---
title: "Likelihood-based inference"
author: "metaGLMM authors"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Likelihood-based inference}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(collapse = TRUE, comment = "#>",
                      fig.width = 6, fig.height = 4)
set.seed(20260821)
library(metaGLMM)
```

## Fit a model

This example uses the same aggregate-data contract for a small Gaussian
random-effects model.

```{r data-fit}
dat <- data.frame(
  study = paste0("Study ", 1:8),
  estimate = c(-0.80, -0.30, 0.10, 0.70, 1.10, -0.50, 0.40, 1.30),
  moderator = c(0, 1, 0, 1, 0, 1, 0, 1),
  vi = c(0.04, 0.05, 0.03, 0.06, 0.04, 0.05, 0.03, 0.05),
  ni = c(100, 90, 120, 80, 110, 95, 130, 85)
)

fit <- metaGLMM(
  estimate ~ moderator,
  data = dat,
  vi = dat$vi,
  ni = dat$ni,
  tau2 = NA,
  tau2_var = TRUE,
  family = gaussian(link = "identity"),
  fast = TRUE
)
summary(fit)
```

## Wald intervals

The default interval is based on the fixed-effect estimate and its covariance
matrix.  Specify a coefficient with `parm` or request all fixed effects.

```{r wald}
confint(fit, method = "wald")
confint(fit, parm = "moderator", level = 0.90, method = "wald")
```

## Profile and SBC intervals

The official `confint()` interface accepts three method names:
`"wald"`, `"profile"`, and `"SBC"`.  Names are case-insensitive and
intervals target fixed effects.  Profile evaluation re-optimizes the nuisance
parameters at each fixed-effect value; SBC applies the simple small-sample
correction to the profile cutoff.

```{r profile, eval=FALSE}
profile_ci <- confint(fit, parm = "moderator",
                      method = "profile", level = 0.95)
profile_ci

sbc_ci <- confint(fit, parm = "moderator",
                  method = "SBC", level = 0.95)
sbc_ci
```

The profile and SBC calculations are more expensive than Wald intervals.  For
a larger analysis, use a fixed QMC sequence and record the optimizer settings
along with the fitted object.

## Inspecting the likelihood fit

The standard methods keep the fixed-effect interface separate from
heterogeneity parameters.

```{r methods}
coef(fit)
vcov(fit)
logLik(fit)
nobs(fit)
fit$tau2
fit$tau
stopifnot(is.finite(fit$tau), fit$tau > 0)
```

A method value outside the three documented choices is rejected rather than
silently selecting a different interval procedure.  The legacy
`ci_metaGLMM()` and low-level profile helpers remain available for existing
scripts, but new code should use `confint()`.