Fit a GAMLSS model for variance decomposition

A convenience wrapper around gamlss::gamlss() for users who want to fit a GAMLSS model without worrying about the syntax. The model simultaneously estimates the conditional mean and conditional (log) standard deviation, which are the inputs to the causal variance decomposition.

Usage

fit_ineqx_model(
  formula_mu,
  formula_sigma,
  data,
  weights = NULL,
  family = NULL,
  ...
)

Arguments

formula_mu

Formula for the mean equation (e.g., y ~ treat * group + controls)

formula_sigma

Formula for the log-SD equation (e.g., ~ treat * group + controls). Note: one-sided formula.

data

A data.frame

weights

Optional character string naming the weight variable in data, or a numeric vector of weights

family

A gamlss.family object specifying the distribution. Default: gamlss.dist::NO() (normal distribution).

...

Additional arguments passed to gamlss::gamlss()

Value

A fitted gamlss object

Details

Users who want more control over the model specification should fit their own gamlss model directly and use ineqx_params to extract the decomposition parameters.

The GAMLSS framework models both the conditional mean and conditional variance of the outcome distribution. The mean equation captures how treatment affects average outcomes within each group. The sigma equation captures how treatment affects the dispersion of outcomes within each group.

For the simple difference estimator, the model is: $$\mu_{ij} = \alpha_j + \beta_{D,j} D_i + Z_i \gamma$$ $$\log(\sigma_{ij}) = \alpha_j^{(\sigma)} + \lambda_{D,j} D_i + Z_i \gamma^{(\sigma)}$$

For the DiD estimator, add pre/post interactions: $$\mu_{ij} = \alpha_j + \beta_{D,j} D_i + \beta_P P_i + \beta_{DP,j} D_i P_i + Z_i \gamma$$

See also

ineqx_params for extracting decomposition parameters from the fitted model