Fig. 1

Scatterplot of the Grade of Membership (GoM) scores for examination 1 by subgroup and sex. Within each chart, subtypes 1–3 are located at the vertices of each triangular region, starting from the upper left side, in clockwise order. The GoM score continuum is triangular because GoM scores locate individuals at or between the indicated subtype vertices. The origin of the coordinate system is located at the centroid of each triangular region; the coordinate axes are scaled to reproduce the distance of \( \sqrt{2} \) GoM score units between all pairs of vertices. Subtype 4 is hidden 1.15 GoM score units directly behind the origin of the coordinate system. Each bubble represents the estimated GoM scores for one subject, except at the vertices for subtypes 1 and 2, where the bubbles represent ten (seven males, three females) and three (female) subjects, respectively; the vertices for subtypes 3 and 4 are unoccupied. The location of each bubble is determined by the subject’s GoM scores on subtypes 1–3. The area of each bubble declines linearly with the GoM score on subtype 4, such that the bubble vanishes at the subtype 4 vertex. This is why the bubbles for subgroup 4 are much smaller than for the other subgroups. The GoM scores for the 229 subjects are listed in Additional file 1: Table A.6