Statistical importance of the parameters.

<p>The negative log-likelihood per cell per time bin for the constant field model (A: data set 1, C: data set 2) and Gaussian field model (B: data set 1, D: data set 2) with different covariates included. Smaller values correspond to better explanatory power. The blue segment of the bar shows the negative log-likelihood. Adding parameters to a model will yield a log-likelihood-value greater than or equal to the model with fewer parameters. To avoid overfitting by including parameters, we performed an Akaike correction on the log-likelihood (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004052#sec004" target="_blank">Material and Methods</a>). The value of the Akaike-correction is shown for each covariate on top of the negative log-likelihood (blue) for each model: head direction (red), theta preference (yellow), and couplings (green). In (C, D), grey is the Akaike-correction due to the Gaussian spatial fields. These two plots show that adding the couplings always increases the explanatory power of the model, e.g. for the model with theta including couplings reduces the negative log-likelihood more than the penalty from the Akaike-correction for the added number of parameters.