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))).
Estimates (R's Estimate).
Standard errors (R's Std. Error).
t statistics (R's t value).
The ML deviance at the estimates, for either kind of fit (R's deviance(fit, REML = FALSE)).
Degrees of freedom of the log-likelihood: the numbers of fixed effects and of θ, plus 1 (for σ).
Fitted values Xβ̂ + Zb̂, one per row used (R's fitted()).
The fixed effects β̂ (R's fixef()).
Names of the columns of the fixed-effects model matrix (aliased columns dropped).
The formula.
The log-likelihood, or the REML log-likelihood for a REML fit (R's logLik()).
R's messages (a rank-deficient fixed-effects matrix, a singular fit).
Number of rows used.
The conditional modes of the random effects, one entry per grouping factor (R's ranef()).
Whether the REML criterion was minimised (otherwise the ML deviance).
The REML criterion at the estimates, for either kind of fit (R's REMLcrit()).
Residuals y − fitted (R's residuals()).
0-based indices of the rows of data used (rows with a missing value in a variable of the formula dropped).
The residual standard deviation (R's sigma()).
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()).
The covariance matrix of the fixed effects (R's vcov()), array of rows.
R's warnings (predictors on very different scales).
Result of lmer: the fit of a linear mixed model and the quantities of R's methods for it.