. 2019 Dec 27;9:19878. doi: 10.1038/s41598-019-56404-z

Table 1.

LME models with different random effects.

$C_{m k i} = β_{0} + \sum_{k = 2}^{2} β_{1 k} T_{m k} + \sum_{i = 2}^{117} β_{2 i} V_{m i} + \sum_{k = 2}^{2} \sum_{i = 2}^{117} β_{3 k i} T_{m k} V_{m i} + ε_{m k i}$	(1)
$C_{m k i n} = β_{0} + \sum_{k = 2}^{2} β_{1 k} T_{m k} + \sum_{i = 2}^{117} β_{2 i} V_{m i} + \sum_{k = 2}^{2} \sum_{i = 2}^{117} β_{3 k i} T_{m k} V_{m i} + β_{0 n} {(S)}_{n} + ε_{m k i n}$	(1a)
$C_{m k i n} = β_{0} + \sum_{k = 2}^{2} β_{1 k} T_{m k} + \sum_{i = 2}^{117} β_{2 i} V_{m i} + \sum_{k = 2}^{2} \sum_{i = 2}^{117} β_{3 k i} T_{m k} V_{m i} + β_{0 n i} {(S ⁎ V)}_{n i} + ε_{m k i n}$	(1b)
$C_{m k i n} = β_{0} + \sum_{k = 2}^{2} β_{1 k} T_{m k} + \sum_{i = 2}^{117} β_{2 i} V_{m i} + \sum_{k = 2}^{2} \sum_{i = 2}^{117} β_{3 k i} T_{m k} V_{m i} + β_{0 n i k} {(S ⁎ V ⁎ T)}_{n i k} + ε_{m k i n}$	(1c)

C = Centrality response variable and the fixed-effects for all models are T and V, T = dummy variable representing 2 training groups categories, V = dummy variable representing 117 VOIs categories (4 white-matter regions were set to the same category, hence 117 instead of 120), S = subjects variable, m = 1,2,3…,4800 (centrality observations indices = 20 subjects x 120 VOIs x 2 training groups), k = 1,2 (T categories indices), i = 1,2,3 … 117 (V categories indices). S*V = intercept variance across V grouped by S, S*V*T = intercept variance across V grouped by T and S.