Table II. Specification of the full model.

Algebraic model terma	Variable or factor	Effect type and assumptionb	Subscript range (main effects) or number of terms (interactions)	Terms in the computational modelc
yghijl	Response variable			log10(MFI)
μ	Mean MFI of phospho-Akt measurements from vehicle-treated samples		1	Intercept
vg	Vehicle main effects	Fixed	g = 1,2	(ligand vehicle)d, dmso
kh	Kit (analyte) main effect	Fixed	h = 1–16	(akt)d, erk, gsk, ikb, jnk, p38, p70, p90, cjun, creb, hsp27, irs, mek, p53, stat3, s6rp
(vk)gh	Vehicle × Kit interaction	Fixed	15	dmso × 15 kits
ti	Treatment main and interaction effects	Fixed	i = 1–17	Main: d, 6, L, N, G
				2-way interactions: d×6, d×L, d×N, d×G, 6×L, 6×N, 6×G, N×G
				3-way interactions: d×6×L, d×6×N, d×6×G, d×N×G
(kt)hi	Treatment × Kit interactions	Fixed	17 treatment effects × 15 kits = 255	Each treatment term × 15 kits
δj	Day main effect	Random	j = 1–3	d1, d2, d3
		d∼N(0,σd2)
(kδ)hj	Day × Kit interaction	Random	3 days × 16 kits = 48	Each day term × each of the 16 Kit terms
		(kd)∼N(0,σkd2)
(tδ)ij	Day × Treatments (main effects only) interaction	Random	3 days × 5 treatments × 2 levels of each treatment = 30	Each day term × each of d, 6, L, N and G
		(td)∼N(0,σtd2)
ωl	Well (sample) effects	Random	l = 1–86	Well addresses (e.g., A9, G12, etc.)
		w∼N(0,σw2)
ϵghijl	Residual error	Random
		e∼N(0,σ2)

^a The algebraic equation is a compact representation of the mixed-effects model that must be translated into a computationally readable form. Although R can handle categorical variables specified in compact form (e.g., specifying a factor such as “Kit” and listing its constituents as levels in the data column), doing so precludes eliminating terms from within that factor during variable selection. We therefore explicitly specified each level of the factor as its own term in models subjected to variable selection. See the spreadsheet file in the Supplementary Information for more details.

^b The random effects were assumed to be independent values of their respective variables that are normally distributed with mean of zero and variance as indicated.

^c Legend: d = Dexamethasone, 6 = interleukin-6, L = interleukin-1α, n = tumor necrosis factor-α, G = transforming growth factor-α, d1 = Day 1, d2 = Day 2, d3 = Day 3.

^d Terms listed in brackets did not have their own terms in the computational model but instead served to estimate the intercept, relative to which the effects of the remaining terms were computed.