Extract coefficient/parameter standard deviations from a fitted `pk` object
# S3 method for pk
coef_sd(obj, model = NULL, method = NULL, suppress.messages = TRUE, ...)A dataframe with one row for each `data_group`, `model` and `method`. The remaining columns include the parameters & hyperparameters as returned by [coef.pk()], as well as their calculated standard deviations.
A [pk] object
Optional: Specify one or more of the fitted models whose coefficients to return. If NULL (the default), coefficients will be returned for all of the models in `obj$stat_model`.
Optional: Specify one or more of the [optimx::optimx()] methods whose coefficients to return. If NULL (the default), coefficients will be returned for all of the models in `obj$settings_optimx$method`.
Logical. `TRUE` (the default) to suppress informative messages. `FALSE` to see them.
Additional arguments. Not in use right now.
Caroline Ring and Gilberto Padilla Mercado
The coefficient standard deviations are estimated by computing a numerical approximation to the model Hessian (the matrix of second derivatives of the model objective function with respect to each model parameter) and then attempting to invert it. This procedure yields a variance/covariance matrix for the model parameters. The square root of the diagonal elements of this matrix represent the parameter standard deviations.
A first attempt is made to invert the Hessian using [solve()] (see [hess_sd1()]). If the Hessian is singular, an attempt is made to calculate a pseudovariance matrix, following the procedure outlined in Gill & King (2004) (see [hess_sd2()]). First, the generalized inverse of the Hessian is calculated using [MASS::ginv()]. Then, a generalized Cholesky decomposition (to ensure positive-definiteness) is calculated using [Matrix::Cholesky] with argument `perm = TRUE`. The generalized inverse is reconstructed from the generalized Cholesky factorization. The square root of the diagonal elements of this matrix represent the parameter standard deviations.
If neither of these procedures is successful, then `NA_real_` is returned for all coefficient standard deviations.
Gill J, King G. (2004) What to Do When Your Hessian is Not Invertible: Alternatives to Model Respecification in Nonlinear Estimation. Sociological Methods & Research 33(1):54-87. DOI: 10.1177/0049124103262681
Other methods for fitted pk objects:
AAFE.pk(),
AFE.pk(),
AIC.pk(),
BIC.pk(),
coef.pk(),
eval_tkstats.pk(),
get_fit.pk(),
get_hessian.pk(),
get_tkstats.pk(),
logLik.pk(),
predict.pk(),
residuals.pk(),
rmse.pk(),
rsq.pk()