test.metaLik {metaLik} | R Documentation |
Hypothesis testing on a scalar fixed-effect component in meta-analysis and meta-regression models
Description
Performs hypothesis testing on a scalar component of the fixed-effects vector in meta-analysis and meta-regression models, using the signed profile log-likelihood ratio test and its higher-order Skovgaard's adjustment (Skovgaard, 1996), as described in Guolo (2012). See Guolo and Varin (2012) for illustrative examples about the usage of metaLik package.
Usage
test.metaLik(object, param=1, value=0, alternative=c("two.sided", "less", "greater"),
print=TRUE)
Arguments
object |
an object of class |
param |
a specification of which parameter is to be given confidence interval, either a number or a name. Default is |
value |
a single number indicating the value of the fixed-effect parameter under the null hypothesis. Default is 0. |
alternative |
a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less". Just the initial letter can be specified. |
print |
logical, whether output information should be printed or not; default is |
Details
test.metaLik
allows hypothesis testing on a scalar component of interest in the fixed-effects vector. The signed profile log-likelihood ratio statistic for inference on scalar component \beta
of \theta
is
r(\beta) = sign(\hat{\beta}-\beta)\sqrt{2 \{l(\hat{\theta})-l(\theta)\} },
where l
is the log-likelihood function and \hat{\theta}
is the maximum likelihood estimate of \theta
.
The Skovgaard's adjustment is defined as
\overline r(\beta) = r(\beta) + \frac{1}{r(\beta)}\log\frac{u(\beta)}{r(\beta)},
where u(\beta)
is a correction term involving the observed and the expected information matrix and covariances of likelihood quantities, as described in Guolo (2012). Skovgaard's statistic has a second-order accuracy in approximating the standard normal distribution. In the rare case of equal within-study variances, Skovgaard's statistic reaches third-order accuracy.
Value
A list with the following components:
r |
the value of the signed profile log-likelihood ratio statistic. |
pvalue.r |
the p-value of the signed profile log-likelihood ratio test. |
rskov |
the value of the Skovgaard's statistic. |
pvalue.rskov |
the p-value of the Skovgaard's test. |
Author(s)
Annamaria Guolo and Cristiano Varin.
References
Guolo, A. (2012). Higher-Order Likelihood Inference in Meta-Analysis and Meta-Regression. Statistics in Medicine 31, 313–327.
Guolo, A. and Varin, C. (2012). The R Package metaLik for Likelihood Inference in Meta-Analysis. Journal of Statistical Software 50 (7), 1–14. http://www.jstatsoft.org/v50/i07/.
Skovgaard, I. M. (1996). An Explicit Large-Deviation Approximation to One-Parameter Tests. Bernoulli 2, 145–165.
See Also
Function metaLik
for fitting meta-analysis and meta-regression models.
Function summary.metaLik
for summaries.
Examples
data(vaccine)
m <- metaLik(y~latitude, data=vaccine, sigma2=sigma2)
## significance test for the intercept coefficient
test.metaLik(m)
## significance test for the 'latitude' coefficient
test.metaLik(m, param=2)
## testing for the 'latitude' coefficient less than 0
test.metaLik(m, param=2, value=0, alternative='less')