Many times throughout these pages we have mentioned the asymptotic covariance matrix, or ACOV matrix. The ACOV matrix is the covariance matrix of parameter estimates. The ACOV matrix is also known variously as the ACM, the VCE (variance-covariance matrix of the estimators), or simply the inverse of the Fisher information matrix (denoted I(q)-1). Elements along the diagonal represent the variance expected of each parameter estimate over repeated sampling, and can be interpreted as indices of precision of estimation. Off-diagonal elements represent covariances of parameter estimates. The standard errors used to conduct significance tests of parameter estimates are simply the square roots of the diagonal elements of the ACOV matrix.
Some (but not all) of the elements of an ACOV matrix are necessary for the computation of standard errors associated with simple intercepts, simple slopes, and simple trajectories. Most statistical software packages provide ACOV matrices, but only if requested to do so. Below are instructions for how to obtain the ACOV matrix in several packages. This list is not exhaustive, but does cover most of the commonly used packages.
Thanks to Dominic Comtois for help with obtaining asymptotic (co)variances in R and Splus, and thanks to 'Alim J. Beveridge for similar help with Stata.
Original version posted September, 2003.