Table 4.

Performance metrics, parameter estimates and approximate T-test results for the twin study example. Standard errors for the fixed effects parameter estimates are given in brackets alongside the corresponding estimates. For each model parameter, a T-statistic, direct-SW degrees of freedom estimate, and p-value are provided, corresponding to the approximate t-test for a nonzero effect. p-values that are significant at the 5% level are indicated using a ${}^{\ast }$ symbol

Estimation method		OLS	Powell	FS
Performance
l (Log-likelihood)		$-2133.49$	$-2005.83$	$-2005.81$
t (Time in seconds)		$<.001$	93.32	2.31
Fixed effects parameters (Standard Errors)
${\beta }_0$ (Intercept)		121.46 (3.61)	118.43 (3.40)	118.34 (3.42)
${\beta }_1$ (Age)		$-0.11$ (0.12)	$-0.04$ (0.11)	$-0.04$ (0.11)
${\beta }_2$ (Sex)		$-10.74$ (5.07)	$-7.22$ (4.64)	$-7.61$ (4.66)
${\beta }_3$ (Age/sex)		0.45 (0.18)	0.33 (0.16)	0.34 (0.16)
${\beta }_4$ (PSQI score)		$-0.49$ (0.12)	$-0.31$ (0.10)	$-0.30$ (0.10)
Covariance parameters
${\sigma }_a^2$ (Additive genetic)		0.00	48.20	50.67
${\sigma }_c^2$ (Common environment)		0.00	27.53	26.89
${\sigma }_e^2$ (Residual error)		110.04	33.57	32.71
Tests for Fixed Effects
	T statistic	33.67	34.83	34.65
Intercept	degrees of freedom	1105.00	920.59	921.57
	p value	$<.{001}^{\ast }$	$<.{001}^{\ast }$	$<.{001}^{\ast }$
	T statistic	$-0.94$	$-0.350$	$-0.320$
Age	degrees of freedom	1105.00	907.44	908.42
	p value	.350	.726	.749
	T statistic	$-2.12$	$-1.56$	$-1.63$
Sex	degrees of freedom	1105.00	833.01	832.96
	p value	$.{034}^{\ast }$	.120	.103
	t-statistic	2.58	2.03	2.10
Age/sex	degrees of freedom	1105.00	830.53	830.61
	p value	$.{010}^{\ast }$	$.{043}^{\ast }$	$.{036}^{\ast }$
	T statistic	$-4.25$	$-3.19$	$-3.17$
PSQI score	degrees of freedom	1105.00	933.67	928.87
	p value	$<.{001}^{\ast }$	$.{001}^{\ast }$	$.{001}^{\ast }$