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Results tagged with generalized-linear-model
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user 129321
A generalization of linear regression allowing for nonlinear relationships via a "link function" and for the variance of the response to depend on the predicted value. (Not to be confused with "general linear model" which extends the ordinary linear model to general covariance structure and multivariate response.)
2
votes
Accepted
quasi-likelihood estimates of beta
The question does not ask you to find the beta estimates or to conduct a test. The only thing you need is the asymptotic covariance matrix, which is given earlier in the same Chapter in the book. You …
- 13.5k
2
votes
Accepted
Count models - how to handle denominator (as offset) when granularity varies
I aggregate the data into the covariate patterns of interest with the count in each category and use the population data for that specific pattern as an offset.
Yes, that is a good approach. You cou …
- 13.5k
5
votes
Accepted
Poisson regression with offset vs poisson regression with weight
I think your question may be prompted by the fact that Poisson log-linear glms can be used to model either counts or frequencies. If count is a vector of counts and w is a vector of positive weights, …
- 13.5k
2
votes
Accepted
One sided likelihood ratio test for a logistic regression model?
A one-sided LRT is straightforward in R using the signed LRT statistic. Fit the logistic regression models with and without the $\beta$ term. Compute the ordinary LRT statistic from the deviance diffe …
- 13.5k
10
votes
What are weights in a binary glm and how to calculate them?
I'm going to give a more detailed answer. Tim and Ivan have correctly advised you not to worry about the weights argument and their answers would be excellent for continuous GLMs. Binary regression wi …
- 13.5k
6
votes
Accepted
Are ordinal models technically a GLM?
The ordinal model that you state is called the proportional odds ordinal logistic regression model (POLR), and was popularized by Peter McCullagh (McCullagh 1980).
Yes, it is a generalized linear mode …
- 13.5k
7
votes
If Y has an exponential family distribution show that $E(\frac{\partial L}{\partial \theta})...
The identities you state are completely general and are indeed well known. They apply to any likelihood function provided the log-likelihood is twice continuously differentiable and the support of the …
- 13.5k
7
votes
For model-averaging a GLM, do we average the predictions on the link or response scale?
The optimal way of combining estimators or predictors depends on the loss function that you are trying to minimize (or the utility function you are trying to maximize).
Generally speaking, if the loss …
- 13.5k
2
votes
Accepted
Multinomial GLM Pearson residuals
The simplest example of a multinomial GLM is binomial regression. Suppose we have fitted a binomial GLM to counts $y_i$, $i=1,\dots, N$.
Write $n_i$ for the number of binomial trials and $\pi_i$ for t …
- 13.5k
8
votes
Accepted
Small Sample Sizes and Zero Inflated Count Data in R
The problem you are observing with lack of significance of GA has nothing to do with zero inflation or with random effects.
It is simply a limitation of Wald tests for count models.
If you replace the …
- 13.5k
3
votes
Constructing a generalized linear model when the dependent variable has a Exponentially modi...
Generalized linear models assume that the response variable follows an exponential dispersion model (EDM) distribution. For fixed dispersion value, an EDM is a linear exponential family (LEF). As alre …
- 13.5k
4
votes
Overdispersion vs Tweedie
The two models you have fitted are identical --- there is no difference.
Quasi families are only more general than regular glms when
they specify a variance function for which there is no true glm or …
- 82.8k
5
votes
Why does the glm residual deviance have a chi-squared asymptotic null distribution?
I assume that you are referring to the total residual deviance that is computed when you fit a generalized linear model.
Your question alludes to a widespread misconception. Regardless of what you mig …
- 13.5k
4
votes
Is there a model for both mean and variance?
The dglm (double generalized linear models) package on CRAN does exactly that. To estimate the model with non-constant variance that you mention in your question, in which $x$ is both a linear predict …
- 13.5k
4
votes
Fisher information matrix for logistic regression using the logit link
The model setup is a binomial generalized linear model with logit link, also called logistic regression.
There are standard and quite simple formulas for the Fisher information matrix (FIM) of a gener …
- 13.5k