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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Distribution of $Z^2 \cdot I(Z > 0)$ where $Z \sim \text{N}(0,1)$
When using the Likelihood Ratio test for testing particular hypotheses and attempting to obtain an size-$\alpha$ test, I run into the expression
$$ \mathbb{P}\left( Z^2 \cdot I(Z > 0) > c \right)...
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Why is it preferable to test the effect of a predictor using a likelihood ratio test?
In their fantastic book Applied Longitudinal Data Analysis: Modeling Change and event Occurrence Singer and Willett advocate a iterative model comparison technique for testing the effect of predictors:...
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How to report results from the likelihood ratio test of two lme models?
I am trying to find an appropriate way to report the results of the likelihood ratio test in a paper. I wrote:
The likelihood ratio tests reported a significant main effect of FE (χ²(1)=6.06, p < 0....
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How to compare 2 multiply imputed nested Cox proportional hazards models?
I've got 2 nested Cox models, which I fit to 10 imputed datasets. Pooling the regression coefficient estimates and associated p-values I've done already.
I'm trying to work out if adding one extra ...
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Constructing a one-sided hypothesis test for joint probabilties of negative binomial distributions
I am conducting research on Codling moth population/trap capture models. The end goal is to have a hypothesis testing model that will provide whether or not (at some significance level $\alpha$) the ...
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How do I work out the significance of main effects in negative binomial models with more than two factors?
I am trying to look at how the number of events X is affected by the three factors A (4 levels), B (2 levels) and C (2 levels) using a negative binomial model as follows:
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Equivalent to likelihood ratio test for null and fitted generalized linear model (Gamma) in R?
I have a dataset of ellipses and I am trying to perform regressions with different categorical variables to see what influences different ellipse parameters the most. As was suggested in the answer to ...
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Can I use the ratio of two p-values under two hypotheses as a likelihood ratio?
I am designing a simple study where I ask participants a problem. Then I code the answers as either correct or incorrect. I have a prediction from the literature that the percentage of correct answers ...
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Does performing Likelihood Ratio Test to compare two nested LASSO models make statistical sense?
From what I've studied, the LRT is used to compare two nested models, i.e. 2 models having different sets of nested features, in my case e.g.
Model1: binary_outcome ~ X1 + X2
Model2: binary_outcome ~ ...
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Karlin-Rubin theorem: relationship between test statistic having the MLR property vs being sufficient
Let's suppose we are trying to compare two hypotheses for a single parameter $\theta$. The null hypothesis $H_0$ is that $\theta = \theta_0$, and the alternative is that $\theta ≥ \theta_0$.
The ...
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Local Linearity vs Regularity Conditions for the asymptotic distribution of the Likelihood Ratio
In his book 'Asymptotic Statistics,' Aad van der Vaart when discussing the asymptotic distribution of the log-likelihood-ratio says:
"The most important conclusion of this chapter is that, under ...
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Permutation test for exponential null hypothesis: really bad?
Having found nice formulas for testing the null hypothesis under exponentially-distributed samples, I wanted to see how well permutation tests could do the job. And the answer, assuming no mistakes, ...
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When and why is a likelihood ratio preferable to a difference as a test statistic?
We want to know whether two sample sets {x} and {y} were drawn from the same distribution. The null hypothesis $H_0$ is that they are. As statisticians we test the hypothesis by calculating the p-...
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What is a *likelihood ratio test* for a specific distribution, and how does it relate to hypothesis tests?
I'm just now being introduced to likelihood-ratio tests (LRT), and I am having trouble following the concept and terminology.
For example, I posed a question about determining whether two samples {x} ...
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Likelihood ratio exponential family under permutation of parameters
I'm reading "ASYMPTOTIC NORMALITY OF MAXIMUM LIKELIHOOD AND ITS VARIATIONAL APPROXIMATION FOR STOCHASTIC BLOCKMODELS" Bickel et al. 2013. In their proof of Lemma 3, they claim a result and I ...
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How to interpret DESeq results with LRT vs. with Wald's test
I am new to the field of RNA-Seq and wanted to ask for advice concerning the proper use of the two DESeq() test options (LRT vs. Wald test).
Briefly, my ...
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UMP two sided tests for exponential families
Consider a random variable $X$ with density $$f(x : θ) = C(θ)e^{η(θ)T(x)}h(x), θ ∈ Θ$$.
Assume that $η(θ)$ is strictly increasing in $θ$ and that the family is full rank. Show that there will not be ...
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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....
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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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p-value ratio for Likelihood Ratio Test with multicollinear data
I have two datasets where my independent variables (of which I have 6) are highly correlated. In one dataset I know for certain that the dependent variable should only depend on 1 independent variable ...
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Likelihood ratio test vs p value for Poisson regression
I have a Poisson regression model, from its summary table, I could see the p-value for a certain variable, e.g. gender. Since the p-value is testing the hypothesis whether the coefficient of gender ...
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Exact Likelihood ratio statistic for discrete distribution
Suppose that the random variables in a sample $Y_1, Y_2, \ldots, Y_n$ are iid with values in $[0,1]$, and that an investigator knows that the underlying probability density $f_Y(y)$ has the form
$f_Y(...
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Using likelihood ratios instead of p-values
I am analysing data from an experiment consisting of 4 treatments, and I am interested in treatment differences of DNA damage caused by a toxicant. I have consulted a statistician to discuss some of ...
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Is it valid to compare nested models even if proportional hazards assumption is violated in Cox models
I am trying to understand when are Cox models still informative and useful even when the proportional hazards (HR) assumption is violated and came across this interesting answer. It includes a link to ...
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UMP test of $H_0:\theta=1$ vs $H_A:\theta\neq1$ for Beta($\theta,\theta$)
Let $X_1,X_2,\dots,X_n$ be iid Beta($\theta,\theta$) samples. Is there a UMP level $\alpha$ test of $H_0:\theta=1$ vs $H_A:\theta\neq1$?
We first test $H_0:\theta=1$ vs $H_A:\theta<1$. The ...
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Why can a likelihood ratio not give evidence for the null since it is a model comparison?
I am curious as to why a likelihood ratio cannot give positive evidence for the null, since it is a model comparison.
Indeed, this is more confusing given the fact that Bayes Factors are similar ...
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Comparison of variances: symmetric F-test is likelihood ratio test?
Suppose $X_i\stackrel{IID}\sim N(\mu,\sigma^2)$ for $i=1,...,n$, where $\mu$ is known. We want to apply the likelihood ratio test to decide between the hypotheses
$$
H_0: \sigma=\sigma_0 \\
H_1: \...
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Why doesn't the G-test's Chi-squared "threshold" scale with sample size?
In the popular likelihood ratio test of goodness-of-fit (also known as the G-test: see, e.g., here), the test statistic is calculated as
$$G(\mathbf{O},\mathbf{E})=2\sum_{i=1}^{M}O_{i}\log\frac{O_{i}}{...
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Likelihood Ratio vs Modified Frequentist Approach (CLs)
I'm a physicist trying to finally get a hold on practical statistics for particle physics and am having problem with the following -- I apologize for the lack of formality below.
Suppose the number of ...
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Generalized Likelihood Ratio Test - Why is the denominator a union
For GLRT, the ratio is:
$$
\Lambda^* = \frac{\max_{\theta \in \omega_0} L(\theta)}{\max_{\theta \in \omega_1}L(\theta)}
$$
but we instead use:
$$
\Lambda = \frac{\max_{\theta \in \omega_0}L(\theta)}{\...
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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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