What is the default variance-covariance structure for random-effects in

`glmer`

or`lmer`

in`lme4`

package? How does one specify other variance-covariance structure for random-effects in the code? I could not find any information regarding this in the`lme4`

documentation.

**Answer**

The default variance-covariance structure is unstructured — that is, the only constraint on the variance-covariance matrix for an vector random effect with $n$ levels is that is positive definite. Separate random effects terms are considered independent, however, so if you want to fit (e.g.) a model with random intercept and slope where the intercept and slope are uncorrelated (not necessarily a good idea), you can use the formula `(1|g) + (0+x|g)`

, where `g`

is the grouping factor; the `0`

in the second term suppresses the intercept. If you want to fit independent parameters of a categorical variable (again, possibly questionable), you probably need to construct numeric dummy variables by hand. You can, sort of, construct a compound-symmetric variance-covariance structure (although with non-negative covariances only) by treating the factor as a nested grouping variable. For example, if `f`

is a factor, then `(1|g/f)`

will assume equal correlations among the levels of `f`

.

For other/more complex variance-covariance structures, your choices (in R) are to (1) use `nlme`

(which has the `pdMatrix`

constructors to allow more flexibility); (2) use `MCMCglmm`

(which offers a variety of structures including unstructured, compound symmetric, identity with different variances, or identity with homogeneous variances); (3) use a special-purpose package such as `pedigreemm`

that constructs a special structured matrix. There is a `flexLambda`

branch on github that eventually hopes to provide more capabilities in this direction.

**Attribution***Source : Link , Question Author : user40451 , Answer Author : Ben Bolker*