Fig. 3
From: Robust estimation of the effect of an exposure on the change in a continuous outcome
Performance of the REM and cprobit model in estimating the transformation parameter in simulation studies. Mean and standard error (panel a), coverage (panel b) and type I error (panel c) of the estimated transformation parameter (\( \hat{\lambda} \)) from the random effects model (REM) and the conditional probit (cprobit) model with the Box-Cox transformation for strong effect (βλ = − 0.06), with \( \lambda =0,\frac{1}{3},1 \), normal and skewed intercept terms, n = 300, 1200. Solid vertical grey lines indicate the true λ values in panel a, and the nominal value of the coverage and type I error in panel b and c. Dashed vertical grey lines indicate ±1% deviation from the nominal values in panel b and c. (Note: Results for the REM with skewed intercepts are beyond the plot range: (a) \( \hat{\lambda}<0.1 \) when λ = 1, \( \hat{\lambda}<-0.1 \) when λ = 1/3, and \( \hat{\lambda}<-0.19 \) when λ = 0 for panel A; (b) coverage at 5.5% or below for panel b; and (c) type I error at 94.5% or above for panel c)