Between-person slope quantile (${\beta }_1+{\tau }_1{\Phi }^{-1}(u)$)

When a person's latent slope has normal distribution $N({\beta }_1,{\tau }_1^2)$, its $u$th quantile is ${\beta }_1+{\tau }_1{\Phi }^{-1}(u)$. Multiply by an elapsed time to obtain the corresponding latent change quantile. This describes population variation between people; it is distinct from a confidence interval for the mean slope and from a prediction interval that includes measurement error.