An object returned by the mvmeta function, inheriting from class "mvmeta", and representing a fitted univariate or multivariate meta-analytical model.
Objects of class "mvmeta" are lists with defined components. Dimensions of such components may refer to \(k\) outcome parameters, \(p\) predictors and \(m\) studies used for fitting the model (the latter can be different from those originally selected due to missing). The following components needs to be included in a legitimate mvmeta object:
coefficients a \(p\)-dimensional vector (for univariate models) or a \(p \times k\) matrix (for multivariate models) of the fixed-effects coefficients.
estimated \(kp \times kp\) (co)variance matrix of the fixed-effects coefficients.
for random-effects models, the estimated \(k \times k\) between-study (co)variance matrix.
a \(m\)-dimensional vector (for univariate models) or \(m \times k\) matrix (for multivariate models) of residuals, that is observed minus fitted values.
a \(m\)-dimensional vector (for univariate models) or \(m \times k\) matrix (for multivariate models) of fitted mean values.
the residual degrees of freedom.
the numeric rank of the fitted model.
the (restricted) log-likelihood of the fitted model. Set to NA for non-likelihood models.
for models with iterative estimation methods, logical scalar indicating if the algorithm eventually converged.
parameters estimated in the optimization process when using likelihood-based estimators. These correspond to trasformations of entries of the between-study (co)variance matrix of random effects, dependent on chosen (co)variance structure. See also the optimizations algorithms for details.
Hessian matrix of the estimated parameters in par above, only returned if hessian=TRUE in mvmeta.control. See the related optimizations algorithms for details.
for models fitted through method of moments, the number of negative eigenvalues in the estimated between-study (co)variance matrix, then set to 0.
a list with the values of the control arguments used, as returned by mvmeta.control.
the estimation method.
a string defining the between-study (co)variance structure in likelihood based models.
a \(m \times k(k+1)/2\) matrix, where each row represents the vectorized entries of the lower triangle of the related within-study (co)variance matrix, taken by column. See mvmeta.
list with the following scalar components: m (number of studies included in estimation, which could be lower than the total number in the presence of missing values), k (number of outcome parameters), p (number of coefficients for each outcome parameter).
list with the following scalar components: nall (number of observations used for estimation, excluding missing values), nobs (equal to nall, minus the number of fixed-effects coefficients in REML models), fixed (number of estimated fixed-effects coefficients), random (number of estimated (co)variance terms).
list with the following label vectors: m for the \(m\) studies, k for the \(k\) outcome parameters, p for the \(p\) predictors (including intercept). The first two are derived from the vector/matrix of outcome parameters in formula, the third from the design matrix derived from model.matrix.
the model frame used for fitting. Reported if model=TRUE in mvmeta. See model.frame.
the function call.
(where relevant) information returned by model.frame on the special handling of NAs. See info on missing values.
the model supplied.
the terms object representing the fitted model.
(where relevant) the contrasts used.
(where relevant) a record of the levels of the factors used in fitting.
A number of methods functions are available for mvmeta objects, most of them common to other regression functions.
Specifically-written method functions are defined for predict (standard predictions) and blup (best linear unbiased predictions). The method function simulate produces simulated outcomes from a fitted model, while qtest performs the Cochran Q test for heterogeneity. Other methods have been produced for summary, logLik, coef, and vcov.
Specific methods are also available for model.frame and model.matrix. In particular, the former produces the model frame (a data frame with special attributes storing the variables used for fitting) with the additional class "data.frame.mvmeta". Methods na.omit and na.exclude for this class are useful for the handling of missing values in mvmeta objects.
Printing functions for the objects of classes defined above are also provided. anova methods for performing tests in mvmeta objects are in development.
All the methods above are visible (exported from the namespace) and documented. In additions, several default method functions for regression are also applicable to objects of class "mvmeta", such as fitted, residuals, AIC, BIC and update, among others.
Sera F, Armstrong B, Blangiardo M, Gasparrini A (2019). An extended mixed-effects framework for meta-analysis.Statistics in Medicine. 2019;38(29):5429-5444. [Freely available here].
Gasparrini A, Armstrong B, Kenward MG (2012). Multivariate meta-analysis for non-linear and other multi-parameter associations. Statistics in Medicine. 31(29):3821--3839. [Freely available here].
See mvmeta. See lm or glm for standard regression functions. See mvmeta-package for an overview of this modelling framework.
# NOT RUN {
# RUN THE MODEL
model <- mvmeta(cbind(PD,AL)~pubyear,S=berkey98[5:7],data=berkey98)
# INSPECT THE OBJECT
names(model)
# LABELS
model$lab
# FORMULA
model$formula
# CONVERGED?
model$converged
# }
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