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Convergence test for mixed effects models

Source: R/is_converged.R
is_converged.Rd

is_converged() provides an alternative convergence test for merMod-objects.

Usage

is_converged(x, tolerance = 0.001, ...)

Arguments

x

A merMod or glmmTMB-object.

tolerance

Indicates up to which value the convergence result is accepted. The smaller tolerance is, the stricter the test will be.

...

Currently not used.

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()
)
#> boundary (singular) fit: see help('isSingular')

is_converged(model)
#> [1] TRUE
#> attr(,"gradient")
#> [1] 8.444729e-05
# \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
# }