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. Author manuscript; available in PMC: 2021 Sep 1.
Published in final edited form as: Psychother Res. 2020 Jun 2;30(7):885–899. doi: 10.1080/10503307.2020.1769875

Table 5.

Two-level simulation results for Random Intercept Cross-Lagged Panel Model, ignoring therapist-level random slopes.

Slope SD = 0.10 Slope SD = 0.15
ICCslope = .05 β SE β SE
NL2 NL3 Est.a Biasb Powerc SDd Est.e Coverg Est.a Biasb Powerc SDd Est.e Coverg
50 5 0.284 −5.3% 83.1% 0.100 0.093 92.7% 0.283 −5.8% 81.2% 0.103 0.094 92.2%
50 10 0.286 −4.8% 82.8% 0.102 0.093 92.4% 0.285 −5.1% 82.2% 0.105 0.094 91.6%
100 5 0.296 −1.3% 98.7% 0.068 0.065 93.8% 0.296 −1.5% 98.3% 0.071 0.066 92.5%
100 20 0.295 −1.6% 98.5% 0.068 0.065 94.0% 0.294 −1.9% 98.1% 0.070 0.066 93.8%
200 5 0.297 −0.9% 100.0% 0.048 0.046 94.2% 0.296 −1.2% 100.0% 0.050 0.046 92.6%
200 20 0.297 −1.0% 100.0% 0.047 0.046 94.7% 0.296 −1.3% 100.0% 0.049 0.046 93.8%
200 40 0.297 −1.0% 100.0% 0.047 0.046 94.7% 0.296 −1.3% 100.0% 0.049 0.046 93.7%
ICCslope = .10 Est.a Biasb Powerc SDd Est.e Coverg Est.a Biasb Powerc SDd Est.e Coverg
50 5 0.284 −5.3% 82.7% 0.100 0.093 92.4% 0.283 −5.8% 80.8% 0.105 0.094 91.9%
50 10 0.286 −4.8% 82.7% 0.102 0.093 92.2% 0.284 −5.2% 82.5% 0.105 0.094 91.5%
100 5 0.296 −1.3% 98.7% 0.069 0.065 93.3% 0.296 −1.4% 98.1% 0.073 0.066 91.9%
100 20 0.295 −1.6% 98.5% 0.068 0.065 94.2% 0.294 −1.9% 98.2% 0.070 0.066 93.4%
200 5 0.297 −0.9% 100.0% 0.049 0.046 93.3% 0.296 −1.2% 100.0% 0.053 0.046 91.4%
200 20 0.297 −1.0% 100.0% 0.047 0.046 94.4% 0.296 −1.3% 100.0% 0.049 0.046 93.8%
200 40 0.297 −1.0% 100.0% 0.047 0.046 94.3% 0.296 −1.3% 100.0% 0.049 0.046 93.8%
ICCslope = .20 Est.a Biasb Powerc SDd Est.e Coverg Est.a Biasb Powerc SDd Est.e Coverg
50 5 0.284 −5.4% 82.2% 0.102 0.093 92.0% 0.283 −5.7% 80.5% 0.107 0.094 91.4%
50 10 0.285 −4.9% 83.0% 0.102 0.093 92.2% 0.284 −5.3% 81.7% 0.106 0.094 91.1%
100 5 0.296 −1.2% 98.3% 0.070 0.065 92.7% 0.296 −1.3% 97.8% 0.0754 0.0658 91.2%
100 20 0.295 −1.7% 98.5% 0.068 0.065 94.2% 0.294 −1.9% 98.0% 0.0705 0.066 93.3%
200 5 0.297 −0.9% 100.0% 0.051 0.046 91.8% 0.296 −1.2% 100.0% 0.0567 0.0461 89.3%
200 20 0.297 −1.0% 100.0% 0.047 0.046 94.6% 0.296 −1.2% 100.0% 0.0502 0.0463 93.4%
200 40 0.297 −1.0% 100.0% 0.047 0.046 94.3% 0.296 −1.3% 100.0% 0.0493 0.0462 93.3%

Note.

a

Average estimate of β over 2000 replications,

b

calculated as β^¯ββ,

c

proportion of 2000 replications yielding significant estimate when β = .30,

d

standard deviation of β over 2000 replications (used as estimate of population standard error),

e

average of estimated standard errors over 2000 replications,

f

calculated as se^¯sdsd,

g

proportion of 2000 replications when 95% confidence intervals contain the population value of β,

h

proportion of 2000 replications yielding significant estimate when β = 0.