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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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 ...
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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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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 $\...
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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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Testing independence and setting constraint matrices in a multinomial logit model in R

I have a data set the looks like this (called rand_df as this is a random subset from the much larger dataframe): ...
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How much detail do I need to report on the model-building process for a mixed effect growth curve analysis?

I am a data analyst on a health research team and I wondering whether I need to report process results and highly detailed process information from the step-by-step model building process for an ...
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Likelihood that observed relative frequencies match a probability distribution

For this question, please assume probability distributions are discrete. If I have $N$ data points ($x_1, x_2, ..., x_N$), and I want to know the likelihood that these samples came from a discrete ...
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Generalized likelihood ratio test for known means and unknown variance

Consider a sequence, $X_1, X_2, \dots, X_n$, of independent random variables. I have two hypotheses: $H_0 : X_k \sim \mathcal{N}(\mu_0, \sigma^2), k=1,2,\dots,n$ $H_1 : X_k \sim \mathcal{N}(\mu_1, \...
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Choose statistical test method: comparing the frequency of a disease (only interested the disease post-procedure) in 2 groups of patients

I am working on 2 groups of patients, group A and group B. The patients in both groups have received a same procedure. We have observed the patients before and after the procedure. Suppose there is a ...
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Likelihood Ratio Test gives different results for bootstrap and chi2 distribution for LMMs

I want to test whether random slopes improve my model: ...
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How can I determine the Simple Likelihood Ratio Test in the case of a Uniform(0,$\theta$) random variable?

Suppose we are given independent random variables $X_{1},\dots,X_{n} \sim \mathrm{Uniform}(0,\theta)$. I'm having some trouble trying to find the most powerful test of size $\alpha$ of the hypothesis: ...
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Practical considerations for EM clustering

EM algorithm guarantees finding a local rather then global minimum of the likelihood. As a consequence, the results are dependent on the initial conditions (e.g., if randomly choosing the initial ...
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Compare linear regression slopes between non-nested models with differing dataset sizes

I'd like to test if the slopes of two linear regression models differ. However, the caveat is that one of the regressions fits a subset of the data, and the other fits the whole dataset. The two ...
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Is the Likelihood Ratio test using cluster robust standard errors fixable by Bootstrap (or someting else)?

There is a common agreement about the invalidity of using likelihood ratio tests when computing Maximum Likelihood Estimates (MLE) using clustered corrected standard errors. The main argument is that ...
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Does modelling higher order interaction terms meaningfully affect type II tests of lower order terms?

My understanding of type II testing is that you compare a model with each tested factor, and all equivalent or lower-order terms, with a model excluding that factor. For example for y ~ a+b + ab, a ...
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Ordinal (likert) dependent variables + categorical independent variable - statistical tests - Chi-square/likelihood or ordinal regression?

Summary: I was wondering what statistical test is most appropriate for my data: for each of my four experimental conditions seperate participants rated my stimuli. I have about 250 stimuli rated on ...
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Likelihood Ratio Test without Chi-square test

Likelihood ratio test (LRT) usually uses a chi-square test to compare two different models. Are there any variants of LRT that does not use chi-square test?
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Likelihood Ratio Test on Ordered Probit Models (Panel Data) in R

I am in desperate need of help. I need to perform a likelihood ratio test on my panel data ordered response models to decide whether it's better to use the standard or the Random Effects Ordered ...
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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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Help with likelihood ratio statistics and hypothesis testing

In MIT's Foundations of Computational and Systems Biology lecture, lecture 8: RNA-sequence analysis there is a section on hypothesis testing. They have two different hypotheses/models for the same ...
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Three-way log likelihood ratio (LLR) / G-test

I have word counts and trigram counts for a text dataset. I want to calculate co-occurences, i.e. "best" trigrams, that most probably represent multiword expressions, using log likelihood ...
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Can null and alternative Hypotheses both be inequalities in a generalized likelihood ratio test?

Can null and alternative Hypotheses both be inequalities in a generalized likelihood ratio test? For example null hypothesis: $H_0:a \geq 0$ and alternative hypothesis: $H_1:a < 0$. Is there a ...
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Likelihood ratio test for one sided test for two variances [closed]

Let $X_{1}, \ldots, X_{n}$ be a random sample from $N\left(\mu_X, \sigma^{2}_X\right)$ and $Y_{1}, \ldots, Y_{m}$ be a random sample from $N\left(\mu_Y, \sigma^{2}_Y\right)$. Assume $\mu_X$ and $\mu_Y$...
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LR test gives contradictory results to R squared

I have a difficult decision here. The R squared suggests that model 1 has a better fit than model 2, but the LR test suggests the model 2 has a better fit. How can I resolve this seemingly ...
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likelihood ratio test for three variables

I believe my question is similar with this one: Likelihood-ratio test for three models? But I do still not understand and my problem is slightly different (maybe). I want to check which model is best, ...
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profile R function, how it works?

In https://lme4.r-forge.r-project.org/book/Ch1.pdf (1.5.1) one can read: "The profile function systematically varies the parameters in a model, assessing the best possible fit that can be ...
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Converting likelihood ratios hypothesis test from equality to inequality

I have the following LR test for proportions (to anyone familiar to applied statistics in finance, this is known as the Christoffersen's unconditional coverage test). We would like to know if $\pi$ is ...
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Distributions fitting, a comparison

I tried to make a comparison among various candidate distributions fitting for my data. These data are daily returns of S&P500 US equity Index. Among others I tried with t-location-scale (https://...
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Common practices on reducing multi-predictor models for likelihood ratio tests?

I am working on a glmer model in R. My model has three predictor variables(a, b and c), two of which share an interaction. This is the formula: ...
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Evaluating Block Bootstrap Confidence Interval

I have an estimation that is obtained by using MCMC. In order to calculate the standard error of the estimation, I use Block Bootstrap approach and using this standard error I create a 95% confidence ...
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Adding covariates in chi-squared test or proportions test?

I am having trouble figuring out what analysis is appropriate for my research question. I've been googling for the past few days but couldn't find the answer. I would greatly appreciate it if anyone ...
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Is it correct to compare two groups' delta G square to approximate an interaction effect?

My experimental design was Group (A vs. B) x Time (1 vs. 2). For group A, from time 1 to 2, ΔG2(1) = 3.97, p=.046 For group B, from time 1 to 2, ΔG2(1) = 1.16, p=.281 Is it correct to calculate a ...
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4 votes
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Likelihood ratio test for random intercept (MATLAB)

I need to program a likelihood ratio test for testing the significance of a random effect in a linear mixed model in MATLAB. But I am having some trouble finding out how to correctly specify the null ...
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Likelihood Ratio Test Equivalent with $t$ test: Difference of Two Means from Constant Variance Normal Distributions

$\newcommand{\szdp}[1]{\!\left(#1\right)} \newcommand{\szdb}[1]{\!\left[#1\right]}$ Problem Statement: Suppose that independent random samples of sizes $n_1$ and $n_2$ are to be selected from normal ...
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3 votes
2 answers
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Likelihood Ratio Test for Common Variance from Two Normal Distribution Samples

$\newcommand{\szdp}[1]{\!\left(#1\right)} \newcommand{\szdb}[1]{\!\left[#1\right]}$ Problem Statement: Let $S_1^2$ and $S_2^2$ denote, respectively, the variances of independent random samples of ...
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4 votes
3 answers
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Binomial Distribution: Likelihood Ratio Test for Equality of Several Proportions

$\newcommand{\szdp}[1]{\!\left(#1\right)} \newcommand{\szdb}[1]{\!\left[#1\right]}$ Problem Statement: A survey of voter sentiment was conducted in four midcity political wards to compare the fraction ...
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Distinguishing 2 alternative hypotheses by relative likelihood

I have a system with a positive, Real parameter x. I can measure x directly, but the measurements are noisy. And probably has a small systematic bias. My priors are that x=a or x=b, where a & b ...
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2 votes
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For Poisson GLMs, when does the residual deviance follow a chi square distribution?

According to Generalized Linear Models by McCullagh and Nelder (I am looking at the 2nd edition, 1999), the deviance function is defined as $$D(y; \hat{\pi}) = 2[l(\tilde{\pi}; y)- l(\hat{\pi}; y)]$$ ...
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Using AIC vs Likelihood Ratio test for comparing Lognormal and Powerlaw distributions

I am interested in comparing whether a lognormal or a power law are a better fit for a given set of data. Both distributions have been fit using MLE, with $x_{min}$ determined using KS-minimization a ...
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