penfa

R package for penalized factor analysis via trust-region algorithm and automatic multiple tuning parameter selection

https://github.com/egeminiani/penfa

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R package for penalized factor analysis via trust-region algorithm and automatic multiple tuning parameter selection

README.Rmd

---
output: github_document
---



```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.path = "man/figures/README-",
  out.width = "100%"
)
```

# penfa



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### Overview

An R package for estimating single- and multiple-group penalized factor models
via a trust-region algorithm with integrated automatic multiple tuning parameter
selection (Geminiani et al., 2021). Supported penalties include lasso, adaptive
lasso, scad, mcp, and ridge.

### Installation


You can install the released version of penfa from CRAN with:

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

And the development version from [GitHub](https://github.com/) with:

``` r
# install.packages("devtools")
devtools::install_github("egeminiani/penfa")
```
### Example

This is a basic example showing how to fit a *PENalized Factor Analysis* model
with the alasso penalty and the automatic tuning procedure. A shrinkage penalty 
is applied to the whole factor loading matrix.

Let's load the data (see `?ccdata` for details).

```{r data}
library(penfa)
data(ccdata)
```

**Step 1** : specify the model syntax

```{r syntax}
syntax = 'help  =~   h1 + h2 + h3 + h4 + h5 + h6 + h7 + 0*v1 + v2 + v3 + v4 + v5
          voice =~ 0*h1 + h2 + h3 + h4 + h5 + h6 + h7 +   v1 + v2 + v3 + v4 + v5'
```

**Step 2**: fit the model

```{r fit}
alasso_fit <- penfa(model  = syntax,
                    data   = ccdata,
                    std.lv = TRUE,
                    pen.shrink = "alasso")
```


```{r show}
alasso_fit
```

**Step 3**: inspect the results

```{r summary}
summary(alasso_fit)
```


### Vignettes and Tutorials

* See `vignette("automatic-tuning-selection")` for the estimation of a penalized
factor model with lasso and alasso penalties. The tuning parameter producing the
optimal amount of sparsity in the factor loading matrix is found through the
automatic tuning procedure.
 
* See `vignette("grid-search-tuning-selection")` for the estimation of a
penalized factor model with scad and mcp penalties. A grid search is conducted,
and the optimal tuning parameter is the one generating the penalized model with
the lowest GBIC (Generalized Bayesian Information Criterion).

* See ["multiple-group-analysis"](https://egeminiani.github.io/penfa/articles/articles/multiple-group-analysis.html) for the estimation of a multiple-group penalized factor model 
with the alasso penalty. This model encourages sparsity in the loading matrices 
and cross-group invariance of loadings and intercepts. The automatic multiple 
tuning parameter procedure is employed for finding the optimal tuning parameter 
vector.

* See ["plotting-penalty-matrix"](https://egeminiani.github.io/penfa/articles/articles/plotting-penalty-matrix.html) for details on how to produce interactive plots of the penalty matrices.


### Literature

* Geminiani, E., Marra, G., & Moustaki, I. (2021). "Single- and Multiple-Group
Penalized Factor Analysis: A Trust-Region Algorithm Approach with Integrated
Automatic Multiple Tuning Parameter Selection." Psychometrika, 86(1), 65-95. [https://doi.org/10.1007/s11336-021-09751-8](https://doi.org/10.1007/s11336-021-09751-8)

* Geminiani, E. (2020). "A Penalized Likelihood-Based Framework for Single and
Multiple-Group Factor Analysis Models." PhD thesis, University of Bologna.
[http://amsdottorato.unibo.it/9355/](http://amsdottorato.unibo.it/9355/).


### How to cite

```{r citation, echo=FALSE}
print(citation("penfa"), bibtex = TRUE)
```

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