Likelihood-based inference

The hardware and bandwidth for this mirror is donated by METANET, the Webhosting and Full Service-Cloud Provider.
If you wish to report a bug, or if you are interested in having us mirror your free-software or open-source project, please feel free to contact us at mirror[@]metanet.ch.

metaGLMM authors

Fit a model

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

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)
#> Aggregate-data generalized linear mixed-effects meta-analysis
#> 
#> Call:
#> metaGLMM(formula = estimate ~ moderator, data = dat, vi = dat$vi, 
#>     ni = dat$ni, tau2 = NA, family = gaussian(link = "identity"), 
#>     tau2_var = TRUE, fast = TRUE)
#> 
#> Family:gaussian(identity)
#> Random-effect structure: row_intercept 
#> Integration: closed_form 
#> 
#> Fixed effects:
#>             Estimate Std. Error z value Pr(>|z|)
#> (Intercept)  0.20051    0.34997   0.573    0.567
#> moderator    0.09754    0.49933   0.195    0.845
#> 
#> Heterogeneity:
#>   tau^2: 0.455 
#>   tau:   0.6745 
#> 
#> Fit diagnostics:
#>   Optimizer: L-BFGS-B 
#>   Convergence code: 0 
#>   Boundary tau^2: no 
#>   Positive-definite Hessian: yes

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.

confint(fit, method = "wald")
#>                  lower     upper
#> (Intercept) -0.4854108 0.8864311
#> moderator   -0.8811343 1.0762113
confint(fit, parm = "moderator", level = 0.90, method = "wald")
#>                lower     upper
#> moderator -0.7237896 0.9188666

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.

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.

coef(fit)
#> (Intercept)   moderator 
#>  0.20051015  0.09753851
vcov(fit)
#>             (Intercept)  moderator
#> (Intercept)   0.1224763 -0.1224765
#> moderator    -0.1224765  0.2493325
logLik(fit)
#> 'log Lik.' -1.231958 (df=3)
nobs(fit)
#> [1] 8
fit$tau2
#> [1] 0.4549558
fit$tau
#> [1] 0.6745041
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().

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.