It conducts univariate and multivariate meta-analysis with maximum likelihood estimation method. Mixed-effects meta-analysis 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.
meta(y, v, x, data, intercept.constraints = NULL, coef.constraints = NULL,
RE.constraints = NULL, RE.startvalues=0.1, RE.lbound = 1e-10,
intervals.type = c("z", "LB"), I2="I2q", R2=TRUE,
model.name="Meta analysis with ML", suppressWarnings = TRUE,
silent = TRUE, run = TRUE, ...)
metaFIML(y, v, x, av, data, intercept.constraints=NULL,
coef.constraints=NULL, RE.constraints=NULL,
RE.startvalues=0.1, RE.lbound=1e-10,
intervals.type=c("z", "LB"), R2=TRUE,
model.name="Meta analysis with FIML",
suppressWarnings=TRUE, silent=TRUE, run=TRUE, ...)A vector of effect size for univariate meta-analysis or a \(k\) x \(p\) matrix of effect sizes for multivariate meta-analysis where \(k\) is the number of studies and \(p\) is the number of effect sizes.
A vector of the sampling variance of the effect size for univariate
meta-analysis or a \(k\) x \(p*\) matrix of the sampling
covariance matrix of the effect sizes for multivariate meta-analysis
where \(p* = p(p+1)/2 \). It is arranged by column
major as used by vech.
A predictor or a \(k\) x \(m\) matrix of predictors where \(m\) is the number of predictors.
An auxiliary variable or a \(k\) x \(m\) matrix of auxiliary variables where \(m\) is the number of auxiliary variables.
An optional data frame containing the variables in the model.
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
t(as.matrix(intercept.constraints)). The default is that the intercepts are free. When there is no predictor, these intercepts are the same as
the pooled effect sizes. The format of this matrix follows
as.mxMatrix. The intercepts can be
constrained equally by using the same labels.
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
as.matrix(). The default is that all \(m\) predictors predict all \(p\) effect sizes. The
format of this matrix follows
as.mxMatrix. The regression coefficients can be
constrained equally by using the same labels.
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
as.matrix(). The default is that all
covariance/variance components are free. The format of this matrix
follows as.mxMatrix. Elements of the variance
components can be constrained equally by using the same labels. If a zero matrix is
specified, it becomes a fixed-effects meta-analysis.
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 off-diagonals of the variance component are all 0. A \(p\) x \(p\) symmetric matrix of starting values is also accepted.
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 off-diagonals of the variance component are set at NA. A \(p\) x
\(p\) symmetric matrix of the lower bounds is also accepted.
Either z (default if missing) or
LB. If it is z, it calculates the 95% Wald confidence
intervals (CIs) based on the z statistic. If it is LB, it
calculates the 95% likelihood-based CIs on the
parameter estimates. Note that the z values and their
associated p values are based on the z statistic. They are not
related to the likelihood-based CIs.
Possible options are "I2q", "I2hm" and
"I2am". They represent the I2 calculated by using a
typical within-study sampling variance from the Q statistic, the
harmonic mean and the arithmetic mean of the within-study sampling
variances (Xiong, Miller, & Morris, 2010). More than one options are possible. If intervals.type="LB", 95% confidence intervals on the heterogeneity indices will be constructed.
Logical. If TRUE and there are predictors, R2 is
calculated (Raudenbush, 2009).
A string for the model name in mxModel.
Logical. If TRUE, warnings are
suppressed. The argument to be passed to mxRun.
Logical. An argument to be passed to mxRun
Logical. If FALSE, only return the mx model without
running the analysis.
Further arguments to be passed to mxRun
An object of class meta with a list of
Object returned by match.call
A data matrix of y, v and x
No. of effect sizes
No. of predictors
A vector indicating whether the predictors are
missing. Studies will be removed before the analysis if they are
TRUE
Types of I2 calculated
Logical
A fitted object returned from
mxRun
A fitted object without any predictor returned from
mxRun
Cheung, M. W.-L. (2008). A model for integrating fixed-, random-, and mixed-effects meta-analyses into structural equation modeling. Psychological Methods, 13, 182-202.
Cheung, M. W.-L. (2009). Constructing approximate confidence intervals for parameters with structural equation models. Structural Equation Modeling, 16, 267-294.
Cheung, M. W.-L. (2013). Multivariate meta-analysis as structural equation models. Structural Equation Modeling, 20, 429-454.
Cheung, M. W.-L. (2015). Meta-analysis: A structural equation modeling approach. Chichester, West Sussex: John Wiley & Sons, Inc.
Hardy, R. J., & Thompson, S. G. (1996). A likelihood approach to meta-analysis with random effects. Statistics in Medicine, 15, 619-629.
Neale, M. C., & Miller, M. B. (1997). The use of likelihood-based confidence intervals in genetic models. Behavior Genetics, 27, 113-120.
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 meta-analysis (2nd ed., pp. 295-315). New York: Russell Sage Foundation.
Xiong, C., Miller, J. P., & Morris, J. C. (2010). Measuring study-specific heterogeneity in meta-analysis: application to an antecedent biomarker study of Alzheimer's disease. Statistics in Biopharmaceutical Research, 2(3), 300-309. doi:10.1198/sbr.2009.0067