meta.ave.gen.rc {vcmeta}

Confidence interval for an average effect size using a random coefficient model

Description

Computes the estimate, standard error, and confidence interval for a weighted average effect from multiple studies using the random coefficient (random-effects) meta-analysis model. An estimate of effect-size heterogeneity (tau-squared) is also computed.

Usage

meta.ave.gen.rc(alpha, est, se, bystudy = TRUE)

Arguments

alpha

alpha level for 1-alpha confidence

est

vector of parameter estimates

se

vector of standard errors

bystudy

logical to also return each study estimate (TRUE) or not

Details

The random coefficient model assumes that the studies in the meta-analysis are a random sample from some definable superpopulation of studies. This assumption is very difficult to justify. The weighted average estimate will be biased regardless of the number of studies or the sample size in each study. The actual confidence interval coverage probability can much smaller than the specified confidence level if the effect sizes are correlated with the weights (which occurs frequently). The confidence interval for tau-squared assumes that the true effect sizes in the superpopulation of studies have a normal distribution. A large number of studies, each with a large sample size, is required to assess the superpopulation normality assumption and to accurately estimate tau-squared. The confidence interval for the population tau-squared is hypersensitive to very minor and difficult-to-detect violations of the superpopulation normality assumption.

The random coefficient model should be used with caution, and the varying coefficient methods in this package are the recommended alternatives. The varying coefficient methods allows the effect sizes to differ across studies but do not require the studies to be a random sample from a definable superpopoulation of studies. This random coefficient function is included in the vcmeta package primarily for classroom demonstrations to illustrate the problimatic characteristics of the random coefficient meta-analysis model.

Value

Returns a matrix. The first row is the average estimate across all studies. If bystudy is true, there is 1 additional row for each study. The matrix has the following columns:

• Estimate - estimated effect size

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

• Hedges LV, Olkin I (1985). Statistical methods for meta-analysis. Academic Press, New York. ISBN 01-233-63802.

• Borenstein M, Hedges LV, Higgins JP, Rothstein HR (2009). Introduction to meta-analysis. Wiley, New York.

See Also

meta.ave.gen

Examples

est <- c(.022, .751, .421, .287, .052, .146, .562, .904)
se <- c(.124, .464, .102, .592, .864, .241, .252, .318)
meta.ave.gen.rc(.05, est, se, bystudy = TRUE)

# Should return: 
#               Estimate        SE          LL        UL
# Tau-squared 0.03772628 0.0518109  0.00000000 0.1392738
# Average     0.35394806 0.1155239  0.12752528 0.5803708
# Study 1     0.02200000 0.1240000 -0.22103553 0.2650355
# Study 2     0.75100000 0.4640000 -0.15842329 1.6604233
# Study 3     0.42100000 0.1020000  0.22108367 0.6209163
# Study 4     0.28700000 0.5920000 -0.87329868 1.4472987
# Study 5     0.05200000 0.8640000 -1.64140888 1.7454089
# Study 6     0.14600000 0.2410000 -0.32635132 0.6183513
# Study 7     0.56200000 0.2520000  0.06808908 1.0559109
# Study 8     0.90400000 0.3180000  0.28073145 1.5272685