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

model allow for quantitatively predicting the RT pattern in a magnitude comparison task. In
all cases, the models can only make ordinal predictions about mean RT differences under
different conditions (e.g., small vs. large distances between the to-be-compared numbers);
however, it is not possible to quantify these differences. At this point, computational models
would be informative as they offer the possibility to evaluate model predictions
quantitatively. Therefore, the current study aimed at differentiating between the three models
of two-digit number processing described above via a computational modelling approach
validated by empirical data from number magnitude comparison. In particular, we intended to
distinguish between the strictly decomposed and the hybrid processing model by means of
their modelled data as these two models cannot be differentiated by empirical RT/error data.
Nevertheless, evaluation of the fit of the data produced by either of these models and the
empirical data would be informative about the plausibility and validity of both strictly
decomposed as well as hybrid processing of two-digit numbers.
Before turning to modelling specifics, differences between the current study and the
rationale behind other recent attempts to implement number magnitude representation into
computational neural networks shall be discussed briefly.
Computational models of number magnitude representation
As already touched on before, computational models offer the possibility to evaluate
the plausibility and validity of a proposed model not only qualitatively but also on a more fine
grain quantitative level. Quantitative computational models allow for a statistical appraisal of
the fit between modelled and empirical data – thereby, qualifying a more objective validation
of models predictions. For the case of number processing, most previous computational
models of number magnitude representation incorporated some kind of number line
assumption (e.g., McCloskey & Lindemann, 1992; Viscuso, Anderson, & Spoehr 1989, Zorzi
& Butterworth, 1999). Following this conceptualization each number is represented by a
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