LRTest {nadiv}

log-Likelihood Ratio Test

Description

Test the null hypothesis that the two models fit the data equally well.

Usage

LRTest(full, reduced, df = 1, boundaryCorrection = FALSE)

Arguments

full

A numeric variable indicating the log-likelihood of the full model

reduced

A numeric variable indicating the log-likelihood of the reduced model

df

The number of degrees of freedom to use, representing the difference between the full and reduced model in the number of parameters estimated

boundaryCorrection

A logical argument indicating whether a boundary correction under one degree of freedom should be included. If the parameter that is dropped from the reduced model is estimated at the boundary of its parameter space in the full model, the boundary correction is often required. See Details for more.

Details

Boundary correction should be applied if the parameter that is dropped from the full model was on the boundary of its parameter space. In this instance, the distribution of the log-likelihood ratio test statistic is approximated by a mix of chi-square distributions (Self and Liang 1987). A TRUE value will implement the boundary correction for a one degree of freedom test. This is equivalent to halving the p-value from a test using a chi-square distribution with one degree of freedom (Dominicus et al. 2006).

Currently, the test assumes that both log-likelihoods are negative or both are positive and will stop if they are of opposite sign. The interpretation is that the model with a greater negative log-likelihood (closer to zero) or greater positive log-likelihood provides a better fit to the data.

Value

a list:

lambda

a numeric log-likelihood ratio test statistic

Pval

a numeric p-value given the lambda tested against a chi-squared distribution with the number of degrees of freedom as specified. May have had a boundary correction applied.

corrected.Pval

a logical indicating if the p-value was derived using a boundary correction. See Details

Author(s)

[e-mail]

References

Self, S. G., and K. Y. Liang. 1987. Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions. Journal of the American Statistical Association 82:605-610.

Dominicus, A., A. Skrondal, H. K. Gjessing, N. L. Pedersen, and J. Palmgren. 2006. Likelihood ratio tests in behavioral genetics: problems and solutions. Behavior Genetics 36:331-340.

See Also

constrainFun

Examples

# No boundary correction
(noBC <- LRTest(full = -2254.148, reduced = -2258.210,
	df = 1, boundaryCorrection = FALSE))
# No boundary correction
(withBC <- LRTest(full = -2254.148, reduced = -2258.210,
	df = 1, boundaryCorrection = TRUE))
stopifnot(noBC$Pval == 2*withBC$Pval)