Akaike's information criterion (R's AIC()).
Schwarz's Bayesian information criterion (R's BIC()).
The coefficient table of the fixed effects (R's coef(summary(fit)), without the p-values).
Estimates (R's Estimate).
Standard errors (R's Std. Error).
Estimates over standard errors (R's z value; R labels it t value for Gamma, inverse.gaussian and gaussian).
The sum of the squared deviance residuals (R's deviance(); not −2 logLik).
Degrees of freedom of the log-likelihood: the numbers of fixed effects and of θ, plus 1 for the families with a dispersion.
The family.
The fitted means μ̂, one per row used (R's fitted(); for a binomial response the probabilities).
The fixed effects β̂ (R's fixef()).
Names of the columns of the fixed-effects model matrix (aliased columns dropped).
The formula.
The linear predictor η̂ = offset + Xβ̂ + Zb̂, one per row used (R's predict()).
The link.
The log-likelihood: of the Laplace approximation, −1/2 times the deviance minimised (R's logLik()), or with
nAGQ > 1 of the quadrature, including the constant of the saturated model that R's logLik() leaves out there
(so that it is comparable with nAGQ = 1 and with glm).
R's messages (a rank-deficient fixed-effects matrix, a singular fit).
1 (the Laplace approximation), 0 (β from the penalised IRLS) or the number of quadrature points (2 to 100).
Number of rows used (rows with prior weight 0 included; R's nobs()).
The Pearson residuals √w (y − μ̂) / √V(μ̂) (R's residuals(fit, "pearson")).
The conditional modes of the random effects, one entry per grouping factor (R's ranef()).
The deviance residuals (R's residuals(), whose default type for glmer is "deviance").
The response residuals y − μ̂ (R's residuals(fit, "response"); y the proportion for cbind(s, f)).
0-based indices of the rows of data used (rows with a missing value in a variable, a weight or the offset dropped).
R's sigma(): 1 for binomial and poisson; otherwise the square root of the sum of the squared Pearson residuals
plus the squared length of the spherical random effects, over nObs.
Whether the fit is singular: a diagonal element of a relative covariance factor below 1e-4 (R's isSingular()).
The estimate of the covariance parameters θ (R's getME(fit, "theta")): the lower triangles of the relative covariance factors, by term, column-major.
The variance components, one entry per random-effects term (R's VarCorr(); not scaled by sigma).
The covariance matrix of the fixed effects (R's vcov()), array of rows.
How vcov was computed: "hessian", 2 times the block of the fixed effects of the inverse Hessian of the
deviance in (θ, β) (R's default for nAGQ = 1 when the fit is not singular, nObs < 10000 and there are fewer than
20 parameters), or "RX", σ² (R_X'R_X)⁻¹ of the penalised IRLS at the conditional mode.
R's warnings (predictors on very different scales, the response, the fallback of vcov).
The working residuals (y − μ̂) / μ'(η̂) (R's residuals(fit, "working")).
Result of glmer: the fit of a generalized linear mixed model and the quantities of R's methods for it.