This vignette details how you can automatically create Mplus model syntax for performing a power analysis for a bivariate random intercept cross-lagged panel model (RI-CLPM) using the Mplus software package. This might be preferred by some researchers as Monte Carlo simulations are much faster in Mplus than in R, or for reasons of convention. A disadvantage of using Mplus is that power analysis cannot be performed across multiple experimental conditions simultaneously, it requires additional effort to understand all of the output one gets, and that it is a paid option.

Using `powRICLPM_Mplus()`

, you can create Mplus model
syntax for multiple experimental conditions simultaneously (although you
would then still need run each script separately in Mplus itself). The
function works similarly to `powRICLPM()`

in that it
implements the procedure for computing population parameter values as
proposed by Mulder (2022).
As such, let’s use the same illustrating example as explained in the
Vignette Get
started.

For our example, we will investigate the power to detect a small standardized cross-lagged effect of \(0.2\) for sample sizes from 100 to 1000 (with incremental steps of 50) for an RI-CLPM with 3, 4 and 5 repeated measures. In total, this results in \(19 \times 3 = 57\) experimental conditions. Moreover, following the example in the Get started Vignette, our population parameter values are:

```
<- matrix(c(.4, .1, .2, .3), ncol = 2, byrow = T)
Phi # The .2 refers to our standardized cross-lagged effect of interest
<- 0.5
ICC <- 0.3 RI_cor
```

To create Mplus model syntax, use the `powRICLPM_Mplus()`

function. You must provide:

- the range of sample sizes to simulate the power for using the
`search_lower`

,`search_upper`

, and`search_step`

arguments, - the number of repeated measures using the
`time_points`

argument, - the population values
`Phi`

,`wSigma`

,`ICC`

, and`RI_cor`

, - the number of MCMC replications you want to perform per condition in
the
`reps`

argument, - a
`seed`

to control the starting point of the random number generator, and - a
`save_path`

, denoting the directory to which to save the Mplus input file to.

For our example, we would specify:

```
powRICLPM_Mplus(search_lower = 100,
search_upper = 1000,
search_step = 50,
time_points = c(3, 4, 5),
ICC = 0.5,
RI_cor = 0.3,
Phi = Phi,
within_cor = 0.3,
reps = 10000,
seed = 123456,
save_path = "./saved")
```

Optionally, you can specify the `constraints`

argument to
extend the basic power analysis setup. This option is further described
in the Vignette Extensions.

The `powRICLPM_Mplus()`

creates an Mplus input file (or
multiple files when multiple experimental conditions are specified) and
writes it to the specified directory. The file contains the Mplus model
syntax needed to run a power analysis for the RI-CLPM in Mplus. More
information about Monte Carlo simulations in Mplus can be found at http://statmodel.com/download/usersguide/Chapter12.pdf.

To get output, run each Mplus model syntax file in Mplus. Each time, an output file is created summarizing the results of the Mplus power analysis. A good source for interpreting this output in the context of a MONTECARLO study is Muthén and Muthén (2002).