. 2017 Mar 17;17:44. doi: 10.1186/s12874-017-0322-8

Table 4.

Simulation results when Y has an asymmetric distribution

		Model A $\hat{Y} = \hat{α} + \hat{β} \cdot X$	Model B $\hat{Y} = \hat{α} + \hat{β} \cdot {log}_{b} (X)$	Model C $\hat{{log}_{a} (Y)} = \hat{α} + \hat{β} \cdot X$	Model D $\hat{{log}_{a} (Y)} = \hat{α} + \hat{β} \cdot {log}_{b} (X)$
Beta-hat coefficient and standard error from regression model		$\hat{β}$ = 0.625 se( $\hat{β}$ ) = 0.254	$\hat{β}$ = 5.834 se( $\hat{β}$ ) = 2.441	$\hat{β}$ = 0.011 se( $\hat{β}$ ) = 0.005	$\hat{β}$ = 0.103 se( $\hat{β}$ ) = 0.044
Absolute change in Y for an absolute change of c units in X	Effect size	0.625	0.557	0.551	0.493
Absolute change in Y for an absolute change of c units in X	95% CI	(0.128–1.122)	(0.101–1.013)	(0.100–1.006)	(0.080–0.909)
Absolute change in Y for a relative change of k times in X	Effect size	0.625	0.557	0.551	0.493
Absolute change in Y for a relative change of k times in X	95% CI	(0.128–1.122)	(0.101–1.013)	(0.100–1.006)	(0.080–0.909)
Relative change in Y for an absolute change of c units in X	Effect size	1.0125	1.0111	1.0110	1.0099
Relative change in Y for an absolute change of c units in X	95% CI	(1.0026–1.0224)	(1.0020–1.0203)	(1.0020–1.0201)	(1.0016–1.0182)
Relative change in Y for a relative change of k times in X	Effect size	1.0125	1.0111	1.0110	1.0099
Relative change in Y for a relative change of k times in X	95% CI	(1.0026–1.0224)	(1.0020–1.0203)	(1.0020–1.0201)	(1.0016–1.0182)

Note: c = 1 and k = 1.1