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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Likelihood ratio vs Bayes Factor
I'm rather evangelistic with regards to the use of likelihood ratios for representing the objective evidence for/against a given phenomenon. However, I recently learned that the Bayes factor serves a ...
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Why is a likelihood-ratio test distributed chi-squared?
Why is the test statistic of a likelihood ratio test distributed chi-squared?
$2(\ln \text{ L}_{\rm alt\ model} - \ln \text{ L}_{\rm null\ model} ) \sim \chi^{2}_{df_{\rm alt}-df_{\rm null}}$
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How to rigorously define the likelihood?
The likelihood could be defined by several ways, for instance :
the function $L$ from $\Theta\times{\cal X}$ which maps $(\theta,x)$ to $L(\theta \mid x)$ i.e. $L:\Theta\times{\cal X} \rightarrow \...
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Allowed comparisons of mixed effects models (random effects primarily)
I've been looking at mixed effects modelling using the lme4 package in R. I'm primarily using the lmer command so I'll pose my question through code that uses that ...
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Why doesn't Wilks' 1938 proof work for misspecified models?
In the famous 1938 paper ("The large-sample distribution of the likelihood ratio for testing composite hypotheses", Annals of Mathematical Statistics, 9:60-62), Samuel Wilks derived the asymptotic ...
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What is the relationship between the GINI score and the log-likelihood ratio
I am studying classification and regression trees, and one of the measures for the split location is the GINI score.
Now I am used to determining best split location when the log of the likelihood ...
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Why does lrtest() not match anova(test="LRT")
I was looking for ways to do a likelihood ratio test in R to compare model fits. I first coded it myself, then found both the default anova() function and also <...
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Has anyone solved PTLOS exercise 4.1?
This an exercise given in Probability Theory: The Logic of Science by Edwin Jaynes, 2003. There is a partial solution here. I have worked out a more general partial solution, and was wondering if ...
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Neyman-Pearson lemma
I have read the Neyman–Pearson lemma from the book Introduction to the Theory of Statistics by Mood, Graybill and Boes. But I have not understood the lemma.
Can anyone please explain the lemma to ...
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How to choose random- and fixed-effects structure in linear mixed models?
Consider the following data from a two-way within subjects design:
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What are the regularity conditions for Likelihood Ratio test
Could anyone please tell me what the regularity conditions are for the asymptotic distribution of Likelihood Ratio test?
Everywhere I look, it is written 'Under the regularity conditions' or 'under ...
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Likelihood ratio vs. score vs. Wald test: Different p values, which to use?
From what I've been reading, amongst others on the site of the UCLA statistics consulting group likelihood ratio tests and Wald tests are pretty similar in testing whether two glm models show a ...
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Non-nested model selection
Both the likelihood ratio test and the AIC are tools for choosing between two models and both are based on the log-likelihood.
But, why the likelihood ratio test can't be used to choose between two ...
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Why does one have to use REML (instead of ML) for choosing among nested var-covar models?
Various descriptions on model selection on random effects of Linear Mixed Models instruct to use REML. I know difference between REML and ML at some level, but I don't understand why REML should be ...
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Have I computed these likelihood ratios correctly?
I'm the author of the ez package for R, and I'm working on an update to include automatic computation of likelihood ratios (LRs) in the output of ANOVAs. The idea is to provide a LR for each effect ...