Restriction of Range and the Potential Bias of Multilevel Autoregressive Models

Abstract

The between-person staging effect states that individuals with more severe levels of depressive symptoms tend to have higher autoregressive and cross-lagged effects. However, it has been suggested that between-person staging for cross-lagged effects can be a methodological artifact due to restriction of range on negative affect variables for healthy individuals. Therefore, the use of inverse Gaussian regression has been recommended since it is theorized to capture the positively skewed distribution of negative affect variables better than the commonly used Gaussian regression. What remains an open research question is what the effect of restriction of range on estimation of the autoregressive effect is. This paper employs a series of simulations to explore whether multilevel autoregressive models using Gaussian regression lead to a bias in the estimation of the autoregressive effect for individuals with different restrictions of range. It shows that Gaussian regression does not lead to the spurious finding of a between-person staging effect. In contrast, inverse Gaussian regression, as well as Gamma regression (which, like the inverse Gaussian, is also a positively skewed distribution) perform badly, and lead to incorrect and contradicting conclusions. Even though using inverse Gaussian or Gamma regression seems logical from a theoretical perspective, the simulations do not show that these types of regressions are more advantageous in this context than Gaussian regression.