Scatter Plots - LTA 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_lta_est, package = "manCULTA")
FigBiasLTAEst(results_lta_est = results_lta_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_lta_est, package = "manCULTA")
FigRMSELTAEst(results_lta_est = results_lta_est)

Coverage

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

data(results_lta_est, package = "manCULTA")
FigCoverageLTAEst(results_lta_est = results_lta_est)

Power

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

data(results_lta_est, package = "manCULTA")
FigPowerLTAEst(results_lta_est = results_lta_est)

Parameters

The parameters are indexed as follows:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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