Imputes univariate missing data using a two-level normal model

## Arguments

- y
Vector to be imputed

- ry
Logical vector of length

`length(y)`

indicating the the subset`y[ry]`

of elements in`y`

to which the imputation model is fitted. The`ry`

generally distinguishes the observed (`TRUE`

) and missing values (`FALSE`

) in`y`

.- x
Numeric design matrix with

`length(y)`

rows with predictors for`y`

. Matrix`x`

may have no missing values.- type
Vector of length

`ncol(x)`

identifying random and class variables. Random variables are identified by a '2'. The class variable (only one is allowed) is coded as '-2'. Random variables also include the fixed effect.- wy
Logical vector of length

`length(y)`

. A`TRUE`

value indicates locations in`y`

for which imputations are created.- intercept
Logical determining whether the intercept is automatically added.

- ...
Other named arguments.

## Details

Implements the Gibbs sampler for the linear multilevel model with heterogeneous with-class variance (Kasim and Raudenbush, 1998). Imputations are drawn as an extra step to the algorithm. For simulation work see Van Buuren (2011).

The random intercept is automatically added in `mice.impute.2L.norm()`

.
A model within a random intercept can be specified by ```
mice(...,
intercept = FALSE)
```

.

## Note

Added June 25, 2012: The currently implemented algorithm does not
handle predictors that are specified as fixed effects (type=1). When using
`mice.impute.2l.norm()`

, the current advice is to specify all predictors
as random effects (type=2).

Warning: The assumption of heterogeneous variances requires that in every
class at least one observation has a response in `y`

.

## References

Kasim RM, Raudenbush SW. (1998). Application of Gibbs sampling to nested variance components models with heterogeneous within-group variance. Journal of Educational and Behavioral Statistics, 23(2), 93--116.

Van Buuren, S., Groothuis-Oudshoorn, K. (2011). `mice`

: Multivariate
Imputation by Chained Equations in `R`

. *Journal of Statistical
Software*, **45**(3), 1-67. doi:10.18637/jss.v045.i03

Van Buuren, S. (2011) Multiple imputation of multilevel data. In Hox, J.J.
and and Roberts, J.K. (Eds.), *The Handbook of Advanced Multilevel
Analysis*, Chapter 10, pp. 173--196. Milton Park, UK: Routledge.

## See also

Other univariate-2l:
`mice.impute.2l.bin()`

,
`mice.impute.2l.lmer()`

,
`mice.impute.2l.pan()`