The default normal conditional-density estimator for HDR non-overlap

hdr_density_normal() builds the default conditional-density estimator used by check_hdr() and check_hdr_seq(). It fits a linear model of the exposure on the covariates, treats the conditional density as Gaussian with the model's residual standard deviation, and supplies a closed-form HDR threshold.

Usage

hdr_density_normal()

Value

An hdr_density estimator object.

Details

The estimator fits lm(exposure ~ covariates), recovering fitted means \(\hat{\mu}(l)\) and a homoskedastic residual standard deviation \(\hat{\sigma}\). The conditional density is \(\hat{f}(a \mid l) = \mathrm{dnorm}(a; \hat{\mu}(l), \hat{\sigma})\). Its HDR at mass mass is a symmetric interval around \(\hat{\mu}(l)\), so the density cutoff is the closed form $$f_\alpha = \mathrm{dnorm}(z) / \hat{\sigma}, \qquad z = \Phi^{-1}\!\left(\frac{1 + \mathrm{mass}}{2}\right).$$ Membership of a target a in the HDR reduces to the interval test \(|a - \hat{\mu}(l)| \le z\,\hat{\sigma}\), and the non-overlap ratio at a is the fraction of fitted means more than \(z\,\hat{\sigma}\) from a.

Because the working model is a single Gaussian, this estimator detects mean-shift support gaps, where a stratum's supported dose moves away from a target, but not multimodal gaps: a hole between two modes of the true conditional density is filled by the fitted normal and reported as supported. Supply a flexible estimator through new_hdr_density() when multimodal structure is expected.

References

Bao Y, Schomaker M (2025). Feasible Dose-Response Curves for Continuous Treatments Under Positivity Violations.

Examples

estimator <- hdr_density_normal()
estimator
#> <positively::hdr_density>
#>  @ fit          : function (formula, data)  
#>  @ density      : function (state, a, newdata)  
#>  @ hdr_threshold: function (state, newdata, mass)  
#>  @ label        : chr "normal"