Table 4.

Spindle characteristics explain little variance in overall spindle frequency

	Frequency (Hz)		Variance Explained
	$\beta$	CI	R2m	R2c
Duration (s)	−0.17	−0.18 to −0.16	0.004	0.378
Intraspindle SD (Hz)	−0.43	−0.43 to −0.42	0.036	0.367
Amplitude (µV)	−1.68e-03	−1.73e-03 to −1.63e-03	0.027	0.417
High γ power (µV2)	0.23	0.23 to 0.24	0.013	0.370
Frequency change (Hz/s)	−3.9e-03	−4.7e-03 to −3.1e-03	6.7e-05	0.370

Results were unchanged after controlling for sleep stage, regional differences, and frequency of seizures (Table 5). We applied a LMEM with nested random effects, channels within patients on 550 475 spindle observations 360 channels, and 20 patients. Estimates, $\beta$, represent linear slopes of the predictors (table rows) on overall spindle frequency with 95% confidence intervals (CIs). for example, the duration $\beta$ of −0.17 indicates that a 1-s increase in spindle duration is associated with a −0.17-Hz decrease in frequency. The columns under “variance explained” are the marginal variance explained R²_m, or that explained by the fixed effect alone (e.g., duration), and the conditional variance explained R²_c, or that explained by both fixed and random effects. The variance explained was estimated for each fixed-effect (row) independently. For example, the additional variance in frequency explained by duration across the entire dataset is very small (0.004) compared with the variance explained by the effect of duration and the grouping of spindles within specific channels and patients (0.378). The parameter estimates and hypothesis test outcomes did not significantly change after improving normalization of residuals by data transformation and outlier removal (Table 5).