is_converged() provides an alternative convergence
test for merMod-objects.
Value
TRUE if convergence is fine and FALSE if convergence
is suspicious. Additionally, the convergence value is returned as attribute.
Convergence and log-likelihood
Convergence problems typically arise when the model hasn't converged to a solution where the log-likelihood has a true maximum. This may result in unreliable and overly complex (or non-estimable) estimates and standard errors.
Inspect model convergence
lme4 performs a convergence-check (see ?lme4::convergence), however, as
discussed here and suggested by
one of the lme4-authors in this comment,
this check can be too strict. is_converged() thus provides an alternative
convergence test for merMod-objects.
Resolving convergence issues
Convergence issues are not easy to diagnose. The help page on ?lme4::convergence
provides most of the current advice about how to resolve convergence issues.
Another clue might be large parameter values, e.g. estimates (on the scale of
the linear predictor) larger than 10 in (non-identity link) generalized linear
model might indicate complete separation, which can be addressed by
regularization, e.g. penalized regression or Bayesian regression with
appropriate priors on the fixed effects.
Convergence versus Singularity
Note the different meaning between singularity and convergence: singularity indicates an issue with the "true" best estimate, i.e. whether the maximum likelihood estimation for the variance-covariance matrix of the random effects is positive definite or only semi-definite. Convergence is a question of whether we can assume that the numerical optimization has worked correctly or not.
Examples
data(cbpp)
set.seed(1)
cbpp$x <- rnorm(nrow(cbpp))
cbpp$x2 <- runif(nrow(cbpp))
model <- glmer(
cbind(incidence, size - incidence) ~ period + x + x2 + (1 + x | herd),
data = cbpp,
family = binomial()
)
is_converged(model)
#> [1] TRUE
#> attr(,"gradient")
#> [1] 0.0002803063
# \donttest{
model <- glmmTMB(
Sepal.Length ~ poly(Petal.Width, 4) * poly(Petal.Length, 4) +
(1 + poly(Petal.Width, 4) | Species),
data = iris
)
#> Warning: Model convergence problem; non-positive-definite Hessian matrix. See vignette('troubleshooting')
#> Warning: Model convergence problem; false convergence (8). See vignette('troubleshooting'), help('diagnose')
is_converged(model)
#> [1] FALSE
# }