2^k factorial-design analysis with main effects + interactions

Returns main effects (difference of means at +1 vs -1 per factor), all interaction effects, and half-normal-plot coordinates for Daniel's method (which lets the user separate active effects from a null half-normal line on the same axes).

Usage

mrm_factorial_2k(data, response_col, factor_cols)

Arguments

data: data.frame with response_col and factor_cols. Factor columns may be coded as +/- 1 or any binary; non-(-1,1) columns are re-coded.
response_col: Numeric response column.
factor_cols: Character vector of factor column names.

Value

Named list with main_effects, interaction_effects, half_normal_coords (data.frame), n, k, interpretation.

Examples

# 2^3 full factorial: 8 runs, factors A, B, C in {-1, +1}.
set.seed(2026)
lvl <- c(-1, 1)
df <- expand.grid(A = lvl, B = lvl, C = lvl)
df$y <- 10 + 2 * df$A + 1.5 * df$B + 0.5 * df$A * df$B + rnorm(8, 0, 0.2)
res <- mrm_factorial_2k(df,
  response_col = "y",
  factor_cols = c("A", "B", "C")
)
res$main_effects
#> $A
#> [1] 3.802065
#> 
#> $B
#> [1] 3.102053
#> 
#> $C
#> [1] -0.221669
#> 
res$interaction_effects
#> $`A x B`
#> [1] 1.147038
#> 
#> $`A x C`
#> [1] -0.015508
#> 
#> $`B x C`
#> [1] 0.040693
#> 
#> $`A x B x C`
#> [1] 0.009409
#>