The likelihood-ratio tag has no wiki summary.
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Likelihood ratio test for a random variable following the Gamma Distribution
Assuming we have a random variable $X\sim \operatorname{Gamma}\left(\alpha,\beta \right )$:$\frac{1}{\Gamma (\alpha )\beta ^{\alpha}}x^{\alpha-1}e^{\frac{-x}{\beta }}$
I'd like to test the ...
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44 views
Understanding Sequential Probability Ratio Test (SPRT) Likelihood Ratio
I am a software developer looking to develop an alternative for the simple hypothesis testing scheme described here. In short, the test works as follows:
Two URLs are compared for their ability to ...
2
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2answers
74 views
Do Bayes factors require multiple comparison correction?
As the title: Do Bayes factors require mutliple comparion correction?
For more context, I am calculating very many likelihood ratio tests and I am thinking about how to handle multiple comparison ...
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2answers
461 views
Why is a likelihood-ratio test distributed chi-squared?
Why is the test statistic of a likelihood ratio test distributed chi-squared?
$2(\ln \text{ L}_{\rm alt\ model} - \ln \text{ L}_{\rm null\ model} ) \sim \chi^{2}_{df_{\rm alt}-df_{\rm null}}$
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Likelihood ratio test: $f(x)=2x$ vs $f(x)=3x^2$: $2n$ degrees of freedom?
Suppose $X_1, . . . , X_n$ are i.i.d. with pdf $f(ยท)$.
We want to test the hypotheses
\begin{align}
H_0 &: f(x) = 2x , \;\, \text{ for } 0 \le x \le 1, \text{ against}, \\
H_1 &: f(x) = 3x^2 , ...
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1answer
186 views
Likelihood ratio tests on linear mixed effect models
I am currently running some analyses on a linguistic data set with a mixed effect model. The problem is, I think that one random factor should be excluded while my colleague thinks it should be ...
2
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1answer
85 views
Markov chain model likelihood ratio test
Suppose I am using two Markov Chain Models, one with order $k=1$ and a second one with order $k=2$. I am "reducing" the higher order model to a $k=1$ model in order to have easier calculation ...
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Likelihood ratio test for MLE (Markov Chain)
As suggested in Calculating log-likelihood for given MLE (Markov Chains) I want to perform a likelihood ratio test for two fitted models (i.e., first and second order markov chains). Simply comparing ...
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40 views
Comparing tests for staging cancer
I am comparing 4 different tests for the evaluation/identification of cancer. One is a continuous variable yielding cut-off values based on both the mean and the median of 5 consecutive measurements ...
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72 views
Computing the LRT and Wald test from a subset of informations
The answer might be really easy, but I have got some doubts about it.
These are all the informations I have.
...
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0answers
140 views
When to use likelihood ratio test vs. incremental F-test in nested nonlinear model selection?
I have two nested nonlinear models and I want to know which provides a better fit to some data. I see descriptions of both the likelihood ratio test and of the incremental F-test (also called the ...
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2answers
355 views
Likelihood ratio test in R
I am in desperate need for help. I am trying to calculate the likehood ratio test in R, but I don't have allot of experience using R.
For example, to calculate the following
Suppose $X_1, ...
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2answers
162 views
Model selection with nonlinear fitting? Statistical tests seem ambiguous
I'm working on fitting an exponential model
$\mathrm{Flux} = A+Bt+F\left(\exp(t_0-t/T_r) + \exp(t-t_0/T_f)\right)^{-1}+...$
to astronomical data (a light curve).
$A$, $B$, $F$, $t_0$, $T_r$, and ...
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93 views
Non-central chi-square for small sample likelihood ratio tests?
I am interested in small sample performance of likelihood ratio tests.
I have found empirically that the null hypothesis distribution (obtained by permutation) in small sample situations can be fit ...
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Is it reasonable to calculate AIC of a subset of the data set which was used to fit the model?
There is a factor variable called "Treatment" in my data set. This factor consists of two levels, "C" and "H". I want to test whether there is there any significant difference between two levels. I ...
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Why do LR and Wald p-values differ by orders of magnitude?
My application is a Cox model with n=685 and one continuous predictor
mod <- coxph(srv ~ predi)
summary(mod) gives a ...
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2answers
203 views
Can I use a likelihood ratio test when the error distributions differ?
This question might sound simple, but in fact I am absolutely unsure whether it is allowed to use an LRT for model comparison when the error distributions differ.
For example, can I compare a model ...
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Reference for implementing generalized likelihood ratio test to determine online whether time-series mean has shifted
What is a reference that describes the "generalized likelihood ratio" test to determine online (i.e., meaning that we add an observation, then check, then add an observation, then check) whether the ...
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How can I calculate the statistical power of a MI based likelihood ratio test with many df?
I'd like to calculate the statistical power of a likelihood ratio test based on mutual information.
I'm using the asymptotic property that the test statistic $G = 2NI$ where $N$ is the sample size ...
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1answer
236 views
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 ...
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1answer
269 views
Finding the p-value
I am a little stuck on the following question.
Skulls were excavated from a dig. The sex of each skull was determined by anatomical appreciation. For Sites A, the data was Male=162, Female=110.
a) ...
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1answer
163 views
Benjamini-Hochberg dependency assumptions justified?
I have a data set where I test for significant differences between three populations with respect to some 50 different variables. I do this using Kruskal-Wallis tests, on one hand, and by likelihood ...
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1answer
191 views
How to choose between z and t in 2 sample (non-paired) tests?
I understand that in the one sample case, z is employed where population variance is known and t for where it is unknown.
In the two sample case: we are trying to test $H_0: \mu_x=\mu_y$ against ...
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Binary classifier probability measure?
I've the following situation.
I've a binary classifier which classifies input feature vectors into either of two classes 'y' or 'n', along with the probability of it being in either of the classes ...
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2answers
269 views
Use likelihood-ratio test to select models in case of nested models
Is it possible to do model selection in this way? Suppose I need to select a good (logistic) model among three variables (var1, var2, var3). The deviance D* (-2*log-likelihood) of this full model ...
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1answer
148 views
Hypothesis testing using the likelihood ratio test
How can I apply the likelihood ratio test when I have the following hypothesis for collocation discovery:
$$H_{1}: P(w^{2}|w^{1}) = p = P(w^{2}| \neg w^{1})$$
$$H_{2}: P(w^{2}|w^{1}) = p_1 \neq p_{2} ...
8
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1answer
328 views
Choose best model between logit, probit and nls
I'm analyzing a certain dataset, and I need to understand how to choose the best model that fits my data. I'm using R.
An example of data I have is the following:
...
3
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3answers
671 views
Using AIC, for model selection when both models are equally weighted, and one model has fewer parameters
I am using AIC (Akaike information criterion) for model selection. There are 2 models. The first model has 2 parameters with log likelihood of -10182.0284 and the second model has 3 parameters with ...
1
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1answer
41 views
Is it correct to compute LR stat after maximising likelihood with bounds?
I use grid search with bounds for example lb=[ 1 1 1 1 1 1]'/1000; ub=[10 10 10 10 10 20]' but it is computationally difficult so it checks 2 points only. Thus i obtain boundary solution consisting ...
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193 views
How do you calculate the likelihood ratio test statistic in this problem?
I am trying to solve this problem but I am not sure how to proceed to get the formula for the test statistic and critical values.
Suppose $X_1,X_2,\ldots X_n$ are i.i.d. observations from a ...
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1answer
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Likelihood ratio test overestimates significance. More appropriate test?
I'm trying to find words that have a significantly distribution in one small portion of a large corpus than they do in the entire corpus. I'm using the standard likelihood-ratio test statistic
...
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How to rigorously define the likelihood?
The likelihood could be defined by several ways, for instance :
the function $L$ from $\Theta\times{\cal X}$ which maps $(\theta,x)$ to $L(\theta \mid x)$
the random function $L(\cdot \mid X)$
we ...
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Likelihood Ratio Testing in Multinomial logistic regression using SPSS
I am doing multinomial logistic regression.
Dependent variable is categorical with 6 categories. 6 Independent variables are measured on an interval scale (included as covariates in SPSS)
Now I am ...
0
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1answer
170 views
Maximizing: likelihood vs likelihood ratio
Say I have an observed data set ($n_i$) and I want to obtain the best fit out of 10 data sets produced by a model dependent on a single parameter $a$ ($m_i(a)\;a=1..10$).
Suppose I use a Poisson ...
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2answers
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Question on cumulative probability
In an article I'm reading the probability of an observed point falling in bin i is written as:
$P_i=\frac{m_i}{\sum\limits_j m_j}$
where $m_i$ is the number of model points in bin i.
Then, the ...
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Likelihood ratio vs Bayes Factor
I'm rather evangelistic with regards to the use of likelihood ratios for representing the objective evidence for/against a given phenomenon. However, I recently learned that the Bayes factor serves a ...
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1answer
401 views
Why use a likelihood ratio (and its relation with p-value)?
Lets' say I have a Poisson distribution for which I use a maximum likelihood defined as:
$P_i=\frac{m_i^{n_i}}{e^{m_i}n_i!}$
where $m_i$ represents the model value of bin $i$ (real, $m_i$> 0) and ...
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2answers
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How do to calculate Likelihood Ratio Test/Power in hypothesis testing?
I am preparing for an exam, I've been reading through Likelihood Ratio Test, but don't get it.
Example 8.2.3 (page 376 in "Statistical Inference" Casella and Berg)
Let ${{x}_{1}},...{{x}_{n}}$ be a ...
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1answer
360 views
How to interpret this criterion of logistic regression result
I run a backward variable selection logistic regression and find out the SAS program selected 12 variables and give me the output like this:
It is funny that my configuration of the SAS ...
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1answer
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Can a -2 Log likelihood be calculated with only one model?
I am using the glmfit function in MATLAB. The function only returns the deviance and not the log likelihood. I understand that the deviance is basically twice the ...
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1answer
150 views
Property of KL-divergence
Let $p_1$ and $p_2$ be two distinct probability distributions. Define
$$
L(q)=D(q||p_1)-D(q||p_2)
$$
where $D$ is the usual Kullback-Leibler divergence. Assume the support of $p_2$ is included in ...
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1answer
113 views
What is the outline for the procedure of model selection, with different models based on likelihood functions?
I have two basic models $M_1$ and $M_2$. They each have a likelihood function;
$L_{M_1} = f(\mathbf{X}|\mathbf{\theta_1})$ and $L_{M_2} = f(\mathbf{X}|\mathbf{\theta_2})$ (here $\mathbf{X}$ is the ...
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1answer
528 views
Non-nested model selection
Both the likelihood ratio test and the AIC are tools for choosing between two models and both are based on the log-likelihood.
But, why the likelihood ratio test can't be used to choose between two ...
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1answer
128 views
Change detection algorithm - likelihood ratio
Consider a sequence of independent random variables $(y_k)_k$ with a
probability density $p_{\theta}(y)$ depending upon only one scalar
parameter. Before the unknown change time $t_0$, the ...
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1answer
486 views
Likelihood ratio tests
Is likelihood ratio test ($F$-test) of significance of difference of two linear models the same as chi-square test of difference of $-2\log L$?
SAS PROC GLM ...
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1answer
297 views
Likelihood ratio test
Is the likelihood ratio test ($-2 \log L$) basically like the partial F-test in that you are using it for logistic regression instead of linear regression?
2
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1answer
277 views
Effective sample size for test of independence
I am interested in applying a test of independence such as chi-square or log-likelihood in the case where the observations are not independent (observations are sequential in time and there is a ...
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2answers
531 views
Allowed comparisons of mixed effects models
I've been looking at mixed effects modelling using the lme4 package in R. I'm primarily using the lmer command so I'll pose my question through code that uses that ...
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2answers
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Practical definition of a UMP test?
I'm trying to make sense of these two statements about UMP (uniformly most powerful) tests:
If $g(t\mid\theta)~$ is a UMP then $~g(t\mid\theta_1)>k g(t\mid\theta_0)~\forall~t\in C$ and ...
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Is it appropriate to use the term “bits” to discuss a log-base-2 likelihood ratio?
I'm quite enamoured with likelihood ratios as a means of quantifying relative evidence in scientific endeavours. However, in practice I find that the raw likelihood ratio can get unprintably large, so ...
