The influence of the place-value structure of the Arabic number ...

Different origins of the compatibility effect in the hybrid and the strictly decomposed
model
When inspecting the development of the connection weights (see Appendix B) in the
strictly decomposed as well as the hybrid model there are similarities but also important
differences. On the one hand, the output of both models was significantly driven by the digits
at the tens position. However, as indicated by a reliable unit-decade compatibility effect
observed for the modelled RT data as well as the significant influence of unit distance in the
stepwise regression analyses there seemed to be a considerable influence of the unit digits as
well. Modelled item RT was reliably longer for incompatible than for compatible number
pairs. Additionally, the compatibility effect was more pronounced for large as compared to
small unit distances. Finally, item RT increased as unit distance decreased. As unit distance is
negative for incompatible number pairs (e.g., 37_ 62 decade distance: 6 - 3 = 3; unit
distance: 2 - 7 = -5) the latter result again corroborates the interpretation of the compatibility
effect to be determined by the magnitude of the unit distance. Taken together, these findings
suggest that the results pattern observed in the empirical data (cf. Nuerk et al., 2001) can be
simulated by both the strictly decomposed as well as the hybrid model of two-digit number
representation.
Nevertheless, a closer look at the development of the connection weights also showed
that the influence of the digits at the unit position was not identical in the strictly decomposed
and the hybrid model. In the decomposed model the compatibility effect is determined by
specific activation differences of the unit digits for compatible and incompatible number pairs
and thus in line with the considerations by Nuerk and Willmes (2005; see also Knops, 2006).
Yet, for the hybrid model, the direct influence of the unit digits on the output was less
emphasized. Instead, the connection weights for the unit digits between the input layer and the
hidden layer of the hybrid model were not altered considerably by the learning procedure and
remained by far smaller than the weights for the tens digits and overall magnitude. As the
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