Animation 1: Boundedness and Ordinal Resolution Bias

The ordinal resolution effect. Ordinal probit estimates of life satisfaction typically show probit-spaced cutpoints: thresholds are denser near the centre of the scale and sparser near the extremes. This means responses near 5 distinguish finer differences in latent wellbeing than responses near 0 or 10. Consequence: for the same true latent σ, distributions centred near 5 are better-resolved and produce a higher observed SD than those near the endpoints — producing an inverted-U in SD, opposite in sign to the pure ceiling/floor effect.

Use all three sliders. Slider 1: latent mean (μ_lat). Slider 2: latent SD (σ_lat) — controls how strongly the bounded scale truncates the distribution. Slider 3: cutpoint compression α (0 = uniform, 1 = strong centre compression — middle categories narrow, edge categories wide; the three central gaps are held equal so response 5 isn't artificially squeezed). The dashed reference curves (recomputed at the current σ_lat) show the two α extremes; the solid curve is the current blend.