Scatter Plots - Weak Coupling

Ivan Jacob Agaloos Pesigan

library(manCTMed)

Population Total, Direct, and Indirect Effects

Total, direct, and indirect effects for the drift matrix

$$\begin{equation} \left( \begin{array}{ccc} −0.050 & 0 & 0 \\ −0.020 & −0.050 & 0 \\ 0.030 & −0.010 & −0.050 \\ \end{array} \right) \end{equation}$$

FigPlotEffects(dynamics = -1)
#> 
#> phi:
#>       x     m     y
#> x -0.05  0.00  0.00
#> m -0.02 -0.05  0.00
#> y  0.03 -0.01 -0.05

Standardized total, direct, and indirect effects for the drift matrix $$\begin{equation} \left( \begin{array}{ccc} −0.050 & 0 & 0 \\ −0.020 & −0.050 & 0 \\ 0.030 & −0.010 & −0.050 \\ \end{array} \right) \end{equation}$$ and process noise covariance matrix $$\begin{equation} \left( \begin{array}{ccc} 0.0343 & 0.0398 & -0.0035 \\ 0.0398 & 0.0698 & 0.0219 \\ -0.0035 & 0.0219 & 0.0330 \\ \end{array} \right) \end{equation}$$

FigPlotEffects(dynamics = -1, std = TRUE)
#> 
#> phi:
#>       x     m     y
#> x -0.05  0.00  0.00
#> m -0.02 -0.05  0.00
#> y  0.03 -0.01 -0.05
#> 
#> sigma:
#>             [,1]       [,2]        [,3]
#> [1,]  0.24455556 0.02201587 -0.05004762
#> [2,]  0.02201587 0.07067800  0.01539456
#> [3,] -0.05004762 0.01539456  0.07553061

Evaluation of Confidence Intervals

Presented below are scatter plots of coverage probabilities and power for the $\eta_X \to \eta_M \ to \eta_Y$ model and type I error rates for the $\eta_Y \to \eta_M \to \eta_X$ model.

data(results, package = "manCTMed")

Coverage Probabilities

Time Intervals 1 to 25

Time Intervals 1 to 4

Time Intervals 5 to 25

Time Intervals 25 to 30

Statistical Power

Type I Error Rate

Coverage Probabilities (Standardized)

Time Intervals 1 to 25

Time Intervals 1 to 4

Time Intervals 5 to 25

Time Intervals 25 to 30

Statistical Power (Standardized)

Type I Error Rate (Standardized)