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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Monte Carlo method for likelihoods ratio density estimation
I recently started reading Stephen Kay's Fundamentals of Statistical Signal Processing - Detection Theory (Volume II) and there is something I do not fully understand about likelihoods and hypothesis ...
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How to approximate Bayes Factor?
I am searching for a computationally simple way to approximate a Bayes Factor. Currently, I'm using an approach which seems pretty logical to me but I would still be interested to know if this is ...
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Comparing Models with Unequal Sample Sizes
I have performed an association analysis where I have associatiated several different perdictor variables to a dependent variable. For each predictor, I run two models and compare them via the ...
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Likelihood ratio test - sample size issue
I am a statistician running into an odd problem, and it feels like I am missing a key point here. I have a true model (generated by me so I know truth), and a PREDICTED model that estimates certain ...
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Using a AIC or LRT for a GLM and LMM
I am trying to compare 2 models (a GLMER with a random effect and a GLM with the random effect removed). However, I was told you can't use an AIC for GLM's but I thought you could!?
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is the likelihood ratio test "best" for finite samples?
Wikipedia says
The Neyman–Pearson lemma states that this likelihood-ratio (lr) test is the most powerful among all level α alpha tests for this case.
Is this only true for infinite sample sizes? Is ...
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Rejection region in LRT test
Let's say I have $X_i \sim Bi(1, \theta$) and want to test $H_0: \theta \geq \theta_0$ vs $H_1: \theta < \theta_0$.
I've found that $\lambda = \frac{\sup_{\theta \in \Theta_0}L(\theta)}{\sup_{\...
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Comparison of two test metrics
I'm trying to compare two test metrics (Metric A and Metric B) to determine which one better predicts a delta value, which represents a Euclidean difference. I am unsure how to determining which ...
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Hypothesis Test Finite Sample Spatial Gaussian Mixture Model
I have $n$ observations of pairs $(x, y)$ and three different models I would like to compare. Model0 is nested within Model1. Model0 is also nested within Model2. I would like to do hypothesis ...
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GLRT of exponential distribution and critical region
Find the Generalized likelihood ratio test (GLRT) for $H_0: \lambda = \lambda_0$ when $H_A: \lambda \ne \lambda_0$ for $X_1 ... X_n$ taken from $X \sim Exp(\lambda;x)$, with a test size of $0.06$, ...
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Likelihood-ratio and score tests of a (non)linear combination of coefficients
The likelihood-ratio and score test are typically used for simple scalar hypotheses such as $\beta_1 = 0$ or $\beta_1 = \beta_2 = 0$. How can we test a linear combination of coefficients using the ...
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Likelihood ratios not distributed as a chi2 distribution with the correct dof (Wilks' theorem)
I perform Bayesian inference on a mixture model such that $\mu$ is the mixture weight for a feature in the mixture
$p(x | \mu, \theta) = \mu p_{f}(x|\theta) + (1-\mu)p_{nf}(x|\theta)$
I have prior $p(\...
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Should p-values for chi-square and likelihood ratio chi-square tests be identical when estimated by Monte Carlo simulation?
The question and answer here suggest that the answer is “yes,” but my own analysis in SPSS suggests otherwise:
Note: I understand that the likelihood ratio chi-square and chi-square test are expected ...
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Why do I get a negative chi-squared value in my type III ANOVA output for my binomial GLM?
I am trying to look at how the likelihood of event X occurring is affected by three factors A (5 levels), B (2 levels) and C (3 levels). To do this I have run a binomial glm followed by a type 3 ANOVA ...
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Why use the Wald test in logistic regression?
Some statistical software use the Wald statistic when reporting on the regression coefficients. As examples, R and Stata report Wald by default.
The logistic regression article on Wikipedia says, ...
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