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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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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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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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 ratio tests on bounded parameters

I am confused by the likelihood ratio test's boundary condition limitation. A commonly stated is that it causes problem for variance parameter because it is bounded below by 0. Can these models ...
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One sided likelihood ratio test for a logistic regression model?

I need to run a one-sided test on one parameter of a logistic regression model: $H_0$: $\beta = 0$ $H_1$: $\beta \geq 0$ I want to avoid Wald-equivalent methods as these are known to have problems ...
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Lower threshold for Sequential Probability Ratio Test on Contingency Table testing

For testing whether a die is fair, we have the log likelihood ratio: $$\Lambda = \frac{1}{2} \sum_{i} \mathrm{observed}_i \log\left(\frac{\mathrm{observed}_i}{\mathrm{expected}_i}\right).$$ Suppose ...
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LR statistics add up for nested models. What about the Wald test?

Consider models M0, M1, M2. Let M0 $\subset$ M1 $\subset$ M2, i.e. let the models nest each other. I test the following pairs of models using the likelihood-ratio (LR) test: M0 vs. M2, M0 vs. M1, M1 ...
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Am I using the correct test statistic for a binomial glm using the type III Anova function in the package car?

I am trying to look at how the likelihood of event Y is influenced by two factors A (5 levels) and B (2 levels) and my model is as follows: ...
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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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equivalence between the likelihood ratio test and t-tests

The linked sites (link1, link2) demonstrate that the likelihood ratio tests and the corresponding one- and two-sample t-tests are equivalent. However, based on my understanding, the null distribution ...
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How to translate the set of contrasts over model coefficients into definitions of two nested models for Likelihood Ratio testing?

With the data as below: Categorical predictor: "Group" with 2 levels: Group 1 and Group 2 Categorical predictor: "Treatment" with 3 levels: A, B, C Categorical binary response: &...
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How to test specific contrasts about levels of categorical variables through nested models? [closed]

This is not about obtaining any dataset. I HAVE the dataset. This is not about debugging code, this is about EXPLAINING the way to obtain statistical relationship between the nested models (LRT ANOVA) ...
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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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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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Comparison of multilevel models via deviance test

I have a question regarding the comparison of the following two multilevel models: Null model: outcome.nullmodel <- lmer(outcome ~ 1 + (1 | ID), data=multileveldata) Random slopes model: outcome....
1 vote
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Likelihood ratio tests vs. ANOVA for interactions in linear mixed model

I am analyzing a longitudinal study where patients received either treatment 1, treatment 2 or no treatment (placebo) using linear mixed models (LMM) in R. I have a baseline measure that is related to ...
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When using a likelihood ratio test to test for significance of a main effect, should I use the most maximal or minimal model as a base model?

Lets suppose I have a set of n covariates, and I want to test for the significance of the main effect of covariate i. I want to do this using a likelihood ratio test; fitting a model with covariate i ...
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Generalized likelihood ratio test for a left-truncated exponential distribution [duplicate]

I am doing self study in statistical inference and am rather confused about how to approach generalized likelihood ratio test (GLRT) problems. I am trying the traditional approach by definition and ...
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How to perform likelihood ratio test for bayesian neural network?

I am building a Bayesian neural network with Poisson likelihood and 50 features for time series prediction. Parameters of the model are learned using variational inference. I am trying to see whether ...
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