TABLE 5.

Results of a linear mixed-effects model of Granger causality between the logarithm of movement speed (Speed) and the z-scored ΔF/F of cholinergic activity (ACh) with four fixed effects, namely the y-intercept, the Granger causality magnitude with two levels of direction, namely from the logarithm of movement speed to cholinergic activity (Speed → ACh) and from cholinergic activity to the logarithm of movement speed (ACh → Speed), lighting condition with two levels, namely light and darkness, and the interaction between direction in Granger causality and lighting condition.

Fixed effects coefficients
Name	Estimate	SE	t-statistic	DF	P-value	95% CI
y-intercept	0.00635	0.00105	6.05	200	<0.0001	[0.00428 0.00842]
ACh –> Speed	–0.00198	0.00105	–1.88	200	0.061	[–0.00406 9.48 × 10–05]
Darkness	0.00018	0.00061	0.29	200	0.773	[–0.00102 0.00137]
(ACh –> Speed)*Darkness	–0.00065	0.00068	–0.96	200	0.338	[0.33829 –0.00199]
Model formula
${\text{y}}_{\text{ijmkl}}{\text{= β}}_{\text{0}}\text{+}{\displaystyle \sum }_{\text{j=2}}^2{\text{β}}_{\text{1j}}{\text{I[S]}}_{\text{ij}}\text{+}{\displaystyle \sum }_{\text{m=2}}^2{\text{β}}_{\text{2m}}\text{I}{\left[\text{D}\right]}_{\text{im}}\text{+}{\displaystyle \sum }_{\text{j=2}}^2{\displaystyle \sum }_{\text{m=2}}^2{\text{β}}_{\text{3jm}}\text{I}{\left[\text{S}*\text{D}\right]}_{\text{ijm}}{\text{+b}}_{\text{0k}}{\text{A}}_{\text{k}}{\text{+b}}_{\text{0l}}{\text{S}}_{\text{l}}{\text{+ b}}_{\text{1kj}}{\text{S}}_{\text{kj}}{\text{+b}}_{\text{1lj}}{\text{S}}_{\text{lj}}{\text{+b}}_{\text{2km}}{\text{D}}_{\text{km}}{\text{+b}}_{\text{2lm}}{\text{D}}_{\text{lm}}{\text{+b}}_{\text{3kjm}}{\text{(S}*\text{D)}}_{\text{kjm}}{\text{+b}}_{\text{3ljm}}{\text{(S}*\text{D})}_{\text{ljm}}{\text{+ ε}}_{\text{ijmkl}}\text{,}$ where index i corresponds to the # of observations, index j corresponds to the direction of Granger causality, index m corresponds to light or darkness, index k corresponds to the animal identity, and index l corresponds to the session identity. Ak represents the kth animal, Sl represents the lth session, I[S]ij is the dummy variable representing level j of direction in Granger causality, I[D]im is the dummy variable representing level m of the darkness type, b the random mixed effects, εijmkl the observation error, and yijmkl the response variable representing z-scored ΔF/F. Random effects and observation error are normally distributed around zero.
Model statistics
AIC: -1762.5	BIC: -1719.4	Log-likelihood: 894.26	Deviance: -1788.5

Random effects of the animal (n = 5) and sessions (n = 102, 55 “light” sessions and 47 “dark” sessions) on all fixed effects were included in addition to a random error term. Total number of observations: 204; Fixed effects coefficients: 4; Random effects coefficients: 428; Covariance parameters: 9. SE, standard error; DF, degree of freedom; CI, confidence interval.