Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

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.

0
votes
0answers
14 views

Likelihood ratio test function- manually in R [on hold]

I am trying to write a function in R, which implements the likelihood ratio test for all well known densities. The input must contain datas, the density function, and the H0 parameter, with its name. ...
1
vote
0answers
18 views

Likelihood ratio test and sample statistics

Given a sample $\mathbf X =(X_1,...,X_n)$ from a parent random variable $X$, Neyman-Pearson's test for two point hypotheses $H_0$ and $H_1$ is the one defined by the critical region $$C=\left\{\mathbf ...
1
vote
1answer
26 views

Non-analytical application of Neyman-Pearson lemma

I have a discrete random variable $N$, from which a random sample $N_1,\dots,N_{15}$ is drawn. I want to test two hypotheses about the distribution of $N$ which are represented by two histograms. In ...
5
votes
1answer
164 views

Likelihood modification in Metropolis Hastings ratio for transformed parameter

I want to use MH to get samples from $p(\theta \mid y) \approx p(y \mid \theta) p(\theta)$. Let's assume $\theta$ is heavily constrained and I transform $\theta$ to $f(\theta)$ so I can sample from ...
1
vote
0answers
32 views

UMP test for $H_0:\theta=\frac{1}{2}$ vs $H_1:\theta>\frac{1}{2}$ when a sample is drawn from $f_{\theta}$

Suppose $X$ has the density $$f_{\theta}(x)=\left(2(1-\theta)x+\theta\right)\mathbf1_{0<x<1}\quad,\,\theta\in[0,2]$$ Is it possible to derive a uniformly most powerful (UMP) test for testing $...
1
vote
0answers
43 views

Can the r-scale value (for Bayes Factor) be directly based on Cohen's d?

I want to set an r-scale value for a Bayesian t-test (i.e. to calculate Bayes Factor likelihood ratio) based on previous results (i.e., from a posterior). But I simply cannot find a straightforward ...
1
vote
2answers
42 views

Understand a statement about likelihood function

I'm reading Agresti - Categorical Data Analysis and it says Consider two models, $M_0$ with fitted values $\hat{\mu}_0$ and $M_1$ with fitted values $\hat{\mu}_1$ with $M_0$ a special case of $M_1$....
0
votes
1answer
28 views

Do we maximize likelihood or likelihood ratio for ML estimation? [closed]

I was reading link. And I rewrite (3), here, in link to simplify notation as follows $$ \Lambda(X) = \frac{\mathcal{L}(\lambda_S | X)}{\mathcal{L}(X)} $$ Here $\lambda_S$, variance in presence of ...
0
votes
1answer
33 views

Is likelihood also defined as ratio of pdfs

My understanding of likelihood is that it is pdf except that it is a function of parameters rather than observations (as in link). I was reading link. Can likelihood be defined as ratio of ...
1
vote
1answer
45 views

Usefulness of Point Estimators: MVU vs. MLE

In a past class, two types of point estimators were introduced: minimum variance unbiased estimators (MVUs) and maximum likelihood estimators (MLEs). Supposedly, the MVU is optimal, unless an unbiased ...
0
votes
0answers
31 views

Likelihood ratio test, Wald test and LM test for variance of a normal distribution

Let y1, y2....yt follow a N(0,sigma^2) distribution. [Note that the mean is zero and you know that it is zero]. Derive the LR, LM and Wald test of hypothesis sigma^2 = 1. I have got the MLE, the ...
1
vote
1answer
25 views

ANOVA selects a model with autocorrelated residuals

I want to know which temperature dataset (Aa1, Bb, Cc, Dd) is/are the best predictor for laying date (medini). First, I used simple linear regression: median...
0
votes
0answers
22 views

Statistical test to compare the mean of two samples

There's a competition with 20 categories, and each category has 3 winners. I have an array of the winner's performance of the next year (60 values), and other array with the average of the competitors ...
1
vote
1answer
52 views

Select mixed model same degree of freedom

When I have a two mixed models (lme function) with different df then ANOVA summary shows the p-value of likelihood ratio test as following : ...
0
votes
1answer
27 views

How much bias am I risking by doing model goodness of fit comparison without accounting for clustering?

I am interested in testing whether an interaction term is statistically significant or not in a logistic regression. Data is large and observations are clustered by family and suffer from sparsity for ...
8
votes
1answer
181 views

Reproduce figure of “Computer Age Statistical Inference” from Efron and Hastie

The summarized version of my question (26th December 2018) I am trying to reproduce Figure 2.2 from Computer Age Statistical Inference by Efron and Hastie, but for some reason that I'm not able to ...
0
votes
0answers
13 views

confusing result from likelihood ratio test when covariate is factor

I got really confusing result from likelihood ratio test. I'm using mtcars data as an example. The following code works as expected. In ...
0
votes
2answers
37 views

Calculating the relative likelihood with AIC values

I'm using AIC for model selection, and would like to use a relative likelihood measure to quantify how many times a model with minimum AIC (AICmin) fits better than the alternative (with AICi). For ...
0
votes
0answers
21 views

Comparing nested models with orthogonal predictors using the t-statistic

Imagine we have a pair of nested models. Model A includes $n$ terms. Model B includes $n+m$ terms. To assess the "value add" of ...
0
votes
1answer
50 views

Calculating Log-Likelihood of Logistic Adaptive-Quadrature GLMM for Comparison with Fixed Model

Fitting a binary logistic GLMM here, with ungrouped data (all responses either 0 or 1). It says in this thread and in the documentation of anova.merMod that the ...
1
vote
0answers
53 views

Degrees of freedom of likelihood ratio test with equal dimension on the null and the parameter space?

Let $x_1,\dots,x_n$ be iid samples from a $N(\mu,\sigma^2)$ and consider the hypotesis $$H_0:\theta\in\Theta_0,\,\,\,\,\,\,vs\,\,\,\,\,\,H_1:\theta\in\Theta _{0}^c$$ where $\Theta _{0} = \{\mu>0,\...
5
votes
1answer
124 views

What should my critical region look like in this LR test for shifted exponential distribution with pdf $e^{-(x-\theta)}\mathbf1_{x>\theta}$?

I have a small confusion over describing the cutoff point for the critical region in a likelihood ratio test when the null hypothesis is composite. Take this exercise in particular: Let $(X_1,X_2,\...
-1
votes
1answer
483 views

Basic likelihood ratio test

I should perform a likelihood ratio test on the following null hypothesis : α = Aψ where α and A (p * m) are known vectors. ψ (m*r) is a matrix of free parameters. The likelihood ratio test is ...
1
vote
1answer
44 views

Why is the false acceptance probability not improving with increasing sample size?

We have a normal distribution with zero mean. We have two hypotheses for the variance $\sigma^2$: $$H_0: \sigma^2=\sigma_0^2$$ $$H_1: \sigma^2=\sigma_1^2$$ We make $n$ independent observations $X_1, ...
2
votes
0answers
17 views

Are EFA and/or ESEM models on the same data set with different factor solutions nested models?

Are EFA and/or ESEM models on the same data set with different factor solutions nested models? If yes, how are they nested? Are EFA and/or ESEM models and more restrictive CFA models on the same data ...
1
vote
1answer
197 views

Different p-values for coefficients and LRT in univariate cox regression (coxph R)

I have used Cox PH to test the relationship between one predictor and survival for 6 patients. Cox PH was used since the predictor is continuous. Using the "cox.zph" function, there was no significant ...
1
vote
0answers
35 views

difference between Wald and LR in Anova(car) and p-values

I am having difficulty understanding the p-values of a Anova(glm) in the car package in terms of Type II error. Are they testing ...
1
vote
0answers
42 views

Why always AIC and BIC are used in mixture model than Vuong test

I am working with mixture models. I fitted more than one model to the data and then try to select the most appropriate model using different selection criteria, for example, AIC. My supervisors asked ...
2
votes
1answer
62 views

Philosophy behind “hypothesis” in Bayes factor

The posterior odds is the ratio of the Bayes factor $\times$ prior odds of the hypotheses. $\frac{p(H_0 | D)}{p(H_1 | D)}$ = $\frac{p(D | H_0)}{p(D | H_1)} \frac{p(H_0)}{p(H_1)}$ It is considered a ...
1
vote
1answer
43 views

How to obtain a power curve from a likelihood ratio test for linear regression as a function of varying a coefficient of the more complex model?

I am currently doing a test of model complexities for two linear regression models: First Model: $Y = \beta_0 + \beta_1X_1 + \beta_2X_2 + \epsilon$ vs. Second Model: $Y = \beta_0 + \beta_1X_1 + \...
5
votes
4answers
263 views

Joint probability of multivariate normal distributions with missing dimensions

Suppose I conduct two experiments, each measuring a subset of possible parameters. From experiment #1 I measure two parameters and estimate the multivariate normal distribution $$ \mathbf{X}_1=\left [...
1
vote
1answer
28 views

Is there a special meaning behind a hypothesis test that consistently report 0.5 as the p-value? [closed]

I have been conducting Likelihood Ratio Tests on Full and Reduced form linear models and there is a specific scenario where I consistently obtain p-values of 0.5. I am wondering if there was a special ...
0
votes
0answers
45 views

Comparison of nested regression models vs predictor's significance within model

I am building regression models to evaluate the effect of several characteristics of genetic variants (my predictors) on a handful of phenotypic parameters (continuous and binary - hence I am building ...
1
vote
1answer
24 views

Is this model “nested” and fit for LR Test?

i want to see if different dummy variables are capturing significanly different effects from one another so i am running LR tests in which two (of the 4) dummies independent variables are merged in ...
0
votes
0answers
13 views

Likelihood ratio test normalization for performance evaluation

I'm performing a log-likelihood ratio test on simulated data and I want to derive a ROC (receiver operating characteristic). In order to do this I follow these steps: I create N false alarm dataset (...
0
votes
0answers
49 views

Likelihood Ratio Testing For Model Selection

I have seen, in various places, the likelihood ratio test being used to compare models. From my understanding, the likelihood ratio statistic is very useful because Wilks Theorem shows that ...
3
votes
1answer
102 views

Reporting betareg outcome - how to compare non-nested models?

I am looking for advice how to gain and report results using beta regression for an ANCOVA-like model. My model is as follows: ...
1
vote
0answers
23 views

LRT and $\text{Uniform}(0, \theta)$

We have one observation of variable $X$ that is distributed uniformly on $[0, \theta]$. Null hypothesis is $H_0 \colon \theta = 1$ and alternative hypothesis is $H_1 \colon \theta = 2$. What is the ...
0
votes
1answer
127 views

Analysing Repeated Measures RCT study. emmeans / lsmeans estimate and back-transform problems. Approach doubts

Background I am writing a project on a big multicenter RCT study, where subjects are following different dietary patterns for 2 years. I have access to their dietary intakes and I am grouping them in ...
0
votes
0answers
191 views

When to use Neyman Pearson or Likelihood ratio

question about Neyman-Pearson lemma vs the likelyhood ratio. From my textbook it says that if you want to test: $H_0: \theta \in \Theta_0$ vs $H_1: \theta \in \Theta_0 ^ c$, then you can use a LRT $...
0
votes
0answers
10 views

LR test of merged dummy coefficients in a Heckman

i'm running a Heckman test and want to demonstrate if different dummy variables have a statistically similar effect. im performing an LR test by first running the full Heckman, storing the log-...
0
votes
0answers
6 views

testing the null hypothesis that two coefficients are equivalent (LR)

I'm running a replication study on Livingston's (2005) examination of reputational effect on online auctions. sellers are divided into dummy quartiles based on their feedback scores. I have run a ...
0
votes
1answer
78 views

LRT of normal distribution - explanation of numerator

Let $X_1,...,X_n$ be random sample of $X$~$N(\mu,\sigma^2)$ with known $\sigma^2$. I am trying to derive test statistic for that distribution I know that $\hat{\mu}=\overline{X}$ $$\lambda(x)=\...
1
vote
0answers
20 views

R or Stata shortcut to significance test interaction term including restricted cubic splines?

I fit the following model in R using the lme4 package, which is a linear mixed effects regression of outcome "WT_abs_change" (absolute weight change) on various factors, including "ns(WT_dtime, df=3)*...
0
votes
0answers
17 views

How to use bootstrap to do a hypothesis test in mixed models

I have a mixed model with multiple covariates. I want to test if some of the covariates are insignificant. Since I have mixed model the LR-test will result in a p-value which is too low, hence I want ...
2
votes
1answer
69 views

Probability of sample point given a Linear Regression

This question may be ill-posed, but hopefully you all can help talk me through it. Given a probability density function $f(\cdot)$ parameterized by one or more parameters $\theta$, we can compute the ...
2
votes
1answer
103 views

LRT for PRT both unknown

I have a random sample of ${X_1,...,X_n}$ from the following pdf: $${\theta \beta^ \theta \over {x^{\theta+1}}}$$ where $\theta>0$, $\beta>0$, $x\ge\beta$ I want to find the LRT to test $H_o:\...
1
vote
0answers
38 views

How to adjust for the number of nested model tests?

How should I adjust for the number of tests I do when using the likelihood ratio difference test in a model estimated using maximum likelihood (or some flavor of), where the null hypothesis of the ...
0
votes
1answer
82 views

Deriving LRT for comparing two sample proportions

I have two sample proportions, and want to test: $$ H_0: p_1 = p_2 \quad \text{vs.} \quad H_a: p_1 \neq p_2 $$ i.e., that they really come from distributions with the same common probability $p$. My ...
0
votes
0answers
73 views

Optimal Neyman Pearson Test and Decision Region

I am working on a problem but i stacked. Suppose that $x_1$ and $x_2$ are jointly distributed Gaussian random variables. There are two hypotheses for their joint distribution. Under either ...