The Problem
Method 1: As Model Comparisons
Method 2: Paternoster et al (1998)
Method 3: emmeans \beta_{\text{n_comps}}\).
Method 2: Paternoster et al (1998)
According to Paternoster et al. (1998), we can compute a t-test to compare the coefficients:
bs <- coef(m)[-1]
V <- vcov(m)[-1, -1]
tibble::tibble(
diff_estim = diff(bs),
diff_SE = sqrt(V[1, 1] + V[2, 2] - 2 * V[1, 2]),
t_stat = diff_estim / diff_SE,
df = df.residual(m),
p_value = 2 * pt(abs(t_stat), df = df, lower.tail = FALSE)
)
#> # A tibble: 1 x 5
#> diff_estim diff_SE t_stat df p_value
#> <dbl> <dbl> <dbl> <int> <dbl>
#> 1 -0.402 0.0251 -16.0 497 6.96e-47
This gives the exact same results as the first method! (\(t^2 = (-16)^2 = 256\) is the ...
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