This function calculates the Fisher information matrix (FIM), an expectation over the data-generating process (DGP). The FIM is a crucial concept in statistics because it provides information about the precision of estimates and the amount of information that data carries about an unknown parameter.
fim(model, ...)A likelihood model
Additional arguments
Function that computes the FIM given a sample and a parameter vector
FIM is a function of the parameters, and is used to compute the standard errors of the parameters. It is also used to compute the covariance matrix of the parameters, which is in turn used to compute standard errors of the parameters.
Additionally, FIM is used to compute the Cramer-Rao lower bound (CRLB), the inverse of the FIM. CRLB represents the lower limit of the variance that an unbiased estimator can attain. This is used to compute the asymptotic relative efficiency (ARE) of an estimator of the parameters, which is the ratio of the variance of the estimator to the CRLB.
The function computes FIM(x)(theta), the FIM of the likelihood model x, is
based on the following formulas:
FIM(x)(theta) = E[-loglik_hessian(x)(ob,theta)]
FIM(x)(theta) = E[score(x)(ob,theta) %*% t(score(x)(ob,theta))]where the expectation is taken with respect to ob ~ DGP. The first formula is the expected hessian of the log-likelihood function, and the second formula is the expected outer product of the score function. The two formulas are equivalent.