Questions tagged [likelihood-ratio]
The likelihood ratio is the ratio of the likelihoods of two models (or a null and alternative parameter value within a single model), which may be used to compare or test the models. If either model is not fully specified then its maximum likelihood over all free parameters is used - this is sometimes called a generalized likelihood ratio.
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Local Linearity vs Regularity Conditions for the asymptotic distribution of the Likelihood Ratio
In his book 'Asymptotic Statistics,' Aad van der Vaart when discussing the asymptotic distribution of the log-likelihood-ratio says:
"The most important conclusion of this chapter is that, under ...
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Permutation test for exponential null hypothesis: really bad?
Having found nice formulas for testing the null hypothesis under exponentially-distributed samples, I wanted to see how well permutation tests could do the job. And the answer, assuming no mistakes, ...
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When and why is a likelihood ratio preferable to a difference as a test statistic?
We want to know whether two sample sets {x} and {y} were drawn from the same distribution. The null hypothesis $H_0$ is that they are. As statisticians we test the hypothesis by calculating the p-...
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What is a *likelihood ratio test* for a specific distribution, and how does it relate to hypothesis tests?
I'm just now being introduced to likelihood-ratio tests (LRT), and I am having trouble following the concept and terminology.
For example, I posed a question about determining whether two samples {x} ...
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Likelihood ratio exponential family under permutation of parameters
I'm reading "ASYMPTOTIC NORMALITY OF MAXIMUM LIKELIHOOD AND ITS VARIATIONAL APPROXIMATION FOR STOCHASTIC BLOCKMODELS" Bickel et al. 2013. In their proof of Lemma 3, they claim a result and I ...
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How to interpret DESeq results with LRT vs. with Wald's test
I am new to the field of RNA-Seq and wanted to ask for advice concerning the proper use of the two DESeq() test options (LRT vs. Wald test).
Briefly, my ...
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UMP two sided tests for exponential families
Consider a random variable $X$ with density $$f(x : θ) = C(θ)e^{η(θ)T(x)}h(x), θ ∈ Θ$$.
Assume that $η(θ)$ is strictly increasing in $θ$ and that the family is full rank. Show that there will not be ...
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What are the degrees of freedom to consider for a G-test when some cells have expected values of 0?
Let's say I conduct a survey where people can mention their favorite
color among four options (red, green, blue, yellow).
After collecting the data, I create a contingency table crossing
gender with ...
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Likelihood ratio as minimal sufficient statistics in infinite parameter space
I just read a question from here (Likelihood ratio minimal sufficient) and have some thoughts. Let me restate the question first:
Consider a family of density functions $f(x|\theta)$ where the ...
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How to use the likelihood ratio test (LRT) to test whether a three-way interaction is significant?
Our hypothesis is that there is a 3-way interaction between A, B, and C.
I have defined a model as follows:
Y=A+B+C+AB+AC+BC+ABC+error
I aim to use the likelihood ratio test (LRT) to determine if the ...
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Likelihood Ratio Testing for Binomial Distributions
I have a feeling this is a silly question. I am working on a research paper, at some point in it we perform a likelihood ratio test. The first guess would be to apply Wilks's theorem. However, if we ...
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Residual likelihood ratio test for fixed effects in a linear mixed model
I know (but now I have doubts) that "Comparing models that are fitted with REML and differ in their fixed effects never makes sense," just as @BenBolker explains in this answer.
I've been ...
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Does the "log-likelihood" measure cover all details about model fit, like covariance structure, adjustments, robust variance estimator, etc?
Just a general statistical question: when any statistical software returns log-likelihood of some model, does it account for all details in it?
For example, when we employ generalized least square ...
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Can be any example of testing contrasts using Wald's approach reproduced with Likelihood Ratio testing?
For illustration I will use R, but the question is general statistical question, totally not R related.
Assume I have a numerical variable and categorical variable with 3 levels, like A, B and C, for ...
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Understanding residuals vs. fitted plot for a linear mixed model
I am modeling body mass (y var) according to indices of dysregulation for different physiologic systems (x vars). I did a likelihood ratio test, which supported using a linear mixed model, with a ...
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