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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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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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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Null model is a better fit for the data compared to experimental model?
I have built a generalised linear mixed effects model fitted to a gamma distribution. I am wanting to compare this experimental model to a nested null model to see whether it is a better fit for the ...
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Subspace test for multivariate normal distribution [duplicate]
Subspace test for multivariate normal distribution
Suppose $X_1, X_2,\ldots, X_n$ are i.i.d. observations from a multivariate normal distribution $N(\mu,\Sigma)$ where $\Sigma$ is known. Furthermore, ...
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Detection limit for a drop in speed, due to stopping between measurements
Assume that a device is traveling at a constant expected speed $\mu$, subject to random variation with standard deviation $\sigma$, for a measurement period of duration $t$. Then the expected travel ...
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Likelihood ratio test for model specification with boundary Null
I am interested in understanding the asymptotic distribution of Likelihood ratio (LR) test statistic for model specification. I am focusing on the case in which the null hypothesis is of the form (i.e....
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Multiple Kolmogorov-Smirnov tests with likelihood ratio
I would like to be able to establish whether a sample (let's call it A) is more likely than another sample (let's call it B) to be drawn from the same distribution as a third sample (let's call it C).
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What regression should i perform in order to obtain an R-squared or pseudo R-squared with my data properties?
I've got a rather hard question concerning my regression.
My data has the following properties.
Dependent variable is count data and is overdispersed and consist of repeated measurements within ...
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Type-2 errors in the likelihood-ratio/G-test?
I am quite new to hypothesis testing, and I am currently trying to familiarize myself with the G-test for independence. In my research, I came up with a question for which I could not fit an answer ...
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Significance test on likelihood ratio of two completely specified models
Suppose that I collect some dataset $Y$ which is a sample from a multinomial distribution with unknown event probabilities $\theta_{truth}=(p_1,p_2,...,p_k)$ where $\sum{p}=1$.
I have two competing ...
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Likelihood ratio test for composite alternative hypothesis
I must admit that my general understanding on how to create critical region to test hypothesis against composite alternative hypothesis is still shaky. Therefore please pardon if my question is too ...
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What is the influence of multicolinearity on the likelihood ratio test?
I learned the two concepts separately and I try to find out how these concepts relate to each other.
To illustrate the question introduce three models. The models establish a relation between age (AGE)...
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