Table 1 Simulation parameter choices. The loading value for variable i is the density value of a normal distribution with mean μ and standard deviation σ, denoted as N(i;μ,σ). The noise terms were drawn from a normal distribution with zero mean. The scores were drawn from a standard normal distribution. The variances of the noise terms are such that the expected sum of squares of the noise account for 100α % (equal to 5 or 50 %) of the total sum of squares

N

500

500

p,q

[100,50]

[500,250]

W

[N(i;60,10)] _{i =1,…,100}

[N(i;300,50)] _{i =1,…,500}

C

[N(i;70,5)] _{i =1,…,50}

[N(i;175,25)] _{i =1,…,250}

P _{Y ⊥}

[N(i;20,20)] _{i =1,…,100}

[N(i;100,100)] _{i =1,…,500}

P _{X ⊥}

[N(i;15,10)] _{i =1,…,50}

[N(i;75,50)] _{i =1,…,250}

B _T

2

2

${\sigma }_T^2,{\sigma }_{T_{\mathit{\text{Y}}\perp }}^2,{\sigma }_{U_{\mathit{\text{X}}\perp }}^2$

[1,1,1]

[1,1,1]

${\sigma }_E^2,{\sigma }_F^2,{\sigma }_H^2$

$\frac{\alpha }{(1-\alpha )}[0.02,0.104,4]$

$\frac{\alpha }{(1-\alpha )}[0.004,0.021,4]$