Fig. 8: Modelling of the weighted cosine systematicity (sys_cos_w) between Standard Chinese (SC) and the Shanghai local dialectal varieties.

The butterfly-scatter-violin-box plots show the value of sys_cos_w (multiplied by 1000 and natural log-transformed) for each time slice (old, middle, and new) and mapping direction (SC to SH local, and SH local to SC). Each translucent point on the scatter plot represents one mapping, with its horizontal coordinate representing the sys_cos_w value (the vertical coordinate is jittered). The coloured violin shapes indicate the probability density of the sys_cos_w values, while the box plots represent the range, quartiles, median and odd values, with means indicated in yellow (for SC to SH local) and red (for SH local to SC). Based on the Linear Mixed Effects results, significance codes are marked on conditions with positive effects, main effects annotated on the grey cross lines at the centre, and interaction effects in the panel relating to the interaction term. Blue shades are added to cells representing positive main effects for the new varieties, and red shades for positive main effects for the old varieties. Additionally, blue shades in the right corner of cells signify positive interaction effects for the mapping SH local to SC, and red shades for negative interaction effects. The subplots are arranged vertically according to the pairs of linguistic varieties, and horizontally according to the phonemic units.