# 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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### SUR estimated by OLS: restricted model has higher likelihood

I have three versions of a system of linear regression models: M, M0 and M00. I think each ...
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### How do I quantify the effect of a factor with many levels?

I want to look at the effect of brood ID on fledging success (a binary variable) in a sample of wild birds. Brood ID has ~150 levels. I have performed a likelihood ratio test comparing two logistic ...
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### Replicate t or F test from regression using regression likelihoods

I've heard that the t-test and F-test we use to get the significance of our regression results are derived from the likelihood ratio test, but I'm having trouble replicating the p-value of the t/F ...
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### Show a composite test is the most powerful after deriving a similar most powerful simple test

Let $X$ be a real-valued random variable with density $f(x) = (2\theta x + 1 - \theta) \mathbb{1}(x \in [0,1])$ where $1$ here is the indicator function and $-1 < \theta < 1$. I am trying to ...
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### application of the Savage - Dickey ratio

The Savage - Dickey ratio is an equivalent, but more useable, form for the Bayes factor for two model, model $M_{0}$ and model $M_{1}$. The definition for the Bayes Factor $BF_{ij}$is as follows: \$BF_{...
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### How to compare 2 estimates from a model fitted by MLE when the covariance of the estimate can't be always estimated?

I have one model, that I fit using MLE. In order to feel what could be a good initial guess for the fitting process, I try different arbitrary smartly chosen initial guess (not random) and report the ...
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### Is it better to select variables before regression or performing regression and then performing tests to select the variables?

I'm working on a regression model that predicts age of clients. The problem is that there aren't many variables to work with. So my question, is it better to study correlations and contingency tables ...
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### Why does the Type-3 ANOVA using LRT via car::Anova() give different result than term-by-term LRT model comparison via anova() in R?

With this very simple data: ...
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### Likelihood Ratio when true/false positive/negative rates are not available

In this paper (PMID 23123231; paywalled), the authors develop a logistic regression prediction model for Alzheimer's disease. In Table 3 the authors then present disease prediction results after ...
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