# Tag Info

### Why GLM don't have an error term and why shouldn't residuals be i.i.d?

GLMs specify a conditional distribution at each combination of predictors. When that conditional distribution is normal with constant variance, then the errors about the mean will be i.i.d. normal and ...
• 284k

### Why GLM don't have an error term and why shouldn't residuals be i.i.d?

GLMs are not supposed to generalize $y = X\beta + \varepsilon$. They generalize the equivalent$^{\dagger}$ notion of $\mathbb E\left[Y\vert X=x\right] = X\beta$. There is no error term in this about ...
• 63.5k

### Why GLM don't have an error term and why shouldn't residuals be i.i.d?

Arguably, regression concerns modeling the expected response. If we focus on this aspect of modeling, the "error" is less something intrinsic to a model than it is a way of calculating the ...
• 63k
1 vote

### Why GLM don't have an error term and why shouldn't residuals be i.i.d?

GLMs (generalized linear models) include a lot of different types of models. It's more of a family than a single model. Notably, the typical linear model is a special case of the GLM. A GLM ...
1 vote
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 ...
• 13k
Accepted

### VGAMs/VGLMs vs Multiple GAMs/GLMs

VGAMs are an extremely flexible model class. Yes, they can be used to model data where the response is actually a vector of responses where each vector gets its own linear predictor. This is not the ...
• 48.2k

### Logistic regression with labels corrupted by known noise model

I'm going to take a Bayesian approach because honestly I'm not sure how to tackle this as a Frequentist. Let's first write out the likelihood for such a model. The likelihood of $y_i$ depends on a ...
1 vote

### Logistic regression with labels corrupted by known noise model

(Started as a comment but got too long) Some obvious references are: Label-noise robust logistic regression and its applications (2012) by Bootkrajang & Kaban and Learning From Noisy Labels By ...
• 44.4k
Accepted

### Hypothesis tests in summary of glm() are always Wald tests?

They are both Wald tests. The column is labelled as t when a variance parameter is estimated and as z when no variance ...
• 39.5k
1 vote

• 116
Accepted

### GLMs and their conditional expectation and variance

I have always wondered about this myself as well. There are proofs for it like using the score in the other answer, or the moment generating function like mentioned in the comments. But they are ...
• 79.8k

### GLMs and their conditional expectation and variance

You have to keep in mind that $Y_i,$ the responses, follow exponential family of distributions. Then we can get our required formula working with the log-likelihood of $\theta, ~\ell(\theta)$ and its ...
• 8,832

### ZIP interpretation

Briefly, zero-inflated Poisson regression assumes that zeros are created by two processes: i) "true" or excess zeros and ii) sampling zeros (from the Poisson distribution). As an example (...
• 30.7k
Accepted

### Interpretation of generalized linear mixed-effects models: How should I proceed with a significant interaction term?

I have some comments before looking at the treatment effect comparison between "old" and "new". This is a linear mixed model (a linear regression with random effects), not a ...
• 10.2k
Accepted

### Exact equations for predictions in the hurdle model?

Root of the problem: You are right about most details but the predict(..., type = "zero") does not give the zero hurdle probability $\pi$ for the hurdle ...
• 15.7k

### How does lmList calculate AIC?

I have discovered that AIC for the multispecies list model is the sum of the AICs for the separate models. Is there anything else we need to know?
• 437

### Why using Newton's method for logistic regression optimization is called iterative re-weighted least squares?

Because error is being calculated according Mean-Squared-Error being minimized - as is Least-Squared technique/approach, used iteratively in Newton-method. in Python Newtons-method looks like (...
• 210

### How Do I Calculate the Scaled Deviance of a GLM with Gamma(Exponential) Distributed Dependent Variable?

The relevant parameter of the exponential in a generalized linear model is $\mu$ (which is indeed a scale parameter); specifically we're dealing with the mean-parameterization of the exponential, of ...
• 284k
Accepted

### Advantage of GLMs over transformation models

The punchline is that the GLM is directly estimating E(y|x), whereas the transformed model is estimating E(ln(y)|x). You don't have a way of generating a prediction of E(y|x) from E(ln(y)|x): the ...
• 6,952
The statistic being reported is $-2\cdot\text{ln}(L_0/L_1)$, where $L$ is the likelihood of two models being compared. For type I sums of squares that would be a model without and with the parameter ...