Description Usage Arguments Value Note Author(s) References See Also
It conducts univariate and multivariate metaanalysis with maximum likelihood estimation method. Mixedeffects metaanalysis can be conducted by including study characteristics as predictors. Equality constraints on intercepts, regression coefficients, and variance components can be easily imposed by setting the same labels on the parameter estimates.
1 2 3 4 5 
y 
A vector of effect size for univariate metaanalysis or a k x p matrix of effect sizes for multivariate metaanalysis where k is the number of studies and p is the number of effect sizes. 
v 
A vector of the sampling variance of the effect size for univariate
metaanalysis or a k x p* matrix of the sampling
covariance matrix of the effect sizes for multivariate metaanalysis
where p* = p(p+1)/2. It is arranged by column
major as used by 
x 
A predictor or a k x m matrix of predictors where m is the number of predictors. 
data 
An optional data frame containing the variables in the model. 
intercept.constraints 
A 1 x p matrix
specifying whether the intercepts of the effect sizes are fixed or
free. If the input is not a matrix, the input is converted into a
1 x p matrix with

coef.constraints 
A p x m matrix
specifying how the predictors predict the effect sizes. If the input
is not a matrix, it is converted into a matrix by

RE.constraints 
A p x p matrix
specifying the variance components of the random effects. If the input
is not a matrix, it is converted into a matrix by

RE.startvalues 
A vector of p starting values on the diagonals of the variance component of the random effects. If only one scalar is given, it will be duplicated across the diagonals. Starting values for the offdiagonals of the variance component are all 0. A p x p symmetric matrix of starting values is also accepted. 
RE.lbound 
A vector of p lower bounds on the
diagonals of the variance component of the random effects. If only one
scalar is given, it will be duplicated across the diagonals. Lower
bounds for the offdiagonals of the variance component are set at 
intervals.type 
Either 
I2 
Possible options are 
R2 
Logical. If 
model.name 
A string for the model name in 
suppressWarnings 
Logical. If 
silent 
Logical. The argument to be passed to 
run 
Logical. If 
... 
Further arguments to be passed to 
An object of class meta
with a list of
call 
Object returned by 
data 
A data matrix of y, v and x 
no.y 
No. of effect sizes 
no.x 
No. of predictors 
miss.x 
A vector indicating whether the predictors are
missing. Studies will be removed before the analysis if they are

I2 
Types of I2 calculated 
R2 
Logical 
mx.fit 
A fitted object returned from

mx0.fit 
A fitted object without any predictor returned from

Missing values (NA) in y and their related elements in v will be removed automatically. When there are missing values in v but not in y, missing values will be replaced by 1e5. Effectively, these effect sizes will have little impact on the analysis.
Mike W.L. Cheung <[email protected]>
Cheung, M. W.L. (2008). A model for integrating fixed, random, and mixedeffects metaanalyses into structural equation modeling. Psychological Methods, 13, 182202.
Cheung, M. W.L. (2009). Constructing approximate confidence intervals for parameters with structural equation models. Structural Equation Modeling, 16, 267294.
Cheung, M. W.L. (2013). Multivariate metaanalysis as structural equation models. Structural Equation Modeling, 20, 429454.
Hardy, R. J., & Thompson, S. G. (1996). A likelihood approach to metaanalysis with random effects. Statistics in Medicine, 15, 619629.
Neale, M. C., & Miller, M. B. (1997). The use of likelihoodbased confidence intervals in genetic models. Behavior Genetics, 27, 113120.
Raudenbush, S. W. (2009). Analyzing effect sizes: random effects models. In H. M. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and metaanalysis (2nd ed., pp. 295315). New York: Russell Sage Foundation.
Xiong, C., Miller, J. P., & Morris, J. C. (2010). Measuring studyspecific heterogeneity in metaanalysis: application to an antecedent biomarker study of Alzheimer's disease. Statistics in Biopharmaceutical Research, 2(3), 300309. doi:10.1198/sbr.2009.0067
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