# Imputation by a two-level normal model using `pan`

Source: `R/mice.impute.2l.pan.R`

`mice.impute.2l.pan.Rd`

Imputes univariate missing data using a two-level normal model with
homogeneous within group variances. Aggregated group effects (i.e. group
means) can be automatically created and included as predictors in the
two-level regression (see argument `type`

). This function needs the
`pan`

package.

## Usage

```
mice.impute.2l.pan(
y,
ry,
x,
type,
intercept = TRUE,
paniter = 500,
groupcenter.slope = FALSE,
...
)
```

## Arguments

- y
Incomplete data vector of length

`n`

- ry
Vector of missing data pattern (

`FALSE`

=missing,`TRUE`

=observed)- x
Matrix (

`n`

x`p`

) of complete covariates.- type
Vector of length

`ncol(x)`

identifying random and class variables. Random effects are identified by a '2'. The group variable (only one is allowed) is coded as '-2'. Random effects also include the fixed effect. If for a covariates X1 group means shall be calculated and included as further fixed effects choose '3'. In addition to the effects in '3', specification '4' also includes random effects of X1.- intercept
Logical determining whether the intercept is automatically added.

- paniter
Number of iterations in

`pan`

. Default is 500.- groupcenter.slope
If

`TRUE`

, in case of group means (`type`

is '3' or'4') group mean centering for these predictors are conducted before doing imputations. Default is`FALSE`

.- ...
Other named arguments.

## Details

Implements the Gibbs sampler for the linear two-level model with homogeneous
within group variances which is a special case of a multivariate linear mixed
effects model (Schafer & Yucel, 2002). For a two-level imputation with
heterogeneous within-group variances see `mice.impute.2l.norm`

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

.

## Note

This function does not implement the `where`

functionality. It
always produces `nmis`

imputation, irrespective of the `where`

argument of the `mice`

function.

## References

Schafer J L, Yucel RM (2002). Computational strategies for multivariate
linear mixed-effects models with missing values. *Journal of
Computational and Graphical Statistics*. **11**, 437-457.

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

## See also

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

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

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

## Author

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

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

## Examples

```
# simulate some data
# two-level regression model with fixed slope
# number of groups
G <- 250
# number of persons
n <- 20
# regression parameter
beta <- .3
# intraclass correlation
rho <- .30
# correlation with missing response
rho.miss <- .10
# missing proportion
missrate <- .50
y1 <- rep(rnorm(G, sd = sqrt(rho)), each = n) + rnorm(G * n, sd = sqrt(1 - rho))
x <- rnorm(G * n)
y <- y1 + beta * x
dfr0 <- dfr <- data.frame("group" = rep(1:G, each = n), "x" = x, "y" = y)
dfr[rho.miss * x + rnorm(G * n, sd = sqrt(1 - rho.miss)) < qnorm(missrate), "y"] <- NA
# empty imputation in mice
imp0 <- mice(as.matrix(dfr), maxit = 0)
predM <- imp0$predictorMatrix
impM <- imp0$method
# specify predictor matrix and method
predM1 <- predM
predM1["y", "group"] <- -2
predM1["y", "x"] <- 1 # fixed x effects imputation
impM1 <- impM
impM1["y"] <- "2l.pan"
# multilevel imputation
imp1 <- mice(as.matrix(dfr),
m = 1, predictorMatrix = predM1,
method = impM1, maxit = 1
)
#>
#> iter imp variable
#> 1 1 y
# multilevel analysis
library(lme4)
#> Loading required package: Matrix
#>
#> Attaching package: ‘Matrix’
#> The following objects are masked from ‘package:tidyr’:
#>
#> expand, pack, unpack
mod <- lmer(y ~ (1 + x | group) + x, data = complete(imp1))
#> boundary (singular) fit: see help('isSingular')
summary(mod)
#> Linear mixed model fit by REML ['lmerMod']
#> Formula: y ~ (1 + x | group) + x
#> Data: complete(imp1)
#>
#> REML criterion at convergence: 13126.5
#>
#> Scaled residuals:
#> Min 1Q Median 3Q Max
#> -3.4498 -0.6620 -0.0145 0.6770 3.8518
#>
#> Random effects:
#> Groups Name Variance Std.Dev. Corr
#> group (Intercept) 0.3460116 0.5882
#> x 0.0001001 0.0100 -1.00
#> Residual 0.7169052 0.8467
#> Number of obs: 5000, groups: group, 250
#>
#> Fixed effects:
#> Estimate Std. Error t value
#> (Intercept) 0.03455 0.03908 0.884
#> x 0.29829 0.01247 23.922
#>
#> Correlation of Fixed Effects:
#> (Intr)
#> x -0.045
#> optimizer (nloptwrap) convergence code: 0 (OK)
#> boundary (singular) fit: see help('isSingular')
#>
# Examples of predictorMatrix specification
# random x effects
# predM1["y","x"] <- 2
# fixed x effects and group mean of x
# predM1["y","x"] <- 3
# random x effects and group mean of x
# predM1["y","x"] <- 4
```