vector of prices each subject sees at every condition.
log_q0_pop: Numeric; population log-Q0.
log_alpha_pop: Numeric; population log-alpha.
delta_q0: Numeric vector of length n_conditions; per-condition shifts on log-Q0. Defaults to 0 for all conditions.
delta_alpha: Numeric vector of length n_conditions; per-condition shifts on log-alpha. Defaults to 0 for all conditions.
sigma_b: Numeric; SD of per-(subject, condition) Q0 random deviation.
sigma_d: Numeric; SD of per-(subject, condition) alpha random deviation.
rho_bd: Numeric; correlation between b and d within (subject, condition).
sigma_e: Numeric; residual SD on log-y.
seed: Optional integer seed for reproducibility.

Value

A tibble with columns id (factor), condition (factor), x (price), and y (consumption). Long-format, one row per (subject, condition, price).

Details

Data-generating process: each subject i at condition c and price p has consumption $$y_{i,c,p} = Q_{0,i,c} \cdot \exp(-\alpha_{i,c} \cdot Q_{0,i,c} \cdot p) \cdot \exp(\epsilon)$$ where $$\log Q_{0,i,c} = \log Q_{0,\text{pop}} + \delta^{Q_0}_c + b_{i,c}$$ $$\log \alpha_{i,c} = \log \alpha_{\text{pop}} + \delta^{\alpha}_c + d_{i,c}$$ with per-condition shifts delta_q0[c], delta_alpha[c] and per-subject per-condition random deviations (b_{i,c}, d_{i,c}) ~ N(0, Sigma).