# Imputation at level 2 by Bayesian linear regression

Source:`R/mice.impute.2lonly.norm.R`

`mice.impute.2lonly.norm.Rd`

Imputes univariate missing data at level 2 using Bayesian linear regression
analysis. Variables are level 1 are aggregated at level 2. The group
identifier at level 2 must be indicated by `type = -2`

in the
`predictorMatrix`

.

## 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
Group identifier must be specified by '-2'. Predictors must be specified by '1'.

- wy
Logical vector of length

`length(y)`

. A`TRUE`

value indicates locations in`y`

for which imputations are created.- ...
Other named arguments.

## Details

This function allows in combination with `mice.impute.2l.pan`

switching regression imputation between level 1 and level 2 as described in
Yucel (2008) or Gelman and Hill (2007, p. 541).

The function checks for partial missing level-2 data. Level-2 data
are assumed to be constant within the same cluster. If one or more
entries are missing, then the procedure aborts with an error
message that identifies the cluster with incomplete level-2 data.
In such cases, one may first fill in the cluster mean (or mode) by
the `2lonly.mean`

method to remove inconsistencies.

## Note

For a more general approach, see
`miceadds::mice.impute.2lonly.function()`

.

## References

Gelman, A. and Hill, J. (2007). *Data analysis using
regression and multilevel/hierarchical models*. Cambridge, Cambridge
University Press.

Yucel, RM (2008). Multiple imputation inference for multivariate multilevel
continuous data with ignorable non-response. *Philosophical
Transactions of the Royal Society A*, **366**, 2389-2404.

Van Buuren, S. (2018).
*Flexible Imputation of Missing Data. Second Edition.*
Chapman & Hall/CRC. Boca Raton, FL.

## See also

`mice.impute.norm`

,
`mice.impute.2lonly.pmm`

, `mice.impute.2l.pan`

,
`mice.impute.2lonly.mean`

Other univariate-2lonly:
`mice.impute.2lonly.mean()`

,
`mice.impute.2lonly.pmm()`

## Author

Alexander Robitzsch (IPN - Leibniz Institute for Science and Mathematics Education, Kiel, Germany), robitzsch@ipn.uni-kiel.de

## Examples

```
# simulate some data
# x,y ... level 1 variables
# v,w ... level 2 variables
G <- 250 # number of groups
n <- 20 # number of persons
beta <- .3 # regression coefficient
rho <- .30 # residual intraclass correlation
rho.miss <- .10 # correlation with missing response
missrate <- .50 # missing proportion
y1 <- rep(rnorm(G, sd = sqrt(rho)), each = n) + rnorm(G * n, sd = sqrt(1 - rho))
w <- rep(round(rnorm(G), 2), each = n)
v <- rep(round(runif(G, 0, 3)), each = n)
x <- rnorm(G * n)
y <- y1 + beta * x + .2 * w + .1 * v
dfr0 <- dfr <- data.frame("group" = rep(1:G, each = n), "x" = x, "y" = y, "w" = w, "v" = v)
dfr[rho.miss * x + rnorm(G * n, sd = sqrt(1 - rho.miss)) < qnorm(missrate), "y"] <- NA
dfr[rep(rnorm(G), each = n) < qnorm(missrate), "w"] <- NA
dfr[rep(rnorm(G), each = n) < qnorm(missrate), "v"] <- NA
# empty mice imputation
imp0 <- mice(as.matrix(dfr), maxit = 0)
predM <- imp0$predictorMatrix
impM <- imp0$method
# multilevel imputation
predM1 <- predM
predM1[c("w", "y", "v"), "group"] <- -2
predM1["y", "x"] <- 1 # fixed x effects imputation
impM1 <- impM
impM1[c("y", "w", "v")] <- c("2l.pan", "2lonly.norm", "2lonly.pmm")
# y ... imputation using pan
# w ... imputation at level 2 using norm
# v ... imputation at level 2 using pmm
imp1 <- mice(as.matrix(dfr),
m = 1, predictorMatrix = predM1,
method = impM1, maxit = 1, paniter = 500
)
#>
#> iter imp variable
#> 1 1 y w v
# Demonstration that 2lonly.norm aborts for partial missing data.
# Better use 2lonly.mean for repair.
data <- data.frame(
patid = rep(1:4, each = 5),
sex = rep(c(1, 2, 1, 2), each = 5),
crp = c(
68, 78, 93, NA, 143,
5, 7, 9, 13, NA,
97, NA, 56, 52, 34,
22, 30, NA, NA, 45
)
)
pred <- make.predictorMatrix(data)
pred[, "patid"] <- -2
# only missing value (out of five) for patid == 1
data[3, "sex"] <- NA
if (FALSE) {
# The following fails because 2lonly.norm found partially missing
# level-2 data
# imp <- mice(data, method = c("", "2lonly.norm", "2l.pan"),
# predictorMatrix = pred, maxit = 1, m = 2)
# > iter imp variable
# > 1 1 sex crpError in .imputation.level2(y = y, ... :
# > Method 2lonly.norm found the following clusters with partially missing
# > level-2 data: 1
# > Method 2lonly.mean can fix such inconsistencies.
}
# In contrast, if all sex values are missing for patid == 1, it runs fine,
# except on r-patched-solaris-x86. I used dontrun to evade CRAN errors.
if (FALSE) {
data[1:5, "sex"] <- NA
imp <- mice(data,
method = c("", "2lonly.norm", "2l.pan"),
predictorMatrix = pred, maxit = 1, m = 2
)
}
```