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https://github.com/jhorzek/lesssem
lessSEM estimates sparse structural equation models.
https://github.com/jhorzek/lesssem
lasso psychometrics r regularization regularized-structural-equation-model sem structural-equation-modeling
Last synced: 25 days ago
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lessSEM estimates sparse structural equation models.
- Host: GitHub
- URL: https://github.com/jhorzek/lesssem
- Owner: jhorzek
- License: gpl-2.0
- Created: 2022-04-05T13:30:25.000Z (over 2 years ago)
- Default Branch: main
- Last Pushed: 2024-07-21T20:30:56.000Z (5 months ago)
- Last Synced: 2024-11-28T16:00:19.001Z (30 days ago)
- Topics: lasso, psychometrics, r, regularization, regularized-structural-equation-model, sem, structural-equation-modeling
- Language: R
- Homepage: https://jhorzek.github.io/lessSEM/
- Size: 14.6 MB
- Stars: 7
- Watchers: 3
- Forks: 1
- Open Issues: 8
-
Metadata Files:
- Readme: README.Rmd
- Changelog: NEWS.md
- License: LICENSE.md
Awesome Lists containing this project
README
---
output: github_document
---
```{r, include = FALSE}
knitr::opts_chunk$set(
collapse = TRUE,
comment = "#>",
fig.path = "man/figures/README-",
out.width = "100%"
)
set.seed(123)
```
# lessSEM
[](https://cranlogs.r-pkg.org/badges/grand-total/lessSEM)
**lessSEM** (**l**essSEM **es**timates **s**parse **SEM**) is an R package for
regularized structural equation modeling (regularized SEM) with non-smooth
penalty functions (e.g., lasso) building on [**lavaan**](https://github.com/yrosseel/lavaan).
**lessSEM** is heavily inspired by the [**regsem**](https://github.com/Rjacobucci/regsem) package
and the [**lslx**](https://github.com/psyphh/lslx) packages that have similar functionality.
**If you use lessSEM, please also cite [regsem](https://github.com/Rjacobucci/regsem) and
and [lslx](https://github.com/psyphh/lslx)!**
The objectives of **lessSEM** are to provide ...
1. a flexible framework for regularizing SEM.
2. optimizers for other packages that can handle non-differentiable penalty functions.
The following penalty functions are currently implemented in **lessSEM**:
The column "penalty" refers to the name of the function call in the **lessSEM** package
(e.g., lasso is called with the `lasso()` function).
The best model can be selected with the
AIC or BIC. If you want to use cross-validation, use `cvLasso`, `cvAdaptiveLasso`,
etc. instead (see, e.g., `?lessSEM::cvLasso`).
## [**regsem**](https://github.com/Rjacobucci/regsem), [**lslx**](https://github.com/psyphh/lslx), and **lessSEM**
The packages [**regsem**](https://github.com/Rjacobucci/regsem),
[**lslx**](https://github.com/psyphh/lslx), and **lessSEM** can all be used to
regularize basic SEM. In fact, as outlined above, **lessSEM** is heavily inspired
by [**regsem**](https://github.com/Rjacobucci/regsem)
and [**lslx**](https://github.com/psyphh/lslx). However, the packages differ in their targets: The objective
of **lessSEM** is not to replace the more mature packages [**regsem**](https://github.com/Rjacobucci/regsem)
and [**lslx**](https://github.com/psyphh/lslx). Instead, our objective is to
provide method developers with a flexible framework for regularized SEM.
The following shows an incomplete comparison of some features implemented in
the three packages:
| | **regsem** | **lslx** | **lessSEM** |
| --- | --- | --- | --- |
| Model specification | based on lavaan | similar to lavaan | based on lavaan |
| Maximum likelihood estimation | Yes | Yes | Yes |
| Least squares estimation | No | Yes | Dev. |
| Categorical variables | No | Yes | No |
| Confidence Intervals | No | Yes | No |
| Missing Data | FIML | Auxiliary Variables | FIML |
| Multi-group models | No | Yes | Yes |
| Stability selection | Yes | No | Dev. |
| Mixed penalties | No | No | Yes |
| Equality constraints | Yes | No | Yes |
| Parameter transformations | diff_lasso | No | Yes |
| Definition variables | No | No | Yes |
> **Warning**
> Dev. refers to features that are supported, but still under development and
may have bugs. Use with caution!
# Installation
If you want to install **lessSEM** from CRAN, use the following commands in R:
```{r, eval = FALSE}
install.packages("lessSEM")
```
The newest version of the package can be installed from GitHub. However, because the
project uses submodules, `devtools::install_github` does not download the entire
R package. To download the development version, the following command needs to
be run in git:
```
git clone --branch development --recurse-submodules https://github.com/jhorzek/lessSEM.git
```
Navigate to the folder to which git copied the project and install the package
with the lessSEM.Rproj file.
If you want to download the main branch, use
```
git clone --recurse-submodules https://github.com/jhorzek/lessSEM.git
```
> **Note**
> The lessSEM project has multiple branches. The **main**
branch will match the version currently available from CRAN. The **development** branch
will have newer features not yet available from CRAN. This branch will have passed all
current tests of our test suite, but may not be ready for CRAN yet (e.g., because
not all objectives of the road map have been met). **gh-pages** is used to create
the [documentation website](https://jhorzek.github.io/lessSEM/). Finally, all other branches
are used for ongoing development and should be considered unstable.
# Introduction
Please visit the [lessSEM website](https://jhorzek.github.io/lessSEM/) for
the latest documentation. You will also find a short introduction to regularized
SEM in `vignette('lessSEM', package = 'lessSEM')`and the documentation of the
individual functions (e.g., see `?lessSEM::scad`).
Finally, you will find templates for a selection of models that can be used with **lessSEM**
(e.g., the cross-lagged panel model) in the package [**lessTemplates**](https://github.com/jhorzek/lessTemplates).
# Example
```{r, results = 'hide', fig.show='hide', message=FALSE, warning=FALSE}
library(lessSEM)
library(lavaan)
# Identical to regsem, lessSEM builds on the lavaan
# package for model specification. The first step
# therefore is to implement the model in lavaan.
dataset <- simulateExampleData()
lavaanSyntax <- "
f =~ l1*y1 + l2*y2 + l3*y3 + l4*y4 + l5*y5 +
l6*y6 + l7*y7 + l8*y8 + l9*y9 + l10*y10 +
l11*y11 + l12*y12 + l13*y13 + l14*y14 + l15*y15
f ~~ 1*f
"
lavaanModel <- lavaan::sem(lavaanSyntax,
data = dataset,
meanstructure = TRUE,
std.lv = TRUE)
# Optional: Plot the model
# if(!require("semPlot")) install.packages("semPlot")
# semPlot::semPaths(lavaanModel,
# what = "est",
# fade = FALSE)
lsem <- lasso(
# pass the fitted lavaan model
lavaanModel = lavaanModel,
# names of the regularized parameters:
regularized = c("l6", "l7", "l8", "l9", "l10",
"l11", "l12", "l13", "l14", "l15"),
# in case of lasso and adaptive lasso, we can specify the number of lambda
# values to use. lessSEM will automatically find lambda_max and fit
# models for nLambda values between 0 and lambda_max. For the other
# penalty functions, lambdas must be specified explicitly
nLambdas = 50)
# use the plot-function to plot the regularized parameters:
plot(lsem)
# use the coef-function to show the estimates
coef(lsem)
# the best parameters can be extracted with:
coef(lsem, criterion = "AIC")
coef(lsem, criterion = "BIC")
# if you just want the estimates, use estimates():
estimates(lsem, criterion = "AIC")
# elements of lsem can be accessed with the @ operator:
lsem@parameters[1,]
# AIC and BIC for all tuning parameter configurations:
AIC(lsem)
BIC(lsem)
# cross-validation
cv <- cvLasso(lavaanModel = lavaanModel,
regularized = c("l6", "l7", "l8", "l9", "l10",
"l11", "l12", "l13", "l14", "l15"),
lambdas = seq(0,1,.1),
standardize = TRUE)
# get best model according to cross-validation:
coef(cv)
#### Advanced ####
# Switching the optimizer:
# Use the "method" argument to switch the optimizer. The control argument
# must also be changed to the corresponding function:
lsemIsta <- lasso(
lavaanModel = lavaanModel,
regularized = paste0("l", 6:15),
nLambdas = 50,
method = "ista",
control = controlIsta(
# Here, we can also specify that we want to use multiple cores:
nCores = 2))
# Note: The results are basically identical:
lsemIsta@parameters - lsem@parameters
```
If you want to regularize all loadings, regressions, variances, or covariances, you
can also use one of the helper functions to extract the respective parameter labels
from **lavaan** and then pass these to **lessSEM**:
```{r}
loadings(lavaanModel)
regressions(lavaanModel)
variances(lavaanModel)
covariances(lavaanModel)
```
# Transformations
**lessSEM** allows for parameter transformations that could, for instance, be used to test
measurement invariance in longitudinal models (e.g., Liang, 2018; Bauer et al., 2020).
A thorough introduction is provided in ``vignette('Parameter-transformations', package = 'lessSEM')``.
As an example, we will test measurement invariance in the `PoliticalDemocracy`
data set.
```{r, results = 'hide', fig.show='hide', message=FALSE}
library(lessSEM)
library(lavaan)
# we will use the PoliticalDemocracy from lavaan (see ?lavaan::sem)
model <- '
# latent variable definitions
ind60 =~ x1 + x2 + x3
# assuming different loadings for different time points:
dem60 =~ y1 + a1*y2 + b1*y3 + c1*y4
dem65 =~ y5 + a2*y6 + b2*y7 + c2*y8
# regressions
dem60 ~ ind60
dem65 ~ ind60 + dem60
# residual correlations
y1 ~~ y5
y2 ~~ y4 + y6
y3 ~~ y7
y4 ~~ y8
y6 ~~ y8
'
fit <- sem(model, data = PoliticalDemocracy)
# We will define a transformation which regularizes differences
# between loadings over time:
transformations <- "
// which parameters do we want to use?
parameters: a1, a2, b1, b2, c1, c2, delta_a2, delta_b2, delta_c2
// transformations:
a2 = a1 + delta_a2;
b2 = b1 + delta_b2;
c2 = c1 + delta_c2;
"
# setting delta_a2, delta_b2, or delta_c2 to zero implies measurement invariance
# for the respective parameters (a1, b1, c1)
lassoFit <- lasso(lavaanModel = fit,
# we want to regularize the differences between the parameters
regularized = c("delta_a2", "delta_b2", "delta_c2"),
nLambdas = 100,
# Our model modification must make use of the modifyModel - function:
modifyModel = modifyModel(transformations = transformations)
)
```
Finally, we can extract the best parameters:
```{r, results = 'hide', message=FALSE}
coef(lassoFit, criterion = "BIC")
```
As all differences (`delta_a2`, `delta_b2`, and `delta_c2`) have been zeroed, we can
assume measurement invariance.
# Experimental Features
The following features are relatively new and you may still experience some bugs.
Please be aware of that when using these features.
## From **lessSEM** to **lavaan**
**lessSEM** supports exporting specific models to **lavaan**. This can be very useful when plotting the
final model.
```{r, results = 'hide', message=FALSE}
lavaanModel <- lessSEM2Lavaan(regularizedSEM = lsem,
criterion = "BIC")
```
The result can be plotted with, for instance, [**semPlot**](https://github.com/SachaEpskamp/semPlot):
```{r, results = 'hide', fig.show='hide', message=FALSE}
library(semPlot)
semPaths(lavaanModel,
what = "est",
fade = FALSE)
```
## Multi-Group Models and Definition Variables
**lessSEM** supports multi-group SEM and, to some degree, definition variables.
Regularized multi-group SEM have been proposed by Huang (2018) and are
implemented in **lslx** (Huang, 2020). Here, differences between groups are regularized.
A detailed introduction can be found in
`vignette(topic = "Definition-Variables-and-Multi-Group-SEM", package = "lessSEM")`.
Therein it is also explained how the multi-group SEM can be used to implement
definition variables (e.g., for latent growth curve models).
## Mixed Penalties
**lessSEM** allows for defining different penalties for different parts
of the model. This feature is new and very experimental. Please keep that
in mind when using the procedure. A detailed introduction
can be found in `vignette(topic = "Mixed-Penalties", package = "lessSEM")`.
To provide a short example, we will regularize the loadings and the regression
parameters of the Political Democracy data set with different penalties. The
following script is adapted from `?lavaan::sem`.
```{r, results = 'hide', message=FALSE}
model <- '
# latent variable definitions
ind60 =~ x1 + x2 + x3 + c2*y2 + c3*y3 + c4*y4
dem60 =~ y1 + y2 + y3 + y4
dem65 =~ y5 + y6 + y7 + c*y8
# regressions
dem60 ~ r1*ind60
dem65 ~ r2*ind60 + r3*dem60
'
lavaanModel <- sem(model,
data = PoliticalDemocracy)
# Let's add a lasso penalty on the cross-loadings c2 - c4 and
# scad penalty on the regressions r1-r3
fitMp <- lavaanModel |>
mixedPenalty() |>
addLasso(regularized = c("c2", "c3", "c4"),
lambdas = seq(0,1,.1)) |>
addScad(regularized = c("r1", "r2", "r3"),
lambdas = seq(0,1,.2),
thetas = 3.7) |>
fit()
```
The best model according to the BIC can be extracted with:
```{r, results = 'hide', message=FALSE}
coef(fitMp, criterion = "BIC")
```
# Optimizers
Currently, **lessSEM** has the following optimizers:
- (variants of) iterative shrinkage and thresholding (e.g., Beck & Teboulle, 2009;
Gong et al., 2013; Parikh & Boyd, 2013); optimization of cappedL1, lsp, scad,
and mcp is based on Gong et al. (2013)
- glmnet (Friedman et al., 2010; Yuan et al., 2012; Huang, 2020)
These optimizers are implemented based on the
[**regCtsem**](https://github.com/jhorzek/regCtsem) package. Most importantly,
**all optimizers in lessSEM are available for other packages.**
There are four ways to implement them which are documented in
`vignette("General-Purpose-Optimization", package = "lessSEM")`.
In short, these are:
1. using the R interface: All general purpose implementations of the functions
are called with prefix "gp" (`gpLasso`, `gpScad`, ...). More information and
examples can be found in the documentation of these functions (e.g., `?lessSEM::gpLasso`,
`?lessSEM::gpAdaptiveLasso`, `?lessSEM::gpElasticNet`). The interface is similar to
the optim optimizers in R.
2. using Rcpp, we can pass C++ function pointers to the general purpose optimizers
`gpLassoCpp`, `gpScadCpp`, ... (e.g., `?lessSEM::gpLassoCpp`)
3. All optimizers are implemented as C++ header-only files in **lessSEM**. Thus,
they can be accessed from other packages using C++. The interface is similar
to that of the [**ensmallen**](https://ensmallen.org/) library. We have implemented
a simple example for elastic net regularization of linear regressions in the
[**lessLM**](https://github.com/jhorzek/lessLM) package. You can also find more
details on the general design of the optimizer interface in `vignette("The-optimizer-interface", package = "lessSEM")`.
4. The optimizers are implemented in the separate C++ header only library
[lesstimate](https://jhorzek.github.io/lesstimate/) that can be used as a submodule
in R packages.
# References
## R - Packages / Software
* [lavaan](https://github.com/yrosseel/lavaan) Rosseel, Y. (2012). lavaan: An R Package for Structural Equation Modeling. Journal of Statistical Software, 48(2), 1-36. https://doi.org/10.18637/jss.v048.i02
* [regsem](https://github.com/Rjacobucci/regsem): Jacobucci, R. (2017). regsem:
Regularized Structural Equation Modeling. ArXiv:1703.08489 [Stat]. https://arxiv.org/abs/1703.08489
* [lslx](https://github.com/psyphh/lslx): Huang, P.-H. (2020). lslx:
Semi-confirmatory structural equation modeling via penalized likelihood. Journal
of Statistical Software, 93(7). https://doi.org/10.18637/jss.v093.i07
* [fasta](https://CRAN.R-project.org/package=fasta):
Another implementation of the fista algorithm (Beck & Teboulle, 2009).
* [ensmallen](https://ensmallen.org/): Curtin, R. R., Edel, M., Prabhu, R. G.,
Basak, S., Lou, Z., & Sanderson, C. (2021). The ensmallen library for flexible
numerical optimization. Journal of Machine Learning Research, 22, 1–6.
* [regCtsem](https://github.com/jhorzek/regCtsem): Orzek, J. H., & Voelkle, M. C. (in press).
Regularized continuous time structural equation models: A network perspective. Psychological Methods.
## Regularized Structural Equation Modeling
* Huang, P.-H., Chen, H., & Weng, L.-J. (2017). A Penalized Likelihood Method
for Structural Equation Modeling. Psychometrika, 82(2), 329–354. https://doi.org/10.1007/s11336-017-9566-9
* Huang, P.-H. (2018). A penalized likelihood method for multi-group structural equation modelling. British Journal of Mathematical and Statistical Psychology, 71(3), 499–522. https://doi.org/10.1111/bmsp.12130
* Jacobucci, R., Grimm, K. J., & McArdle, J. J. (2016). Regularized Structural
Equation Modeling. Structural Equation Modeling: A Multidisciplinary Journal, 23(4),
555–566. https://doi.org/10.1080/10705511.2016.1154793
## Penalty Functions
* Candès, E. J., Wakin, M. B., & Boyd, S. P. (2008). Enhancing Sparsity by
Reweighted l1 Minimization. Journal of Fourier Analysis and Applications, 14(5–6),
877–905. https://doi.org/10.1007/s00041-008-9045-x
* Fan, J., & Li, R. (2001). Variable selection via nonconcave penalized
likelihood and its oracle properties. Journal of the American Statistical
Association, 96(456), 1348–1360. https://doi.org/10.1198/016214501753382273
* Hoerl, A. E., & Kennard, R. W. (1970). Ridge Regression: Biased Estimation
for Nonorthogonal Problems. Technometrics, 12(1), 55–67. https://doi.org/10.1080/00401706.1970.10488634
* Tibshirani, R. (1996). Regression shrinkage and selection via the lasso.
Journal of the Royal Statistical Society. Series B (Methodological), 58(1), 267–288.
* Zhang, C.-H. (2010). Nearly unbiased variable selection under minimax concave penalty.
The Annals of Statistics, 38(2), 894–942. https://doi.org/10.1214/09-AOS729
* Zhang, T. (2010). Analysis of Multi-stage Convex Relaxation for Sparse Regularization.
Journal of Machine Learning Research, 11, 1081–1107.
* Zou, H. (2006). The adaptive lasso and its oracle properties. Journal of the
American Statistical Association, 101(476), 1418–1429. https://doi.org/10.1198/016214506000000735
* Zou, H., & Hastie, T. (2005). Regularization and variable selection via the
elastic net. Journal of the Royal Statistical Society: Series B, 67(2), 301–320.
https://doi.org/10.1111/j.1467-9868.2005.00503.x
## Optimizer
### GLMNET
* Friedman, J., Hastie, T., & Tibshirani, R. (2010). Regularization paths for
generalized linear models via coordinate descent. Journal of Statistical
Software, 33(1), 1–20. https://doi.org/10.18637/jss.v033.i01
* Yuan, G.-X., Ho, C.-H., & Lin, C.-J. (2012). An improved GLMNET for
l1-regularized logistic regression. The Journal of Machine Learning Research,
13, 1999–2030. https://doi.org/10.1145/2020408.2020421
### Variants of ISTA
* Beck, A., & Teboulle, M. (2009). A Fast Iterative Shrinkage-Thresholding
Algorithm for Linear Inverse Problems. SIAM Journal on Imaging Sciences, 2(1),
183–202. https://doi.org/10.1137/080716542
* Gong, P., Zhang, C., Lu, Z., Huang, J., & Ye, J. (2013). A general iterative
shrinkage and thresholding algorithm for non-convex regularized optimization problems.
Proceedings of the 30th International Conference on Machine Learning, 28(2)(2), 37–45.
* Parikh, N., & Boyd, S. (2013). Proximal Algorithms. Foundations and
Trends in Optimization, 1(3), 123–231.
## Miscellaneous
* Liang, X., Yang, Y., & Huang, J. (2018). Evaluation of structural relationships in autoregressive cross-lagged models under longitudinal approximate invariance: A Bayesian analysis. Structural Equation Modeling: A Multidisciplinary Journal, 25(4), 558–572. https://doi.org/10.1080/10705511.2017.1410706
* Bauer, D. J., Belzak, W. C. M., & Cole, V. T. (2020). Simplifying the Assessment of Measurement Invariance over Multiple Background Variables: Using Regularized Moderated Nonlinear Factor Analysis to Detect Differential Item Functioning. Structural Equation Modeling: A Multidisciplinary Journal, 27(1), 43–55. https://doi.org/10.1080/10705511.2019.1642754
# LICENSE NOTE
THE SOFTWARE IS PROVIDED 'AS IS', WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED,
INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
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