mmLSTrf_SimulatedDataExample: Dataset mmLSTrf_SimulatedDataExample.
| mmLSTrf_SimulatedDataExample | R Documentation |
Dataset mmLSTrf_SimulatedDataExample.
Description
A simulated dataset illustrating data for a study design with two fixed situations, three measurement occasions, two methods and three indicators.
Format
A data frame with 500 rows and 36 variables
Details
The variables are named according to the following format: Y_{imts}
(i = indicator, m = method, t = occasion, s = fixed situation)
-
Y_{1111} -
Y_{2111} -
Y_{3111} -
Y_{1211} -
Y_{2211} ...
-
Y_{2132} -
Y_{3132} -
Y_{1132} -
Y_{2232} -
Y_{3232}
This format reflects the order of indicator variables in a path diagram, where indicators are first grouped by fixed situations, within those they are then grouped by occasions and within those they are lastly grouped by methods. The resulting nested structure has indicators nested within methods, nested within occasions, nested within fixed situations.
The specified population values underlying the simulated data are:
-
E(T_{111})= 2.75 -
Comm(T_{112})= 0.44 -
E(T_{112})= 3.25 -
\epsilon_{imts}= 0.15 -
Var(T_{111})= 0.40 -
\alpha_{ims}= 0.00 -
Var(T_{112})= 0.45 -
\lambda_{ims}= 1.00 -
Var(O_{11t1})= 0.20 -
\delta_{ims}= 1.00 -
Var(O_{11t2})= 0.30 -
\gamma_{ims}= 1.00 -
Var(TM_{ims})= 0.10 -
\beta_{1112}* = 0.35 -
Var(OM_{mts})= 0.10 -
\beta_{0112}= 1.31 -
Var(\omega_{11s})= 0.25
*\beta_{1112} represents the standardized beta coefficient.
Trait factors are essentially parallel, other latent variables are essentially
equivalent. Scalar measurement invariance holds across fixed situations and
methods. Latent variables are orthogonal apart from trait factors.
