meta3L | R Documentation |
It conducts three-level univariate meta-analysis with maximum likelihood estimation method. Mixed-effects meta-analysis can be conducted by including study characteristics as predictors. Equality constraints on the intercepts, regression coefficients and variance components on the level-2 and on the level-3 can be easily imposed by setting the same labels on the parameter estimates.
## Depreciated in the future
meta3(y, v, cluster, x, data, intercept.constraints = NULL,
coef.constraints = NULL , RE2.constraints = NULL,
RE2.lbound = 1e-10, RE3.constraints = NULL, RE3.lbound = 1e-10,
intervals.type = c("z", "LB"), I2="I2q",
R2=TRUE, model.name = "Meta analysis with ML",
suppressWarnings = TRUE, silent = TRUE, run = TRUE, ...)
## Depreciated in the future
meta3X(y, v, cluster, x2, x3, av2, av3, data, intercept.constraints=NULL,
coef.constraints=NULL, RE2.constraints=NULL, RE2.lbound=1e-10,
RE3.constraints=NULL, RE3.lbound=1e-10, intervals.type=c("z", "LB"),
R2=TRUE, model.name="Meta analysis with ML",
suppressWarnings=TRUE, silent = TRUE, run = TRUE, ...)
meta3L(y, v, cluster, x, data, intercept.constraints = NULL,
coef.constraints = NULL , RE2.constraints = NULL,
RE2.lbound = 1e-10, RE3.constraints = NULL, RE3.lbound = 1e-10,
intervals.type = c("z", "LB"), I2="I2q",
R2=TRUE, model.name = "Meta analysis with ML",
suppressWarnings = TRUE, silent = TRUE, run = TRUE, ...)
meta3LFIML(y, v, cluster, x2, x3, av2, av3, data, intercept.constraints=NULL,
coef.constraints=NULL, RE2.constraints=NULL, RE2.lbound=1e-10,
RE3.constraints=NULL, RE3.lbound=1e-10, intervals.type=c("z", "LB"),
R2=TRUE, model.name="Meta analysis with ML",
suppressWarnings=TRUE, silent = TRUE, run = TRUE, ...)
y |
A vector of |
v |
A vector of |
cluster |
A vector of |
x |
A predictor or a |
x2 |
A predictor or a |
x3 |
A predictor or a |
av2 |
A predictor or a |
av3 |
A predictor or a |
data |
An optional data frame containing the variables in the model. |
intercept.constraints |
A |
coef.constraints |
A |
RE2.constraints |
A scalar or a |
RE2.lbound |
A scalar or a |
RE3.constraints |
A scalar of a |
RE3.lbound |
A scalar or a |
intervals.type |
Either |
I2 |
Possible options are |
R2 |
Logical. If |
model.name |
A string for the model name in |
suppressWarnings |
Logical. If |
silent |
Logical. An argument to be passed to |
run |
Logical. If |
... |
Further arguments to be passed to
|
y_{ij} = \beta_0 + \mathbf{\beta'}*\mathbf{x}_{ij} + u_{(2)ij} + u_{(3)j} + e_{ij}
where y_{ij}
is the effect size for the ith study in the jth cluster,
\beta_0
is the intercept, \mathbf{\beta}
is the
regression coefficients, \mathbf{x}_{ij}
is a vector of predictors, u_{(2)ij} \sim N(0, \tau^2_2)
and u_{(3)j} \sim N(0, \tau^2_3)
are the level-2 and level-3 heterogeneity variances,
respectively, and e_{ij} \sim N(0, v_{ij})
is the conditional known sampling variance.
meta3L()
does not differentiate between level-2 or level-3
variables in x
since both variables are treated as a design
matrix. When there are missing values in x
, the data will be
deleted. meta3LFIML()
treats the predictors x2
and x3
as level-2 and level-3 variables. Thus, their means and covariance
matrix will be estimated. Missing values in x2
and x3
will be handled by (full information) maximum likelihood (FIML) in meta3LFIML()
. Moreover,
auxiliary variables av2
at level-2 and av3
at level-3 may
be included to improve the estimation. Although meta3LFIML()
is more
flexible in handling missing covariates, it is more likely to encounter
estimation problems.
Mike W.-L. Cheung <mikewlcheung@nus.edu.sg>
Cheung, M. W.-L. (2014). Modeling dependent effect sizes with three-level meta-analyses: A structural equation modeling approach. Psychological Methods, 19, 211-229.
Enders, C. K. (2010). Applied missing data analysis. New York: Guilford Press.
Graham, J. (2003). Adding missing-data-relevant variables to FIML-based structural equation models. Structural Equation Modeling: A Multidisciplinary Journal, 10(1), 80-100.
Konstantopoulos, S. (2011). Fixed effects and variance components estimation in three-level meta-analysis. Research Synthesis Methods, 2, 61-76.
reml3L
, Cooper03
, Bornmann07
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