I’m excited to introduce tidyLPA, an R package for carrying out Latent Profile Analysis (LPA). This is the result of a collaborative project with Jennifer Schmidt, Patrick Beymer, and Rebecca Steingut, and is the result of a long period of learning about *cluster analysis* (see here) and, recently, **model-based cluster analysis**. Here, I introduce and describe LPA as a particular type of model-based cluster analysis.

**Note: This post has been updated to reflect the latest version of tidyLPA**

## Note

tidyLPA has undergone some major changes. You can read about them here.

## Background

Latent Profile Analysis (LPA) is a statistical modeling approach for estimating distinct profiles, or groups, of variables. In the social sciences and in educational research, these profiles could represent, for example, how different youth experience dimensions of being engaged (i.e., cognitively, behaviorally, and affectively) at the same time.

tidyLPA provides the functionality to carry out LPA in R. In particular, tidyLPA provides functionality to specify different models that determine whether and how different parameters (i.e., means, variances, and covariances) are estimated and to specify (and compare solutions for) the number of profiles to estimate. The package is designed and documented to be easy to use, especially for beginners to LPA, but with fine-grained options available for estimating models and evaluating specific output as part of more complex analyses.

## Installation

You can install tidyLPA from CRAN with:

`install.packages("tidyLPA")`

You can also install the development version of tidyLPA from GitHub with:

```
install.packages("devtools")
devtools::install_github("data-edu/tidyLPA")
```

## Examples

### Mclust

Here is a brief example using the built-in `pisaUSA15`

data set and variables for broad interest, enjoyment, and self-efficacy. Note that we first type the name of the data frame, followed by the unquoted names of the variables used to create the profiles. We also specify the number of profiles and the model. See `?estimate_profiles`

for more details.

In these examples, we pass the results of one function to the next by *piping* (using the `%>%`

operator, loaded from the `dplyr`

package). We pass the data to a function that selects relevant variables, and then to `estimate_profiles`

:

```
library(tidyLPA)
library(tidyverse)
```

```
pisaUSA15[1:100, ] %>%
select(broad_interest, enjoyment, self_efficacy) %>%
single_imputation() %>%
estimate_profiles(3)
```

### Mplus

We can use Mplus simply by changing the package argument for `estimate_profiles()`

:

```
pisaUSA15[1:100, ] %>%
select(broad_interest, enjoyment, self_efficacy) %>%
single_imputation() %>%
estimate_profiles(3, package = "MplusAutomation")
```

A simple summary of the analysis is printed to the console (and its posterior probability). The resulting object can be further passed down a pipeline to other functions, such as `plot`

, `compare_solutions`

, `get_data`

, `get_fit`

, etc. This is the “tidy” part, in that the function can be embedded in a tidy analysis pipeline.

If you have Mplus installed, you can call the version of this function that uses MPlus in the same way, by adding the argument `package = "MplusAutomation`

.

### Plotting the profiles

We can plot the profiles by piping the output to `plot_profiles()`

.

```
pisaUSA15[1:100, ] %>%
select(broad_interest, enjoyment, self_efficacy) %>%
single_imputation() %>%
scale() %>%
estimate_profiles(3) %>%
plot_profiles()
```

## Model specification

In addition to the number of profiles (specified with the `n_profiles`

argument), the model can be specified in terms of whether and how the variable variances and covariances are estimated.

The models are specified by passing arguments to the `variance`

and `covariance`

arguments. The possible values for these arguments are:

`variances`

: “equal” and “zero”`covariances`

: “varying”, “equal”, and “zero”

If no values are specified for these, then the variances are constrained to be equal across classes, and covariances are fixed to 0 (conditional independence of the indicators).

These arguments allow for four models to be specified:

- Equal variances and covariances fixed to 0 (Model 1)
- Varying variances and covariances fixed to 0 (Model 2)
- Equal variances and equal covariances (Model 3)
- Varying variances and varying covariances (Model 6)

Two additional models (Models 4 and 5) can be fit using MPlus. More information on the models can be found in the vignette.

Here is an example of specifying a model with varying variances and covariances (Model 6; not run here):

```
pisaUSA15[1:100, ] %>%
select(broad_interest, enjoyment, self_efficacy) %>%
single_imputation() %>%
estimate_profiles(3,
variances = "varying",
covariances = "varying")
```

## Comparing a wide range of solutions

The function `compare_solutions()`

compares the fit of several estimated models, with varying numbers of profiles and model specifications:

```
pisaUSA15[1:100, ] %>%
select(broad_interest, enjoyment, self_efficacy) %>%
single_imputation() %>%
estimate_profiles(1:3,
variances = c("equal", "varying"),
covariances = c("zero", "varying")) %>%
compare_solutions(statistics = c("AIC", "BIC"))
```

## More information

To learn more:

## Citing tidyLPA

Rosenberg, J. M., Beymer, P. N., Anderson, D. J., & Schmidt, J. A. (2018). tidyLPA: An R Package to Easily Carry Out Latent Profile Analysis (LPA) Using Open-Source or Commercial Software.

Journal of Open Source Software, 3(30), 978, https://doi.org/10.21105/joss.00978

You can also cite the most latest version with the following citation:

Rosenberg, J. M., van Lissa, C. J., Beymer, P. N., Anderson, D. J., Schell, M. J. & Schmidt, J. A. (2019). tidyLPA: Easily carry out Latent Profile Analysis (LPA) using open-source or commercial software [R package]. https://data-edu.github.io/tidyLPA/

## Accessing the previous version

The last version of tidyLPA can no longer be downloaded from CRAN but can be downloaded with the following question

`devtools::install_github("data-edu/tidyLPA", ref = "ab36357")`

## Contributing and Contact Information

One of the easiest but also most important ways to contribute is to post a question or to provide feedback. Both positive *and* negative feedback is welcome and helpful. You can get in touch by . . .

- Sending a message via tidylpa@googlegroups.com or view the the tidyLPA group page (
*preferred*) - Filing an issue on GitHub here

Contributions are also welcome via by making pull requests (PR), e.g. through this page on GitHub. It may be easier if you first file an issue outlining what you will do in the PR. You can also reach out via the methods described above.

Please note that this project is released with a Contributor Code of Conduct. By participating in this project you agree to abide by its terms.

## Some acknowledgments!

As I mentioned earlier, this package is the result of a lot of learning that started awhile ago. Thank you to Christina Krist and Stephanie Wormington for introducing me to cluster analysis and LPA, respectively. Also, thank you to Kristy Robinson and You-kyung Lee for their invaluable help in learning about LPA.