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.
Questions tagged [likelihood-ratio]
645 questions
9
votes
1 answer
I Just Ran Two Million Regressions - Integrated Likelihood
I am currently working on trying to implement a method used in a popular paper titled "I Just Ran Two Million Regressions". The basic idea behind it is that there are certain cases where it is not obvious what controls should be included in the…
NikolaiB
- 121
3
votes
0 answers
Is it a valid likelihood ratio test?
We know a valid LRT should compare nested models. Suppose there are four models:
model1 = gamm4(y ~ x + s(t))
model2 = glmer(y ~ x + t)
model3 = gamm4(y ~ 1 + s(t), random = ~(1|t))
model4 = gam(y ~ x + s(t))
I am not sure they are nested model.…
User329532
- 41
- 1
3
votes
0 answers
Time Series Analysis, Model Change: Dealing with Outliers
I have time series, and I know the models underlying this time series. So, for example, first 100 points are generated with model $H_1$, next 50 with model $H_2$ and so on.
The problem is: I am interested only in long shifts of model. In other…
German Demidov
- 1,731
- 13
- 27
2
votes
1 answer
Hypothesis test on variance of normal sample
This question is a follow-up to this discussion:
https://math.stackexchange.com/questions/634914/distribution-of-likelihood-ratio-in-a-test-on-the-unknown-variance-of-a-normal-s/635371?noredirect=1#comment1339933_635371
Could someone audit the…
user114618
- 177
2
votes
1 answer
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 the restricted model.
the unrestricted model is…
Tom Witten
- 219
2
votes
1 answer
Does likelihood ratio test tell about anything else than whether two models are "different"?
Does likelihood ratio test tell about anything else than whether two models are "different"?
Wikipedia says:
The test is based on the likelihood ratio, which expresses how many
times more likely the data are under one model than the other.
But…
mavavilj
- 4,109
2
votes
1 answer
A test statistic that equals a constant under $H_{0}$
I was designing a hypothesis test, using the likelihood ratio test, and I found out that, under $H_{0}$, the test statistic $\Lambda$ equals the same constant $k$ no matter what the observations may be. Does that mean that the rejection region is of…
Toney Shields
- 882
2
votes
0 answers
How to deal with zero-valued probability?
I have a few models which I would like to combine later on; for each model I have the sensitivity and specificity. I then calculate for each model the likelihood ratio to get a feel of how well the model performs: $LR_{+} =…
1
vote
1 answer
Does mulligan matter?
I'm a TCG player, and in the game in question you work with a 50 card deck and with the limit of 4 copies of a single card, the game proceeds as follows:
Draw 5 cards from your deck
Decide if you like your hand or put the 5 cards into your deck…
Alyosha OL
- 21
1
vote
1 answer
likelihood ratio test for non-nested hypotheses
I'm reading the statistics textbook written by Hogg, Tanis & Zimmermann and wanted to ask here if this book is correct about the likelihood ratio test.
In the section about the likelihood ratio test, the book explains how to construct a likelihood…
Nownuri
- 409
1
vote
1 answer
Can the log likelihood ratio for a simple vs simple hypothesis take a negative value?
Can the log likelihood ratio for a simple vs simple hypothesis take a negative value? Since it approximately follows a chi-square distribution for large sample sizes and since a chi-square distribution takes only positive values do we reject or…
Nuzhi
- 291
1
vote
0 answers
Tying out Likelihood-ratio with a t-test exactly?
I've been trying to get my head around the likelihood ratio test, and I think I understand now how it all works, roughly. But I've read a few posts showing how you can derive the t-test formula via a likelihood test. However, I was wondering, is…
justme
- 775
1
vote
0 answers
Is it possible to combine likelihood ratios if independence cannot be assumed?
Given a dataset with multiple likelihood ratios (LRs) for predicting Heart Failure:
Previous Heart Failure = LR 2
Classical Exam Findings = LR 4
Previous Hypertension = LR 6
Assuming LR(Previous Heart Failure) and LR(Classical Exam Findings) are…
David H
- 11
1
vote
1 answer
Likelihood Ratio and Expected Value Relationship
I am to prove that:
1) The expected value of $(Λ^n|H_1) = E(Λ^{(n+1)}|H_0)$
2) The expected value of $(Λ|H_0) = 1 $
where $Λ$ is the likelihood ratio. I know that the likelihood ratio is equal to $f(x|H_1)/f(x|H_0)$ but my textbook does not mention…
Raptors1102
- 141
0
votes
1 answer
Likelihood ratio test - sample size issue
I am a statistician running into an odd problem, and it feels like I am missing a key point here. I have a true model (generated by me so I know truth), and a PREDICTED model that estimates certain parameters of the true model, and I want to test…
