---
title: "6. Unified SEM (uSEM)"
output:
  rmarkdown::html_vignette:
    toc: true
vignette: >
  %\VignetteIndexEntry{6. Unified SEM (uSEM)}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(
  collapse = TRUE, comment = "#>", message = FALSE, warning = FALSE,
  fig.width = 7, fig.height = 5.5
)
```

```{r libraries}
library(idiographic)
set.seed(42)
vars <- c("A", "B")
has_cograph <- requireNamespace("cograph", quietly = TRUE)
```

`build_usem()` fits a **unified SEM** over lagged and contemporaneous paths for
each person. Supply `id` plus either a `time` column or `day`/`beep` columns so
lagged rows are formed in the correct within-person order.

The vignette uses a small simulated panel so it builds quickly and deterministi-
cally on every machine. The first pass is a stable fixed autoregressive model
plus residual covariances; broader contemporaneous search models should be
checked against convergence diagnostics before interpretation.

```{r usem}
panel <- do.call(rbind, lapply(seq_len(4), function(i) {
  n <- 30
  ri <- stats::rnorm(length(vars), 0, 0.5)
  e <- matrix(stats::rnorm(n * length(vars)), ncol = length(vars))
  for (t in 2:n) {
    e[t, ] <- 0.35 * e[t - 1L, ] + e[t, ]
  }
  values <- as.data.frame(sweep(e, 2, ri, "+"))
  names(values) <- vars
  data.frame(
    id = i,
    day = rep(1:3, each = 10),
    beep = rep(1:10, 3),
    values
  )
}))

usem_fit <- tryCatch(
  build_usem(panel, vars = vars, id = "id", day = "day", beep = "beep",
             temporal = "ar", contemporaneous = "none", residual_cov = TRUE),
  error = function(e) {
    message("uSEM model did not converge in this R/lavaan build: ",
            conditionMessage(e))
    NULL
  }
)

if (!is.null(usem_fit)) usem_fit
```

# Tidy tables

```{r usem-tables, eval=!is.null(usem_fit)}
head(edges(usem_fit))

summary(usem_fit)
```

```{r usem-matrices, eval=!is.null(usem_fit)}
matrices(usem_fit)
```

# Plot

```{r plot-usem, eval=has_cograph && !is.null(usem_fit)}
plot(usem_fit, layer = "temporal")
```

```{r plot-usem-contemp, eval=has_cograph && !is.null(usem_fit)}
plot(usem_fit, layer = "contemporaneous")
```