---
title: "Stepwise unregularized GGM"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Stepwise unregularized GGM}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r setup, include = FALSE}
knitr::opts_chunk$set(collapse = TRUE, comment = "#>", fig.width = 6, fig.height = 5)
has_cograph <- requireNamespace("cograph", quietly = TRUE)
```

```{r}
library(psychnets)
```

`method = "ggm"` is a different philosophy from the graphical lasso. The lasso
*shrinks* every edge toward zero; the stepwise GGM uses the lasso path only to
**propose** candidate graphs, then refits the **unregularized** maximum-likelihood
precision on each and picks the best by extended BIC, refining it with a greedy
edge add/drop search. The retained edges are therefore **not shrunk** -- they are
the exact partial correlations for the selected structure. It is equivalent to
`qgraph::ggmModSelect()` (accepted as the alias `"ggmModSelect"`) and
self-certified by the constrained-MLE stationarity residual.

```{r}
ms <- psychnet(SRL_GPT, method = "ggm")
ms
certificate(ms)
```

## Regularized vs unregularized

Because it does not shrink, the stepwise GGM's retained edges are larger in
magnitude than the lasso's on the same data. Compare the two edge lists:

```{r}
as.data.frame(psychnet(SRL_GPT, method = "glasso"))   # shrunk
as.data.frame(ms)                                      # unshrunk
```

The default `gamma` is `0` (plain BIC), matching `qgraph::ggmModSelect()` -- the
unregularized refit does not need the extra EBIC penalty.

## Predictability

```{r}
net_predict(ms)
```

## Plotting

Pass the network object to `cograph::splot()` with `psych_styling = TRUE`
(spring layout, green = positive, red = negative). For a non-glasso network
ask for the predictability ring explicitly with `predictability = TRUE`.

```{r ggmms-plot, eval = has_cograph}
cograph::splot(ms, psych_styling = TRUE, predictability = TRUE)
```

See `net_crosswalk("ggmModSelect")` for the argument map against `qgraph`.