Latent difference score (LDS) models combine benefits derived from autoregressive and latent growth curve models allowing for time-dependent influences and systematic change. The specification and descriptions of LDS models include an initial level of ability or trait plus an accumulation of changes. A limitation of this specification is that the intercept is always located at the beginning of the process or observation period. In this article, LDS models are reformulated to allow the intercept to be centered at any time point. Additionally, I describe how the constant change factor can be rescaled to alter its interpretation. (Contains 1 table, 4 figures and 1 footnote.)