# 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 statistic differs when computed from logLik, deviance, and anova functions in R

I'm confused about getting different results when trying to perform the likelihood ratio test (LRT) with R in different ways that are supposed to be equivalent. Below is the R code with some simulated ...
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### anova to compare two breakpoint models from R package strucchange

I want to compare two models with differing number of breaks, fitted with breakpoints from the strucchange package. As the the package developer @Achim Zeileis ...
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### How to perform a likelihood ratio test in a new dataset？

I understood the purpose of likelihood ratio test. However, I am confused by the table below from a published investigation. Clearly the author compare a nested model (VMNS) and a full model (VMNS + ...
1 vote
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### the Wald, Likelihood Ratio (LR) the Lagrange Multiplier (LM) test statistics Are monotonic function of F statistics

Consider a classic linear regression model. I want to show that the Wald, Likelihood Ratio (LR) the Lagrange Multiplier (LM) test statistics for the null hypothesis $H_0: R\beta =r$ for a constant ...
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### Interpretation of likelihood ratio test for MANOVA model using an asymptotic distribution

I'm studying multivariate linear models and I wanna test a hypothesis on the form \begin{equation} \begin{gathered} H_0: \textbf{CB = 0} \\ \text{vs.} \\ H_A: \textbf{CB $\neq$ 0}, \end{gathered} ...
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### Choosing parameters for an artificial neural network with a likelihood ratio test

I am currently trying to choose which parameters to use in my artificial neural network. Because the end goal is a comparison between the logistic regression and the neural network and I have already ...
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### What exactly do Anova sums of squares represent in lmer models?

In a lme4::lmer model, the anova function returns an sequential analysis of variance table. As explained on page 34 of http://...
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### Choosing between univariate GLMMs to assess inclusion in a multivariate model

I am currently doing a project on environmental determinants of malaria vector distributions. I'm using remote sensing data for environmental variables linked via GIS. I have run univariate (binomial) ...
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### Is this decision rule well-known/optimal in some setting?

First, you'll have to forgive me if my exposition of this is not the best, I am a computer scientist, not statistician. I have a certain classification task where I am given two (say discrete for ...
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### Is the Karlin-Rubin theorem test the same as a one-sided monotone likelihood-ratio test?

Is the test described in the Karlin-Rubin theorem test the same as a one-sided monotone likelihood-ratio test?
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### References on the likelihood-ratio, score, and wald-tests with the most examples of solved problems?

What books discuss the likelihood-ratio, score, and wald-tests with the most examples on solving these problems?
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### How to eliminate constant to derive the decision rule in terms of the sufficient statistic $\bar{X}$ for normal distribution means hypothesis test?

Suppose that we have a random sample, of size $n$, from a population that is normally-distributed. Both the mean, $\mu$, and the standard deviation, $\sigma$, of the population are unknown. We want to ...
1 vote
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### Does there always exist for n small, a non-chi-squared test-statistic for the likelihood-ratio (neyman-pearson, karlin-rubin), score, and wald-tests?

An additional reason that the chi-squared distribution is widely used is that it turns up as the large sample distribution of generalized likelihood ratio tests (LRT). LRTs have several desirable ...
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### Mixed Models: can restricted models have larger likelihood than complete model?

I have estimated a mixed model of the form $\underline{Y} = \mathbf{X}\underline{\alpha} + \mathbf{Z}\underline{\beta} + \underline{\varepsilon}$, which has a few interaction terms and individually ...
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### Quadratic Approximation for Log-Likelihood Ratio Processes, Why and How

I'm trying to understand why the quadratic equation can approximate the log likelihood ratio. Is this approximated using Taylor's series or normal distribution equation or anything else?
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### How to use the Likelihood Ratio Test and Wald Statistic when also using Cross Validation?

I am currently writing a paper for uni and stumbled across the following problem: I want to use the 10 Fold Cross Validation method to validate the results of a logistic regression, but I am unsure ...
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1 vote
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### Does the likelihood ratio test violate the likelihood principle?

I've been going over Berger's famous example of negative binomial vs binomial sampling leading to two different p-values conditional on the same observed data. To summarize, suppose we observe 9 tails ...
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### all variables at one of my level is not significant

I am modelling a logistic regression multilevel with 3 levels. Level 1 is individual, level 2 is household characteristic, and level 3 is regional characteristics. The results of the random effect ...
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### Likelihood ratio test: train two models or one?

I have a dataset with features A, B and C and an output label D. I want to perform the likelihood ratio test to see if feature C contributes to the performance of a regression model. Do I: train two ...
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### Regarding the type 2 or 3 ANOVA, does the analysis via model reduction correspond to LRT and via contrasts - to Wald approach?

I noticed, that in R we can obtain type 2 and type 3 ANOVA in many ways in unbalanced designs: For example, for type-2 car::Anova(...type=2), by running anova() over a sequence of models with swapped ...
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### Likelihood ratio tests in Growth Mixture Modelling with large sample sizes

I recently conducted Growth Mixture Modelling in a Structural Equation Modelling framework using a sample of n~300,000. I found that for any number of trajectories I fitted, the Vuong-Lo-Mendell-Rubin ...
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### LRT output interpretation in deseq2 reduced model

This is the code implementation of my the reduced model in deseq2 dds_lrt <- DESeq(dds, test="LRT", reduced = ~ 1) In ‘full’ model only has one factor ...
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### GLM tests involving deviance and likelihood ratios

I'm a little confused about the different common tests for GLMs. There is the null deviance, which is similar to a likelihood ratio for the difference between the saturated model and the model with ...
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### Post test probability with a ROC curve

I have data that is normally distributed related to risk of a particular disease. At the median of the distribution, you would expect to observe the population prevalence level of disease P0=0.01. For ...
1 vote
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### Should SPRT use explicit hypotheses or reflect observed differences in the data?

Sequential Probability Ratio Testing (SPRT) compares the log-likelihood ratio of the observed data under the null and alternative hypotheses to thresholds based on desired alpha and beta levels. I am ...
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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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### Comparing nested regression models on multiple data sets

Suppose we have two nested models $M_1(p_1)$ and $M_2(p_2)$ where $p_1$ and $p_2$ are the parameter sets of the models. Consider that $M_1$ is a restricted version of $M_2$ so $p_1$ set is a special ...
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### Is the two sample z-test a Wald or Score test?

I saw the R prop.test returns the Chi square p-value, and it got me thinking this: Is the z-test with pooled standard error corresponding to score test, and the one with unpooled SE corresponding to ...
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1 vote
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### Pooling Profile Penalised LTRs in multiple imputation

I am analysizing data from a clinical trial. I used multiple imputation to impute the (binary) outcome variable, which is the only variable with missing data. All of the covariates are categorical and ...
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### Likelihood Ratio Test for Bivariate Normal in a Restricted Parameter Space

Let $(X_{1i},X_{2i})$ follow a bivariate normal distribution for $i=1,\dots,n$ with means $(\theta_1,\theta_2)$ and an identity variance matrix. Suppose that the parameter space is restricted to \$\...
1 vote
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### Why use an ANOVA/LRT to test for significance of a factor?

I've been asked to use a likelihood ratio test to test for the significance of a main effect in a linear model. I have done so as follows: anova(model1, model2) ...
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