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

egression model evaluating the data produced by the hybrid model, but not in the regression
model for the strictly decomposed data as the latter model does not incorporate a
representation of overall magnitude. Finally, following Occam’s razor the hybrid model
should only be chosen as the model predicting the empirical data in the best way when its
performance is found to be reliably superior to the performance of the strictly decomposed
model which is the more parsimonious one.
In the next section the architecture and the implementation of the three models will be
described before actually reporting the models’ performance in two-digit number comparison.
METHODS
Model description
According to the model assumptions on the mental representation of two-digit numbers
put forward to account for the empirical data, three different neural network models were
programmed: (i) a holistic model in which to-be-compared two-digit numbers (i.e., indicated
as #1 and #2) are represented as integrated entities (see Figure 1, Panel A), (ii) a strictly
decomposed model with two distinct representations of tens and units (see Figure 1, Panel B)
and (iii) a hybrid model in which the characteristics of the former two models are combined
so that separate representations of tens and units operate in parallel with a holistic
representation of overall magnitude of the respective number (see Figure 1, Panel C). The
neural networks reflecting each of these models were programmed using MatLab 7.4.0.
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