BIFIE.twolevelreg: Two Level Regression

Description

This function computes the hierarchical two level model with random intercepts and random slopes. The full maximum likelihood estimation is conducted by means of an EM algorithm (Raudenbush & Bryk, 2002).

Usage

BIFIE.twolevelreg( BIFIEobj, dep, formula.fixed, formula.random, idcluster,
   wgtlevel2=NULL, wgtlevel1=NULL, group=NULL, group_values=NULL,
   recov_constraint=NULL, se=TRUE, globconv=1E-6, maxiter=1000 )
# S3 method for BIFIE.twolevelreg
summary(object,digits=4,...)
# S3 method for BIFIE.twolevelreg
coef(object,...)
# S3 method for BIFIE.twolevelreg
vcov(object,...)

Value

A list with following entries

stat: Data frame with coefficients and different sources of variance.
output: Extensive output with all replicated statistics
...: More values

Arguments

BIFIEobj: Object of class BIFIEdata
dep: String for the dependent variable in the regression model
formula.fixed: An R formula for fixed effects
formula.random: An R formula for random effects
idcluster: Cluster identifier. The cluster identifiers must be sorted in the BIFIE.data object.
wgtlevel2: Name of Level 2 weight variable
wgtlevel1: Name of Level 1 weight variable. This is optional. If it is not provided, wgtlevel is calculated from the total weight and wgtlevel2.
group: Optional grouping variable
group_values: Optional vector of grouping values. This can be omitted and grouping values will be determined automatically.
recov_constraint: Matrix for constraints of random effects covariance matrix. The random effects are numbered according to the order in the specification in formula.random. The first column in recov_constraint contains the row index in the covariance matrix, the second column the column index and the third column the value to be fixed.
se: Optional logical indicating whether statistical inference based on replication should be employed. In case of se=FALSE, standard errors are computed as maximum likelihood estimates under the assumption of random sampling of level 2 clusters.
globconv: Convergence criterion for maximum parameter change
maxiter: Maximum number of iterations
object: Object of class BIFIE.twolevelreg
digits: Number of digits for rounding output
...: Further arguments to be passed

Details

The implemented random slope model can be written as $$y_{ij}=\bold{X}_{ij} \bold{\gamma} + \bold{Z}_{ij} \bold{u}_j + \varepsilon_{ij}$$ where $y_{ij}$ is the dependent variable, $\bold{X}_{ij}$ includes the fixed effects predictors (specified by formula.fixed) and $\bold{Z}_{ij}$ includes the random effects predictors (specified by formula.random). The random effects $\bold{u}_j$ follow a multivariate normal distribution.

The function also computes a variance decomposition of explained variance due to fixed and random effects for the within and the between level. This variance decomposition is conducted for the predictor matrices $\bold{X}$ and $\bold{Z}$. It is assumed that $ \bold{X}_{ij}=\bold{X}_j^B + \bold{X}_{ij}^W$. The different sources of variance are computed by formulas as proposed in Snijders and Bosker (2012, Ch. 7).

References

Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical linear models: Applications and data analysis methods. Thousand Oaks: Sage.