Compute Hessian matrix at the MLE

Usage

hessian(mod, numerical = FALSE)

Arguments

mod: an object of class bbdml
numerical: Boolean. Defaults to FALSE. Indicator of whether to use the numeric Hessian (not recommended).

Value

Hessian matrix at the MLE. In this setting, it's hard to compute expectations to calculate the information matrix, so we return the consistent estimate using sample moments: \(\hat{A}(\hat{\theta}) = \sum_i \frac{\partial^2}{\partial \theta \partial \theta^T} l(\theta, W_i)\) evaluated at \(\theta = \hat{\theta}\).

Examples

data(soil_phylum_small_otu1)
mod <- bbdml(formula = cbind(W, M - W) ~ DayAmdmt,
phi.formula = ~ DayAmdmt,
data = soil_phylum_small_otu1)
hessian(mod)
#>             (Intercept)  DayAmdmt21 (Intercept) DayAmdmt21
#> (Intercept) 3587.083848 2816.656102   -4.254135  -2.521716
#> DayAmdmt21  2816.656102 2816.656102   -2.521716  -2.521716
#> (Intercept)   -4.254135   -2.521716   15.826817   7.827544
#> DayAmdmt21    -2.521716   -2.521716    7.827544   7.827544