
<!-- README.md is generated from README.Rmd. Please edit that file -->

# lcsm: An R Package for Latent Change Score Modeling

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This package offers some helper functions to specify and analyse
univariate and bivariate latent change score models (LCSM) using
[lavaan](https://lavaan.ugent.be/) (Rosseel,
[2012](https://www.jstatsoft.org/v48/i02/)). For details about this
method see for example McArdle
([2009](https://pubmed.ncbi.nlm.nih.gov/18817479/)), Ghisletta
([2012](https://pubmed.ncbi.nlm.nih.gov/25505366/)), Grimm et
al. ([2012](https://pmc.ncbi.nlm.nih.gov/articles/PMC3638891/)), and
Grimm, Ram & Estabrook
([2017](https://www.guilford.com/books/Growth-Modeling/Grimm-Ram-Estabrook/9781462526062)).

The `lcsm` package combines the strengths of other R packages like
[lavaan](https://lavaan.ugent.be/),
[broom](https://github.com/tidymodels/broom/), and
[semPlot](https://CRAN.R-project.org/package=semPlot/) by generating
lavaan syntax that helps these packages work together. This is work in
progress and feedback is very welcome!

## Installation

You can install the released version of `lcsm` from
[CRAN](https://CRAN.R-project.org/package=lcsm/) with:

``` r
install.packages("lcsm")
```

The development version can be installed from
[GitHub](https://github.com/milanwiedemann/lcsm/) using:

``` r
# install.packages("devtools")
devtools::install_github("milanwiedemann/lcsm")
```

## Overview of the functions

The `lcsm` package contains the functions listed below. A more detailed
description of these functions is available in this README or vignettes.
The interactive online application
**[`shinychange`](https://milanwiedemann.shinyapps.io/shinychange/)**
also illustrates some functions of this package.

- Functions to generate [lavaan](https://lavaan.ugent.be/) syntax for
  different model specifications:
  - `specify_uni_lcsm()`: Generate syntax for univariate LCSM
  - `specify_bi_lcsm()`: Generate syntax for bivariate LCSM
- Functions to fit models using [lavaan](https://lavaan.ugent.be/):
  - `fit_uni_lcsm()`: Fit univariate LCSM
  - `fit_bi_lcsm()`: Fit bivariate LCSM
- Functions to extract results from models using
  [broom](https://broom.tidymodels.org/):
  - `extract_fit()`: Extract fit statistics
  - `extract_param()`: Extract estimated parameters
- Simulate data using [lavaan](https://lavaan.ugent.be/):
  - `sim_uni_lcsm()`: Simulate data by specifying parameters for a
    univariate LCSM
  - `sim_bi_lcsm()`: Simulate data by specifying parameters for a
    bivariate LCSM
- Helper functions:
  - `plot_lcsm()`: Visualise LCSM using
    [semPlot](https://github.com/SachaEpskamp/semPlot/)
  - `select_uni_cases()`: Select cases for analysis based on available
    scores on one construct
  - `select_bi_cases()`: Select cases for analysis based on available
    scores on two construct

## How to use `lcsm`

Here are a few examples how to use the `lcsm` package.

``` r
# Load the package
library(lcsm)
#> This is lcsm 0.3.3
#> Please report any issues or ideas at:
#> https://github.com/milanwiedemann/lcsm/issues
#> 
```

### Visualise data

Longitudinal data can be visualised using the `plot_trajectories()`
function. Here only 30% of the data is visualised using the argument
`random_sample_frac = 0.3`. Only consecutive measures are connected by
lines as specified in `connect_missing = FALSE`.

``` r
# Create plot for construct x
plot_x <- plot_trajectories(data = data_bi_lcsm,
                            id_var = "id", 
                            var_list = c("x1", "x2", "x3", "x4", "x5", 
                                         "x6", "x7", "x8", "x9", "x10"),
                            xlab = "Time", ylab = "X Score",
                            connect_missing = FALSE, 
                            random_sample_frac = 0.3)

# Create plot for construct y
plot_y <- plot_trajectories(data = data_bi_lcsm,
                            id_var = "id", 
                            var_list = c("y1", "y2", "y3", "y4", "y5", 
                                        "y6", "y7", "y8", "y9", "y10"),
                            xlab = "Time", ylab = "Y Score",
                            connect_missing = FALSE, 
                            random_sample_frac = 0.3)

# Arrange plots next to each other using patchwork
library(patchwork)
plot_x + plot_y + plot_annotation(tag_levels = 'A')
#> Warning: Removed 18 rows containing missing values or values outside the scale range
#> (`geom_line()`).
#> Warning: Removed 85 rows containing missing values or values outside the scale range
#> (`geom_point()`).
#> Warning: Removed 37 rows containing missing values or values outside the scale range
#> (`geom_line()`).
#> Warning: Removed 172 rows containing missing values or values outside the scale range
#> (`geom_point()`).
```

<img src="man/figures/README-unnamed-chunk-3-1.png" alt="" width="100%" />

### Fit LCSMs

The functions `fit_uni_lcsm()` and `fit_bi_lcsm()` can be used to fit
univariate and bivariate LCSM with different model specifications. In a
first step, these two function generate the user specified lavaan syntax
by calling the `specify_uni_lcsm()` or `specify_bi_lcsm()` functions.

The following table describes some of the different model specifications
that the `model` arguments can take. More detail can be found in the
help files `help(fit_uni_lcsm)`.

#### Fit univariate LCSMs

| Model specification | Description                     |
|:--------------------|:--------------------------------|
| alpha_constant      | Constant change factor          |
| beta                | Proportional change factor      |
| phi                 | Autoregression of change scores |

The example below shows how to specify a generic univariate latent
change score model using the function `specify_uni_lcsm()`. A table of
the description of all parameters that can be estimated is shown
[here](#overview-of-estimated-lcs-model-parameters).

``` r
specify_uni_lcsm(timepoints = 5,
                 var = "x",  
                 change_letter = "g",
                 model = list(alpha_constant = TRUE, 
                              beta = TRUE, 
                              phi = TRUE))
```

<details>

<summary>

Click here to see the <code>lavaan</code> syntax specified above.
</summary>

<p>

    # Specify latent true scores 
    lx1 =~ 1 * x1 
    lx2 =~ 1 * x2 
    lx3 =~ 1 * x3 
    lx4 =~ 1 * x4 
    lx5 =~ 1 * x5 
    # Specify mean of latent true scores 
    lx1 ~ gamma_lx1 * 1 
    lx2 ~ 0 * 1 
    lx3 ~ 0 * 1 
    lx4 ~ 0 * 1 
    lx5 ~ 0 * 1 
    # Specify variance of latent true scores 
    lx1 ~~ sigma2_lx1 * lx1 
    lx2 ~~ 0 * lx2 
    lx3 ~~ 0 * lx3 
    lx4 ~~ 0 * lx4 
    lx5 ~~ 0 * lx5 
    # Specify intercept of obseved scores 
    x1 ~ 0 * 1 
    x2 ~ 0 * 1 
    x3 ~ 0 * 1 
    x4 ~ 0 * 1 
    x5 ~ 0 * 1 
    # Specify variance of observed scores 
    x1 ~~ sigma2_ux * x1 
    x2 ~~ sigma2_ux * x2 
    x3 ~~ sigma2_ux * x3 
    x4 ~~ sigma2_ux * x4 
    x5 ~~ sigma2_ux * x5 
    # Specify autoregressions of latent variables 
    lx2 ~ 1 * lx1 
    lx3 ~ 1 * lx2 
    lx4 ~ 1 * lx3 
    lx5 ~ 1 * lx4 
    # Specify latent change scores 
    dx2 =~ 1 * lx2 
    dx3 =~ 1 * lx3 
    dx4 =~ 1 * lx4 
    dx5 =~ 1 * lx5 
    # Specify latent change scores means 
    dx2 ~ 0 * 1 
    dx3 ~ 0 * 1 
    dx4 ~ 0 * 1 
    dx5 ~ 0 * 1 
    # Specify latent change scores variances 
    dx2 ~~ 0 * dx2 
    dx3 ~~ 0 * dx3 
    dx4 ~~ 0 * dx4 
    dx5 ~~ 0 * dx5 
    # Specify constant change factor 
    g2 =~ 1 * dx2 + 1 * dx3 + 1 * dx4 + 1 * dx5 
    # Specify constant change factor mean 
    g2 ~ alpha_g2 * 1 
    # Specify constant change factor variance 
    g2 ~~ sigma2_g2 * g2 
    # Specify constant change factor covariance with the initial true score 
    g2 ~~ sigma_g2lx1 * lx1
    # Specify proportional change component 
    dx2 ~ beta_x * lx1 
    dx3 ~ beta_x * lx2 
    dx4 ~ beta_x * lx3 
    dx5 ~ beta_x * lx4 
    # Specify autoregression of change score 
    dx3 ~ phi_x * dx2 
    dx4 ~ phi_x * dx3 
    dx5 ~ phi_x * dx4 

</p>

</details>

The function `fit_uni_lcsm()` can be used to fit a univariate LCSM using
the sample data set `data_uni_lcsm`. This functions first writes the
lavaan syntax specified in the `model` argument and passes it on to
`lavaaan::lavaan()`.

``` r
# Fit univariate latent change score model
fit_uni_lcsm(data = data_uni_lcsm, 
             var =  c("x1", "x2", "x3", "x4", "x5",
                      "x6", "x7", "x8", "x9", "x10"),
             model = list(alpha_constant = TRUE, 
                          beta = FALSE, 
                          phi = TRUE))
#> lavaan 0.7-2 ended normally after 67 iterations
#> 
#>   Estimator                                         ML
#>   Optimization method                           NLMINB
#>   Number of model parameters                        23
#>   Number of equality constraints                    16
#> 
#>   Number of observations                           500
#>   Number of missing patterns                       273
#> 
#> Model Test User Model:
#>                                               Standard      Scaled
#>   Test Statistic                                75.389      74.400
#>   Degrees of freedom                                58          58
#>   P-value (Chi-square)                           0.062       0.072
#>   Scaling correction factor                                  1.013
#>     Yuan-Bentler correction (Mplus variant)
```

It is also possible to show the lavaan syntax that was created to fit
the model by the function `specify_uni_lcsm()`. The lavaan syntax
includes comments describing some parts of the syntax in more detail. To
save the syntax in an object the argument `return_lavaan_syntax` has to
be set to `TRUE`. This object looks a bit funny, it’s one very long line
of text, but can be formatted to look more beautiful and readable using
`cat(syntax)`.

``` r
# Fit univariate latent change score model
syntax <- fit_uni_lcsm(data = data_uni_lcsm, 
                       var =  c("x1", "x2", "x3", "x4", "x5",
                                "x6", "x7", "x8", "x9", "x10"),
                       model = list(alpha_constant = TRUE, 
                                    beta = FALSE, 
                                    phi = TRUE),
                      return_lavaan_syntax = TRUE)

# Return lavaan syntax in easy to read format
cat(syntax)
```

<details>

<summary>

Click here to see the lavaan syntax specified in <code>syntax</code>.
</summary>

<p>

    # Specify latent true scores 
    lx1 =~ 1 * x1 
    lx2 =~ 1 * x2 
    lx3 =~ 1 * x3 
    lx4 =~ 1 * x4 
    lx5 =~ 1 * x5 
    lx6 =~ 1 * x6 
    lx7 =~ 1 * x7 
    lx8 =~ 1 * x8 
    lx9 =~ 1 * x9 
    lx10 =~ 1 * x10 
    # Specify mean of latent true scores 
    lx1 ~ gamma_lx1 * 1 
    lx2 ~ 0 * 1 
    lx3 ~ 0 * 1 
    lx4 ~ 0 * 1 
    lx5 ~ 0 * 1 
    lx6 ~ 0 * 1 
    lx7 ~ 0 * 1 
    lx8 ~ 0 * 1 
    lx9 ~ 0 * 1 
    lx10 ~ 0 * 1 
    # Specify variance of latent true scores 
    lx1 ~~ sigma2_lx1 * lx1 
    lx2 ~~ 0 * lx2 
    lx3 ~~ 0 * lx3 
    lx4 ~~ 0 * lx4 
    lx5 ~~ 0 * lx5 
    lx6 ~~ 0 * lx6 
    lx7 ~~ 0 * lx7 
    lx8 ~~ 0 * lx8 
    lx9 ~~ 0 * lx9 
    lx10 ~~ 0 * lx10 
    # Specify intercept of obseved scores 
    x1 ~ 0 * 1 
    x2 ~ 0 * 1 
    x3 ~ 0 * 1 
    x4 ~ 0 * 1 
    x5 ~ 0 * 1 
    x6 ~ 0 * 1 
    x7 ~ 0 * 1 
    x8 ~ 0 * 1 
    x9 ~ 0 * 1 
    x10 ~ 0 * 1 
    # Specify variance of observed scores 
    x1 ~~ sigma2_ux * x1 
    x2 ~~ sigma2_ux * x2 
    x3 ~~ sigma2_ux * x3 
    x4 ~~ sigma2_ux * x4 
    x5 ~~ sigma2_ux * x5 
    x6 ~~ sigma2_ux * x6 
    x7 ~~ sigma2_ux * x7 
    x8 ~~ sigma2_ux * x8 
    x9 ~~ sigma2_ux * x9 
    x10 ~~ sigma2_ux * x10 
    # Specify autoregressions of latent variables 
    lx2 ~ 1 * lx1 
    lx3 ~ 1 * lx2 
    lx4 ~ 1 * lx3 
    lx5 ~ 1 * lx4 
    lx6 ~ 1 * lx5 
    lx7 ~ 1 * lx6 
    lx8 ~ 1 * lx7 
    lx9 ~ 1 * lx8 
    lx10 ~ 1 * lx9 
    # Specify latent change scores 
    dx2 =~ 1 * lx2 
    dx3 =~ 1 * lx3 
    dx4 =~ 1 * lx4 
    dx5 =~ 1 * lx5 
    dx6 =~ 1 * lx6 
    dx7 =~ 1 * lx7 
    dx8 =~ 1 * lx8 
    dx9 =~ 1 * lx9 
    dx10 =~ 1 * lx10 
    # Specify latent change scores means 
    dx2 ~ 0 * 1 
    dx3 ~ 0 * 1 
    dx4 ~ 0 * 1 
    dx5 ~ 0 * 1 
    dx6 ~ 0 * 1 
    dx7 ~ 0 * 1 
    dx8 ~ 0 * 1 
    dx9 ~ 0 * 1 
    dx10 ~ 0 * 1 
    # Specify latent change scores variances 
    dx2 ~~ 0 * dx2 
    dx3 ~~ 0 * dx3 
    dx4 ~~ 0 * dx4 
    dx5 ~~ 0 * dx5 
    dx6 ~~ 0 * dx6 
    dx7 ~~ 0 * dx7 
    dx8 ~~ 0 * dx8 
    dx9 ~~ 0 * dx9 
    dx10 ~~ 0 * dx10 
    # Specify constant change factor 
    g2 =~ 1 * dx2 + 1 * dx3 + 1 * dx4 + 1 * dx5 + 1 * dx6 + 1 * dx7 + 1 * dx8 + 1 * dx9 + 1 * dx10 
    # Specify constant change factor mean 
    g2 ~ alpha_g2 * 1 
    # Specify constant change factor variance 
    g2 ~~ sigma2_g2 * g2 
    # Specify constant change factor covariance with the initial true score 
    g2 ~~ sigma_g2lx1 * lx1
    # Specify autoregression of change score 
    dx3 ~ phi_x * dx2 
    dx4 ~ phi_x * dx3 
    dx5 ~ phi_x * dx4 
    dx6 ~ phi_x * dx5 
    dx7 ~ phi_x * dx6 
    dx8 ~ phi_x * dx7 
    dx9 ~ phi_x * dx8 
    dx10 ~ phi_x * dx9 

</p>

</details>

#### Fit bivariate LCSMs

The function `fit_bi_lcsm()` allows to specify two univariate LCSMs
using the arguments `model_x` and `model_x`. These two constructs can
then be connected using the `coupling` argument. More details can be
found in the help files `help(fit_bi_lcsm)`.

| Coupling specification | Description |
|:---|:---|
| coupling_piecewise | Piecewise coupling parameters |
| coupling_piecewise_num | Changepoint of piecewise coupling parameters |
| delta_con_xy | Change score x (t) determined by true score y (t) |
| delta_con_yx | Change score y (t) determined by true score x (t) |
| delta_lag_xy | Change score x (t) determined by true score y (t-1) |
| delta_lag_yx | Change score y (t) determined by true score x (t-1) |
| xi_con_xy | Change score x (t) determined by change score y (t) |
| xi_con_yx | Change score y (t) determined by change score x (t) |
| xi_lag_xy | Change score x (t) determined by change score y (t-1) |
| xi_lag_yx | Change score y (t) determined by change score x (t-1) |

``` r
fit_bi_lcsm(data = data_bi_lcsm, 
            var_x = c("x1", "x2", "x3", "x4", "x5",
                      "x6", "x7", "x8", "x9", "x10"),
            var_y = c("y1", "y2", "y3", "y4", "y5", 
                      "y6", "y7", "y8", "y9", "y10"),
            model_x = list(alpha_constant = TRUE, 
                           beta = TRUE, 
                           phi = FALSE),
            model_y = list(alpha_constant = TRUE, 
                           beta = TRUE, 
                           phi = TRUE),
            coupling = list(delta_lag_xy = TRUE, 
                            xi_lag_yx = TRUE))
#> lavaan 0.7-2 ended normally after 116 iterations
#> 
#>   Estimator                                         ML
#>   Optimization method                           NLMINB
#>   Number of model parameters                        87
#>   Number of equality constraints                    65
#> 
#>   Number of observations                           500
#>   Number of missing patterns                       210
#> 
#> Model Test User Model:
#>                                               Standard      Scaled
#>   Test Statistic                               191.851     193.021
#>   Degrees of freedom                               208         208
#>   P-value (Chi-square)                           0.782       0.764
#>   Scaling correction factor                                  0.994
#>     Yuan-Bentler correction (Mplus variant)
```

### Extract fit statistics and parmeters

The main underlying functions to extract parameters and fit statistics
come from the `broom` package: `broom::tidy()` and `broom::glance()`.
The functions `extract_param()` and `extract_fit()` offer some tools
that I find helpful when running LCSMs in R, for example:

- `extract_param()`: only one row per estimated parameter,
- `extract_fit()`: fit statistics for multiple lavaan objects can be
  extracted.

A table of the description of all parameters that can be estimated is
shown [here](#overview-of-estimated-lcs-model-parameters).

``` r
# First create a lavaan object
bi_lcsm_01 <- fit_bi_lcsm(data = data_bi_lcsm, 
                          var_x = c("x1", "x2", "x3", "x4", "x5",
                                    "x6", "x7", "x8", "x9", "x10"),
                          var_y = c("y1", "y2", "y3", "y4", "y5", 
                                    "y6", "y7", "y8", "y9", "y10"),
                          model_x = list(alpha_constant = TRUE, 
                                         beta = TRUE, 
                                         phi = FALSE),
                          model_y = list(alpha_constant = TRUE, 
                                         beta = TRUE, 
                                         phi = TRUE),
                          coupling = list(delta_lag_xy = TRUE, 
                                          xi_lag_yx = TRUE))

# Now extract parameter estimates
# Only extract first 7 columns for this example by adding [ , 1:7]
param_bi_lcsm_01 <- extract_param(bi_lcsm_01, printp = TRUE)[ , 1:7]

# Print table of parameter estimates
kable(param_bi_lcsm_01, digits = 3)
```

| label        | estimate | std.error | statistic | p.value | std.lv | std.all |
|:-------------|---------:|----------:|----------:|:--------|-------:|--------:|
| gamma_lx1    |   21.066 |     0.036 |   588.187 | \< .001 | 30.014 |  30.014 |
| sigma2_lx1   |    0.493 |     0.037 |    13.485 | \< .001 |  1.000 |   1.000 |
| sigma2_ux    |    0.201 |     0.004 |    45.301 | \< .001 |  0.201 |   0.290 |
| alpha_g2     |   -0.309 |     0.053 |    -5.834 | \< .001 | -0.492 |  -0.492 |
| sigma2_g2    |    0.395 |     0.028 |    14.330 | \< .001 |  1.000 |   1.000 |
| sigma_g2lx1  |    0.155 |     0.022 |     7.017 | \< .001 |  0.351 |   0.351 |
| beta_x       |   -0.106 |     0.003 |   -30.818 | \< .001 | -0.120 |  -0.120 |
| gamma_ly1    |    5.025 |     0.029 |   172.786 | \< .001 | 11.009 |  11.009 |
| sigma2_ly1   |    0.208 |     0.019 |    10.860 | \< .001 |  1.000 |   1.000 |
| sigma2_uy    |    0.193 |     0.005 |    39.698 | \< .001 |  0.193 |   0.481 |
| alpha_j2     |   -0.203 |     0.039 |    -5.217 | \< .001 | -0.666 |  -0.666 |
| sigma2_j2    |    0.093 |     0.008 |    11.766 | \< .001 |  1.000 |   1.000 |
| sigma_j2ly1  |    0.017 |     0.008 |     2.156 | .031    |  0.122 |   0.122 |
| beta_y       |   -0.197 |     0.005 |   -39.562 | \< .001 | -0.293 |  -0.293 |
| phi_y        |    0.144 |     0.029 |     4.963 | \< .001 |  0.126 |   0.126 |
| sigma_su     |    0.009 |     0.003 |     2.581 | .01     |  0.009 |   0.044 |
| sigma_ly1lx1 |    0.185 |     0.021 |     8.905 | \< .001 |  0.577 |   0.577 |
| sigma_g2ly1  |    0.072 |     0.016 |     4.437 | \< .001 |  0.251 |   0.251 |
| sigma_j2lx1  |    0.093 |     0.012 |     7.916 | \< .001 |  0.437 |   0.437 |
| sigma_j2g2   |    0.005 |     0.012 |     0.463 | .643    |  0.029 |   0.029 |
| delta_lag_xy |    0.140 |     0.006 |    23.837 | \< .001 |  0.103 |   0.103 |
| xi_lag_yx    |    0.360 |     0.037 |     9.634 | \< .001 |  0.640 |   0.640 |

### Plot simplified path diagrams of LCSMs

This function is work in progress and can only plot univariate and
bivariate LCSMs that were specified with `fit_uni_lcsm()` or
`fit_bi_lcsm()`. Modified LCSMs will probably return errors as the
layout matrix that gets created by this plot function only supports the
specifications that can be modelled with this package. The input
arguments for plotting a simplified path diagram are:

- the estimated lavaan object `lavaan_object`,
- the `lavaan_syntax` and ,
- `lcsm` indicating whether the LCSMs is “univariate” or “bivariate”

Optional arguments can be used to change the look of the plot, for
example:

- `lcsm_colours` can be used to highlight the different parts of the
  latent change score model
  - white: observed scores
  - green: latent true scores
  - blue: latent change scores
  - yellow: latent change scores

Further arguments can be passed on to `semPlot::semPaths()`, for
example:

- `what`, **“path”** to show unweighted gray edges, **“par”** to show
  parameter estimates as weighted (green/red) edges\
- `whatLabels`, **“label”** to show edege names as label or **“est”**
  for parameter estimates, **“hide”** to hide edge labels

#### Univariate LCSM

``` r
# Fit bivariate lcsm and save the results 
uni_lavaan_results <- fit_uni_lcsm(data = data_uni_lcsm, 
                                   var = c("x1", "x2", "x3", "x4", "x5"),
                                   model = list(alpha_constant = TRUE, 
                                                beta = TRUE, 
                                                phi = TRUE)
                                  )
#> Warning: lavaan->lav_data_full():  
#>    some cases are empty and will be ignored: 239.

# Save the lavaan syntax that is used to create the layout matrix for semPlot
uni_lavaan_syntax <- fit_uni_lcsm(data = data_uni_lcsm, 
                                  var = c("x1", "x2", "x3", "x4", "x5"),
                                  model = list(alpha_constant = TRUE, 
                                               beta = TRUE, 
                                               phi = TRUE),
                                  return_lavaan_syntax = TRUE)

# Plot the results
plot_lcsm(lavaan_object = uni_lavaan_results,
          lavaan_syntax = uni_lavaan_syntax,
          edge.label.cex = .9,  
          lcsm_colours = TRUE,
          lcsm = "univariate")
```

<img src="man/figures/README-unnamed-chunk-9-1.png" alt="" width="100%" />

#### Bivariate LCSM

``` r
# Fit bivariate lcsm and save the results 
bi_lavaan_results <- fit_bi_lcsm(data = data_bi_lcsm, 
                                 var_x = c("x1", "x2", "x3", "x4", "x5"),
                                 var_y = c("y1", "y2", "y3", "y4", "y5"),
                                 model_x = list(alpha_constant = TRUE, 
                                                beta = TRUE, 
                                                phi = FALSE),
                                 model_y = list(alpha_constant = TRUE, 
                                                beta = TRUE, 
                                                phi = TRUE),
                                 coupling = list(delta_lag_xy = TRUE, 
                                                 xi_lag_yx = TRUE))

# Save the lavaan syntax that is used to create the layout matrix for semPlot
bi_lavaan_syntax <- fit_bi_lcsm(data = data_bi_lcsm, 
                                var_x = c("x1", "x2", "x3", "x4", "x5"),
                                var_y = c("y1", "y2", "y3", "y4", "y5"),
                                model_x = list(alpha_constant = TRUE, 
                                               beta = TRUE, 
                                               phi = FALSE),
                                model_y = list(alpha_constant = TRUE, 
                                               beta = TRUE, 
                                               phi = TRUE),
                                coupling = list(delta_lag_xy = TRUE, 
                                                xi_lag_yx = TRUE),
                                return_lavaan_syntax = TRUE)

# Plot the results
plot_lcsm(lavaan_object = bi_lavaan_results, 
          lavaan_syntax = bi_lavaan_syntax,
          lcsm_colours = TRUE,
          whatLabels = "hide",
          lcsm = "bivariate")
```

<img src="man/figures/README-unnamed-chunk-10-1.png" alt="" width="100%" />

### Simulate data

The functions `sim_uni_lcsm()` and `sim_bi_lcsm()` simulate data based
on some some parameters that can be specified. See the tables
[here](#overview-of-estimated-lcs-model-parameters) for a full list of
parameters that can be specified for the data simulation.

``` r
# Simulate some data 
sim_uni_lcsm(timepoints = 5, 
             model = list(alpha_constant = TRUE, beta = FALSE, phi = TRUE), 
             model_param = list(gamma_lx1 = 21, 
                                sigma2_lx1 = 1.5,
                                sigma2_ux = 0.2,
                                alpha_j2 = -0.93,
                                sigma2_j2 = 0.1,
                                sigma_j2lx1 = 0.2,
                                phi_x = 0.3),
             sample.nobs = 1000,
             na_pct = 0.3)
#> Parameter estimates for the data simulation are taken from the argument 'model_param'.
#> Warning: The following parameters are specified in the LCSM but no parameter estimates have been entered in 'model_param':
#> -  alpha_g2
#> -  sigma2_g2
#> -  sigma_g2lx1
#> # A tibble: 1,000 × 6
#>       id    x1    x2    x3    x4    x5
#>    <int> <dbl> <dbl> <dbl> <dbl> <dbl>
#>  1     1  20.0  NA    NA    18.0  16.4
#>  2     2  20.0  19.9  18.1  17.4  NA  
#>  3     3  19.6  17.5  NA    13.0  10.9
#>  4     4  20.9  NA    NA    18.6  19.4
#>  5     5  20.7  NA    22.5  23.5  24.0
#>  6     6  21.2  20.6  21.2  20.7  20.5
#>  7     7  20.3  NA    NA    NA    24.2
#>  8     8  20.6  21.3  23.6  25.8  NA  
#>  9     9  21.7  NA    20.1  19.9  NA  
#> 10    10  NA    22.4  NA    23.8  24.2
#> # ℹ 990 more rows
```

It is also possible to return the lavaan syntax instead of simulating
data for further manual specifications. The modified object could then
be used to simulate data using `lavaan::simulateData()`.

``` r
# Return lavaan syntax based on the following argument specifications
simsyntax <- sim_bi_lcsm(timepoints = 5, 
                         model_x = list(alpha_constant = TRUE, beta = TRUE, phi = FALSE),
                         model_x_param = list(gamma_lx1 = 21,
                                              sigma2_lx1 = .5,
                                              sigma2_ux = .2,
                                              alpha_g2 = -.4,
                                              sigma2_g2 = .4,
                                              sigma_g2lx1 = .2,
                                              beta_x = -.1),
                         model_y = list(alpha_constant = TRUE, beta = TRUE, phi = TRUE),
                         model_y_param = list(gamma_ly1 = 5,
                                              sigma2_ly1 = .2,
                                              sigma2_uy = .2,
                                              alpha_j2 = -.2,
                                              sigma2_j2 = .1,
                                              sigma_j2ly1 = .02,
                                              beta_y = -.2,
                                              phi_y = .1),
                         coupling = list(delta_lag_xy = TRUE, 
                                         xi_lag_yx = TRUE),
                         coupling_param = list(sigma_su = .01,
                                               sigma_ly1lx1 = .2,
                                               sigma_g2ly1 = .1,
                                               sigma_j2lx1 = .1,
                                               sigma_j2g2 = .01,
                                               delta_lag_xy = .13,
                                               xi_lag_yx = .4),
                         return_lavaan_syntax = TRUE)
```

<details>

<summary>

Click here to see the lavaan syntax specified in <code>simsyntax</code>.
</summary>

<p>

    # Specify parameters for construct x ----
    # Specify latent true scores 
    lx1 =~ 1 * x1 
    lx2 =~ 1 * x2 
    lx3 =~ 1 * x3 
    lx4 =~ 1 * x4 
    lx5 =~ 1 * x5 
    # Specify mean of latent true scores 
    lx1 ~ 21 * 1 
    lx2 ~ 0 * 1 
    lx3 ~ 0 * 1 
    lx4 ~ 0 * 1 
    lx5 ~ 0 * 1 
    # Specify variance of latent true scores 
    lx1 ~~ 0.5 * lx1 
    lx2 ~~ 0 * lx2 
    lx3 ~~ 0 * lx3 
    lx4 ~~ 0 * lx4 
    lx5 ~~ 0 * lx5 
    # Specify intercept of obseved scores 
    x1 ~ 0 * 1 
    x2 ~ 0 * 1 
    x3 ~ 0 * 1 
    x4 ~ 0 * 1 
    x5 ~ 0 * 1 
    # Specify variance of observed scores 
    x1 ~~ 0.2 * x1 
    x2 ~~ 0.2 * x2 
    x3 ~~ 0.2 * x3 
    x4 ~~ 0.2 * x4 
    x5 ~~ 0.2 * x5 
    # Specify autoregressions of latent variables 
    lx2 ~ 1 * lx1 
    lx3 ~ 1 * lx2 
    lx4 ~ 1 * lx3 
    lx5 ~ 1 * lx4 
    # Specify latent change scores 
    dx2 =~ 1 * lx2 
    dx3 =~ 1 * lx3 
    dx4 =~ 1 * lx4 
    dx5 =~ 1 * lx5 
    # Specify latent change scores means 
    dx2 ~ 0 * 1 
    dx3 ~ 0 * 1 
    dx4 ~ 0 * 1 
    dx5 ~ 0 * 1 
    # Specify latent change scores variances 
    dx2 ~~ 0 * dx2 
    dx3 ~~ 0 * dx3 
    dx4 ~~ 0 * dx4 
    dx5 ~~ 0 * dx5 
    # Specify constant change factor 
    g2 =~ 1 * dx2 + 1 * dx3 + 1 * dx4 + 1 * dx5 
    # Specify constant change factor mean 
    g2 ~ -0.4 * 1 
    # Specify constant change factor variance 
    g2 ~~ 0.4 * g2 
    # Specify constant change factor covariance with the initial true score 
    g2 ~~ 0.2 * lx1
    # Specify proportional change component 
    dx2 ~ -0.1 * lx1 
    dx3 ~ -0.1 * lx2 
    dx4 ~ -0.1 * lx3 
    dx5 ~ -0.1 * lx4 
    # Specify parameters for construct y ----
    # Specify latent true scores 
    ly1 =~ 1 * y1 
    ly2 =~ 1 * y2 
    ly3 =~ 1 * y3 
    ly4 =~ 1 * y4 
    ly5 =~ 1 * y5 
    # Specify mean of latent true scores 
    ly1 ~ 5 * 1 
    ly2 ~ 0 * 1 
    ly3 ~ 0 * 1 
    ly4 ~ 0 * 1 
    ly5 ~ 0 * 1 
    # Specify variance of latent true scores 
    ly1 ~~ 0.2 * ly1 
    ly2 ~~ 0 * ly2 
    ly3 ~~ 0 * ly3 
    ly4 ~~ 0 * ly4 
    ly5 ~~ 0 * ly5 
    # Specify intercept of obseved scores 
    y1 ~ 0 * 1 
    y2 ~ 0 * 1 
    y3 ~ 0 * 1 
    y4 ~ 0 * 1 
    y5 ~ 0 * 1 
    # Specify variance of observed scores 
    y1 ~~ 0.2 * y1 
    y2 ~~ 0.2 * y2 
    y3 ~~ 0.2 * y3 
    y4 ~~ 0.2 * y4 
    y5 ~~ 0.2 * y5 
    # Specify autoregressions of latent variables 
    ly2 ~ 1 * ly1 
    ly3 ~ 1 * ly2 
    ly4 ~ 1 * ly3 
    ly5 ~ 1 * ly4 
    # Specify latent change scores 
    dy2 =~ 1 * ly2 
    dy3 =~ 1 * ly3 
    dy4 =~ 1 * ly4 
    dy5 =~ 1 * ly5 
    # Specify latent change scores means 
    dy2 ~ 0 * 1 
    dy3 ~ 0 * 1 
    dy4 ~ 0 * 1 
    dy5 ~ 0 * 1 
    # Specify latent change scores variances 
    dy2 ~~ 0 * dy2 
    dy3 ~~ 0 * dy3 
    dy4 ~~ 0 * dy4 
    dy5 ~~ 0 * dy5 
    # Specify constant change factor 
    j2 =~ 1 * dy2 + 1 * dy3 + 1 * dy4 + 1 * dy5 
    # Specify constant change factor mean 
    j2 ~ -0.2 * 1 
    # Specify constant change factor variance 
    j2 ~~ 0.1 * j2 
    # Specify constant change factor covariance with the initial true score 
    j2 ~~ 0.02 * ly1
    # Specify proportional change component 
    dy2 ~ -0.2 * ly1 
    dy3 ~ -0.2 * ly2 
    dy4 ~ -0.2 * ly3 
    dy5 ~ -0.2 * ly4 
    # Specify autoregression of change score 
    dy3 ~ 0.1 * dy2 
    dy4 ~ 0.1 * dy3 
    dy5 ~ 0.1 * dy4 
    # Specify residual covariances 
    x1 ~~ 0.01 * y1 
    x2 ~~ 0.01 * y2 
    x3 ~~ 0.01 * y3 
    x4 ~~ 0.01 * y4 
    x5 ~~ 0.01 * y5 
    # Specify covariances betweeen specified change components (alpha) and intercepts (initial latent true scores lx1 and ly1) ----
    # Specify covariance of intercepts 
    lx1 ~~ 0.2 * ly1 
    # Specify covariance of constant change and intercept within the same construct 
    ly1 ~~ 0.1 * g2 
    # Specify covariance of constant change and intercept within the same construct 
    lx1 ~~ 0.1 * j2 
    # Specify covariance of constant change factors between constructs 
    g2 ~~ 0.01 * j2 
    # Specify between-construct coupling parameters ----
    # Change score x (t) is determined by true score y (t-1)  
    dx2 ~ 0.13 * ly1 
    dx3 ~ 0.13 * ly2 
    dx4 ~ 0.13 * ly3 
    dx5 ~ 0.13 * ly4 
    # Change score y (t) is determined by change score x (t-1)  
    dy3 ~ 0.4 * dx2 
    dy4 ~ 0.4 * dx3 
    dy5 ~ 0.4 * dx4 

</p>

</details>
