Polynomial coding sets the grand mean as the intercept. Each contrast tests a trend (linear, quadratic, cubic, etc.). This is only suitable for ordered factors.
contr_code_poly(fct, levels = NULL)the factor to contrast code (or a vector)
the levels of the factor in order
the factor with contrasts set
df <- sim_design(within = list(time = 1:6),
mu = 1:6 + (1:6-3.5)^2,
long = TRUE, plot = FALSE)
df$time <- contr_code_poly(df$time)
lm(y ~ time, df) %>% broom::tidy()
#> # A tibble: 6 × 5
#> term estimate std.error statistic p.value
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 (Intercept) 6.36 0.0404 158. 0
#> 2 time^1 4.13 0.0989 41.8 7.85e-179
#> 3 time^2 6.21 0.0989 62.8 1.64e-264
#> 4 time^3 0.122 0.0989 1.23 2.18e- 1
#> 5 time^4 0.0571 0.0989 0.578 5.64e- 1
#> 6 time^5 -0.0155 0.0989 -0.157 8.75e- 1