Scatter Plots - CULTA Estimates

Ivan Jacob Agaloos Pesigan

library(manCULTA)

Bias

Bias is computed as the difference between the population parameter and the mean of the parameter estimates obtained from the simulation.

data(results_culta_est, package = "manCULTA")
FigBiasCULTAEst(results_culta_est = results_culta_est)

RMSE

Root mean square error (RMSE) is the square root of the average squared difference between the simulation estimates and the population parameter.

data(results_culta_est, package = "manCULTA")
FigRMSECULTAEst(results_culta_est = results_culta_est)

Coverage

Coverage probability is the proportion of simulation replications in which the confidence interval contains the population parameter.

data(results_culta_est, package = "manCULTA")
FigCoverageCULTAEst(results_culta_est = results_culta_est)

Power

Statistical power is the proportion of simulation replications in which the null hypothesis was correctly rejected.

data(results_culta_est, package = "manCULTA")
FigPowerCULTAEst(results_culta_est = results_culta_est)

Parameters

The parameters are indexed as follows:

1. $\phi_{0}$ parameter.
   Autoregressive coefficient for profile 0.

2. $\phi_{1}$ parameter.
   Autoregressive coefficient for profile 1.

3. $\psi_{T}$ parameter.
   Variance in the common trait; reflects stable between-person differences.

4. $\lambda_{t2}$ parameter.
   Factor loading for the common trait and item 2.

5. $\lambda_{t3}$ parameter.
   Factor loading for the common trait and item 3.

6. $\lambda_{t4}$ parameter.
   Factor loading for the common trait and item 4.

7. $\psi_{p11}$ parameter.
   Trait-specific item 1 variance.

8. $\psi_{p22}$ parameter.
   Trait-specific item 2 variance.

9. $\psi_{p33}$ parameter.
   Trait-specific item 3 variance.

10. $\psi_{p44}$ parameter.
    Trait-specific item 4 variance.

11. $\psi_{s0}$ parameter.
    Initial-day variance of the common state; reflects variability in intoxication levels at observation start.

12. $\psi_{s}$ parameter.
    Residual state variance over days; captures within-person daily fluctuations not explained by trait or AR effects.

13. $\lambda_{s2}$ parameter.
    Factor loading for the common state and item 2.

14. $\lambda_{s3}$ parameter.
    Factor loading for the common state and item 3.

15. $\lambda_{s4}$ parameter.
    Factor loading for the common state and item 4.

16. $\theta_{11}$ parameter.
    Unique state variance for item 1.

17. $\theta_{22}$ parameter.
    Unique state variance for item 2.

18. $\theta_{33}$ parameter.
    Unique state variance for item 3.

19. $\theta_{44}$ parameter.
    Unique state variance for item 4.

20. $\nu_{0}$ parameter.
    Intercept for initial log-odds of profile 0 (vs. profile 1) when $X = 0$.

21. $\kappa_{0}$ parameter.
    Covariate effect on initial profile membership; higher $X$ increases odds of profile 0.

22. $\alpha_{0}$ parameter.
    Baseline log-odds of being in profile 0 across days.

23. $\beta_{00}$ parameter.
    Increased odds of staying in profile 0 if previously in that profile; reflects persistence.

24. $\gamma_{00}$ parameter.
    Covariate effect on staying in profile 0; higher $X$ increases persistence.

25. $\gamma_{10}$ parameter.
    Covariate effect on switching from state to profile 0; higher $X$ increases transition odds.

26. $\mu_{10}$ parameter.
    Profile specific mean for profile 0 and item 1.

27. $\mu_{20}$ parameter.
    Profile specific mean for profile 0 and item 2.

28. $\mu_{30}$ parameter.
    Profile specific mean for profile 0 and item 3.

29. $\mu_{40}$ parameter.
    Profile specific mean for profile 0 and item 4.

30. $\mu_{11}$ parameter.
    Profile specific mean for profile 1 and item 1.

31. $\mu_{21}$ parameter.
    Profile specific mean for profile 1 and item 2.

32. $\mu_{31}$ parameter.
    Profile specific mean for profile 1 and item 3.

33. $\mu_{41}$ parameter.
    Profile specific mean for profile 1 and item 4.