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. 2021 Feb 1;51(3):237–249. doi: 10.1007/s10519-020-10035-7

Table 3.

Means and standard deviation of parameter estimates in simulation 1–3 based on 500 replications (Nmz = 1000; Ndz = 1000)

b
est		 σ2Ap σ2Aq σ2C* σ2F σ2C = 
σ2C* + σ2F 		σ2E σA,C
Simulation 1
True 0.20 0.30 0.20 0 0.20 0.30 0.00
 Mean No 0.199 0.298 0.197 – – 0.301 0.003
 s.d. 0.026 0.045 0.058 – – 0.013 0.033
 s.e.(mean) 0.0012 0.0020 0.0026 0.0006 0.0015
 Mean Yes 0.184* 0.316* 0.199 – – 0.300 0.001
 s.d. 0.026 0.047 0.063 – – 0.013 0.036
 s.e.(mean) 0.0012 0.0021 0.0028 0.0006 0.0016
Simulation 2
True 0.20 0.30 0 0.091 0.091 0.30 0.125
 Mean No 0.200 0.300 – 0.087 – 0.301 0.126
 s.d. 0.026 0.047 – 0.078 – 0.013 0.037
 s.e.(mean) 0.0012 0.0021 0.0035 0.0006 0.0017
 Mean 2 Yes 0.189* 0.315* – 0.090 – 0.300 0.124
 s.d. 0.025 0.046 – 0.079 – 0.013 0.038
 s.e.(mean) 0.0011 0.0021 0.0035 0.0006 0.0017
Simulation 3
True 0.20 0.30 0.20 0.108 0.308 0.30 0.125
 Mean No 0.200 0.302 – – 0.302 0.300 0.126
 s.d. 0.026 0.045 – – 0.077 0.013 0.039
 s.e.(mean) 0.0012 0.0020 0.0034 0.0006 0.0017
 Mean Yes 0.185* 0.320* – – 0.304 0.299 0.125
 s.d. 0.026 0.050 – – 0.087 0.013 0.041
 s.e.(mean) 0.0012 0.0022 0.0039 0.0006 0.0018
Simulation 2a
 True 0.20 0.30 0 0.091 0.091 0.30 0.125
 Mean Yes 0.189* 0.314* – 0.095 – 0.299 0.122
 s.d. 0.025 0.045 – 0.061 – 0.013 0.032
 s.e.(mean) 0.0011 0.0020 0.0027 0.0006 0.0014

Values shown in bold are the true parameter values

Simulation 2a: subject to constraints of positive definiteness of the Ap–C and Aq–C covariance matrices

b est: weights for PRS estimated (yes), or fixed to true values (no)

Simulation 1: r(A,F + C) = 0; σ2Ph = 0.20 + 0.30 + 0.20 + 0.30 = 1; r(MZ) = 0.70 & r(DZ) = 0.45; prPH = 0.2; pr2σAC = 0.0

Simulation 2: r(A,F + C) = 0.125/sqrt(0.5*0.091) = 0.586; σ2Ph = 1.141; r(MZ) = 0.74 & r(DZ) = 0.52; prPH = 0.141; pr2σAC = 0.353

Simulation 3: r(A,F + C) = 0.125/sqrt(0.5*0.308) = 0.318; σ2Ph = 1.358; r(MZ) = 0.78 & r(DZ) = 0.59; prPH = 0.147; pr2σAC = 0.368

*Deviation from true value is significant given α = 0.01

Note in fitting the model we estimated the single variance term σ2C, which equals σ2F + σ2C*. In simulations 1, σ2F is zero and σAC = 0; in simulation 2 σ2C* is zero, σAC > 0; in simulation 3, σ2F > 0, σ2C* > 0, and σAC > 0