Description Usage Arguments Details Value References Examples
View source: R/Parameter_estimation_and_hypothesis_testing.R
Likelihood ratio test for the hypotheses H_0: \: ψ_1=ψ_2=...=ψ_d and
H_1: \: ψ_1 \neq ψ_2 \neq ... \neq ψ_d, where ψ_1,ψ_2,...,ψ_d are the
dispersal parameters of the d samples in the columns of the input data array x
.
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x |
The data array to be tested. Each column of |
Calculates the Likelihood Ratio Test statistic
-2log(L(\hat{ψ})/L(\hat{ψ}_1, \hat{ψ}_2, ..., \hat{ψ}_d)),
where L is the likelihood function of observing the d input samples given a single ψ in the numerator and d different parameters ψ_1,ψ_2,...,ψ_d for each sample respectively in the denominator. According to the theory of Likelihood Ratio Tests, this statistic converges in distribution to a χ_{d-1}^2-distribution when the null-hypothesis is true, where d-1 is the difference in the amount of parameters between the considered models. To calculate the statistic, the Maximum Likelihood Estimate for ψ_1,\: ψ_2,\: ..., \: ψ_d of H_1 and the shared ψ of H_0 are calculated.
Gives a vector with the Likelihood Ratio Test -statistic Lambda
, as well as the
p-value of the test p
.
Neyman, J., & Pearson, E. S. (1933). On the problem of the most efficient tests of statistical hypotheses. Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical Or Physical Character, 231(694-706), 289-337. <doi: 10.1098/rsta.1933.0009>.
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