Algebraic model term^{a} | Variable or factor | Effect type and assumption^{b} | Subscript range (main effects) or number of terms (interactions) | Terms in the computational model^{c} |
---|---|---|---|---|

y_{ghijl} | Response variable | log_{10}(MFI) | ||

μ | Mean MFI of phospho-Akt measurements from vehicle-treated samples | 1 | Intercept | |

v_{g} | Vehicle main effects | Fixed | g = 1,2 | (ligand vehicle)^{d}, dmso |

k_{h} | 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 |

t_{i} | 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 |

δ_{j} | Day main effect | Random | j = 1–3 | d1, d2, d3 |

d∼N(0,σ_{d}^{2}) | ||||

(kδ)_{hj} | Day × Kit interaction | Random | 3 days × 16 kits = 48 | Each day term × each of the 16 Kit terms |

(kd)∼N(0,σ_{kd}^{2}) | ||||

(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,σ_{td}^{2}) | ||||

ω_{l} | Well (sample) effects | Random | l = 1–86 | Well addresses (e.g., A9, G12, etc.) |

w∼N(0,σ_{w}^{2}) | ||||

ϵ_{ghijl} | Residual error | Random | ||

e∼N(0,σ^{2}) |

↵

^{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.