mu_y = m mu_x + mu_z, sigma_y = sqrt(m^2 sigma_x^2 + sigma_z^2),
r = m sigma_x / sigma_y, the reverse slope r sigma_x / sigma_y,
the regression-to-the-mean factor r^2 and the excess-score factor
sqrt((1-r)/(1+r)). Mirrors morie.fn ch6 model modules (and the
misnamed "10e6").
Usage
morie_linear_corr_model(m, sigma_x, sigma_z, mu_x = 0, mu_z = 0)
Arguments
- m
slope of the underlying relation.
- sigma_x, sigma_z
spreads of signal and noise.
- mu_x, mu_z
means of signal and noise.
Value
list: mu_y, sigma_y, r, reverse_slope, r_squared,
excess_factor.
References
Morin (2016), eqs. (6.3)-(6.6), (6.17), (6.36),
(6.40), (6.76), (6.81).
Examples
morie_linear_corr_model(1, 7.5, 10.6)$sigma_y
#> [1] 12.98499
