# 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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11 views

### 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 ...
33 views

### 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 ...
9 views

### 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 ...
52 views

### 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 ...
65 views

### Likelihood Ratio Test Equivalent with $t$ test: Difference of Two Means from Constant Variance Normal Distributions

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

$\newcommand{\szdp}{\!\left(#1\right)} \newcommand{\szdb}{\!\left[#1\right]}$ Problem Statement: Let $S_1^2$ and $S_2^2$ denote, respectively, the variances of independent random samples of ...
98 views

### Binomial Distribution: Likelihood Ratio Test for Equality of Several Proportions

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

### 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 ...
35 views

### 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 $$D(y; \hat{\pi}) = 2[l(\tilde{\pi}; y)- l(\hat{\pi}; y)]$$ ...
25 views

### 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 ...
35 views

### Comparison between Nested and Non-nested Model: BIC and LRT

I would like to select the best model for predicting breast cancer risk, specifically, it is the comparisons between weight/BMI/height, as other covariates remain the same in all the models. But I got ...
83 views

### Significant coefficients but non-significant likelihood ratio test [closed]

Following a comment on this thread, I have a question about interpreting a logistic regression model with significant coefficients, but non significant likelihood ratio test. I have a super simple ...
20 views

### Where to find information on likelihood ratio tests [duplicate]

Can someone please recommend a good resource that explains the theory and logic behind likelihood ratio tests?
80 views

### ANOVA vs likelihood ratio test (different result)

I found the likelihood ratio test has a very similar setup as ANOVA: we are essentially testing if adding an additional variable would significantly increase the fitness. So I run both statistical ...
32 views

### What statistic am I actually looking for and how do I properly calculate it?

I think I am looking at odds or likelihood ratios in this scenario, but I'm having trouble figuring out how to actually calculate my numbers to get an answer to my questions. I have 309,508 total 3rd ...
85 views

### Does ( P(B|A) - P(B|~A) ) / P(B|A) have a name?

Without going into the details, which are unnecessary here, this morning I found uses for the quantity $$S = \dfrac{P(B|A) - P(B|\overline A)}{P(B|A)} ,$$ something like the amount of "...
31 views

### Do I have to drop a random slope if I drop the fixed effect in mixed-models for model comparison?

I'm performing a model comparison using the likelihood ratio test in R with two mixed models fitted with lme4. My model is: ...
18 views

### Mixed-models and PROC MI

I am running into a problem that I cannot seem to figure out. I am fitting a mixed-models logistic regression using PROC GLIMMIX using complex survey data from the Behavioral Risk Factor Surveillance ...
14 views