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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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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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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AIC versus Likelihood Ratio Test in Model Variable Selection
The software that I am currently using to build a model compares a "current run" model to a "reference model" and reports (where applicable) both a chi-squared p-value based on likelihood ratio tests ...
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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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Generalized log likelihood ratio test for non-nested models
I understand that if I have two models A and B and A is nested in B then, given some data, I can fit the parameters of A and B using MLE and apply the generalized log likelihood ratio test. In ...
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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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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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Likelihood ratio, Wald, and Score are equivalent?
In Foundations of Linear and Generalized Linear Models, Agresti makes a comment on page 131 about likelihood ratio, Wald, and Score testing of regression parameters.
For the best-known GLM, the ...
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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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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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Likelihood Ratio for two-sample Exponential distribution
Let $X$ and $Y$ be two independent random variables with respective pdfs:
$$f \left(x;\theta_i \right) =\begin{cases} \frac{1}{\theta_i} e^{-x/ {\theta_i}} \quad 0<x<\infty, 0<\theta_i< \...
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AIC and BIC criterion for Model selection, how is it used in this paper?
I'm reading Model selection and inference: Facts and fiction by Leeb & Pötscher (2005) (link), in this paper they look at an example in linear regression:
Let $$Y_i = \alpha x_{i1}+\beta x_{i2}+\...
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Exact equivalence of LR and Wald in linear regression under known error variance
Is it true that the LR statistic and the Wald statistic are numerically equivalent when testing a nested hypothesis in a linear regression when the error variance is known? Hence, is a squared t-...
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Intuition for Wilks' theorem
I'm trying to wrap my head around why it is intuitive that (under certain conditions) the likelihood ratio statistic follows a chi-squared distribution, asymptotically.
I've looked at the excellent ...
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