A Note on Implementing a Special Case of the LEAR Covariance Model in Standard Software

TL;DR

This paper introduces a reparameterization of the LEAR covariance model, enabling its implementation in standard statistical software for equally spaced data, thereby broadening its practical application in repeated measures analysis.

Contribution

It presents a simplified reparameterization of the LEAR model for easier implementation in common software packages for equally spaced data.

Findings

Facilitates implementation of LEAR model in standard software.

Supports analysis of data with equally spaced intervals.

Enhances the practical use of flexible correlation structures.

Abstract

Repeated measures analyses require proper choice of the correlation model to ensure accurate inference and optimal efficiency. The linear exponent autoregressive (LEAR) correlation model provides a flexible two-parameter correlation structure that accommodates a variety of data types in which the correlation within-sampling unit decreases exponentially in time or space. The LEAR model subsumes three classic temporal correlation structures, namely compound symmetry, continuous-time AR(1), and MA(1), while maintaining parsimony and providing appealing statistical and computational properties. It also supplies a plausible correlation structure for power analyses across many experimental designs. However, no commonly used statistical packages provide a straightforward way to implement the model, limiting its use to those with the appropriate programming skills. Here we present a reparameterization of the LEAR model that allows easily implementing it in standard software for the special case of data with equally spaced temporal or spatial intervals.