Utilities

For manipulation of output or inputs, there are several basic utility functionalities for transformation of variables, predicted parameters, or computations. Some are used internally by the built-in estimating equations but these methods are also made available to users.

Data transformations

`logit`(prob)	Logistic transformation.
`inverse_logit`(logodds)	Inverse logistic transformation.
`identity`(value)	Identity transformation.
`robust_loss_functions`(residual, loss, k[, a, b])	Loss functions for robust mean and robust regression estimating equations.
`aggregate_efuncs`(est_funcs, group)	Aggregate estimating function contributions from the individual-level to the specified group-level.
`spline`(variable, knots[, power, restricted, ...])	Generate generic polynomial spline terms for a given NumPy array and pre-specified knots.
`polygamma`(n, x)	Polygamma function.
`digamma`(z)	Digamma function.
`standard_normal_cdf`(x)	Cumulative distribution function for the standard normal distribution.
`standard_normal_pdf`(x)	Probability density function for the standard normal distribution.

Design matrices

additive_design_matrix(X, specifications[, ...])

Generate an additive design matrix for generalized additive models (GAM) given a set of spline specifications to apply.

Model predictions

`regression_predictions`(X, theta, covariance)	Generate predicted values of the outcome given a design matrix, point estimates, and covariance matrix.
`aft_predictions_individual`(X, times, theta, ...)	Compute predicted survival analysis measures from an accelerated failure time (AFT) model for given a design matrix and times.
`aft_predictions_function`(X, times, theta, ...)	Compute estimated functions for survival analysis measures from an accelerated failure time (AFT) model across a specified time period.
`plogit_predict`(theta, t, delta, X[, S, ...])	Compute predicted survival analysis measures from a pooled logistic regression model for given a design matrix and times.

Differentiation

`approx_differentiation`(xk, f[, epsilon, method])	Numerical approximation to compute the gradient.
`auto_differentiation`(xk, f)	Forward-mode automatic differentiation.

Variance Estimators

`compute_sandwich`(stacked_equations, theta[, ...])	Compute the empirical sandwich variance estimator for a given set of estimating equations and parameter estimates.
`delta_method`(theta, g, covariance[, ...])	Function to apply the Delta Method for a given parameter vector and transformation.