Supplementary materials
1. AICc calculations for model best fit
The Akaike Information Criterion with small sample correction (AICc) was used for model selection
(Burnham and Anderson, 2002; Sugiura, 1978; Akaike, 1974). AICc assesses the relationship between the
goodness of fit of models and their number of parameters, penalizing models that over-fit data. AICc is
calculated using the formula:
Where k is the number of parameters in the model, SSE is the sum of squared errors for the model fit,
and n is the sample size. Using this selection process, models with lower AICc values are considered to
be better (Akaike, 1981).
Previous models have fit adaptation data with exponential models (Bock et al., 2005, Krakauer et al.,
2005). Here we compared three exponential decay models:
Two parameter model:
Three parameter model:
Four parameter model:
The two parameter model predicts the error in epoch n by estimating an initial level of error i and a decay
constant λ. The three parameter model adds a constant term c. The four parameter model predicts a
double exponential process to model error reduction, separating the curve into two parts with separate
initial error levels (i1 and i2) and decay constants (λ1 and λ2).
We calculated AICc scores for each model based on the fit to the mean data for each group. The two
parameter model provided the best (lowest) AICc scores in each condition, and was therefore used for
furher analysis of the data (see main text).
Adaptation
Deadaptation
Older
Younger
Older
Older
Younger
Older
Sham
Sham
Anodal
Sham
Sham
Anodal
2 parameter model
3.67
3.97
3.16
5.57
2.05
4.37
3 parameter model
6.00
5.46
5.19
9.09
5.68
8.06
4 parameter model
14.65
16.7
16.29
16.79
12.10
14.21
Supplementary Table 1: AICc values for the each model fit to the mean data for each group. Note that
lower AICc values are indicative of a ‘better’ model.
Supplementary References
Akaike, H. 1974. A new look at the statistical model identification. IEEE Transactions on Automatic
Control, 19, 716-723.
Burnham, K.P., Anderson, D.R. 2002. Model selection and multimodal inference: a practical information
theoretic approach (2nd ed.), Springer-Verlag, ISBN 0-387-95364-7.
Sugiura, N. 1978. Furhter analysis of the data by Akaike’s information criterion and the finite corrections.
Communications in Statistics – Theory and Methods A7: 13-26.
Krakauer, J.W., Ghez, C., Ghilardi, M.F., 2005. Adaptation to visuomotor transformations:
consolidataion, interference and forgetting. J Neurosci,25, 473-478.