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### Pseudo R squared formula for GLMs

I found a formula for pseudo $R^2$ in the book Extending the Linear Model with R, Julian J. Faraway (p. 59). $$1-\frac{\text{ResidualDeviance}}{\text{NullDeviance}}$$. Is this a common formula for ...
2k views

### Compare glm.nb vs glm(…, negative.binomial(k), ..) models

My $Y$ is a count variable and I am estimating it using a negative binomial function. I am not sure how I can decide which model is better. In the first model I am selecting a value for $k$, and the ...
749 views

### Sum of squared Poisson probability masses

Let $(p_k)_{k=0, \dots, \infty}$ denote the probability masses of a Poisson distribution with parameter $\lambda$. I'm looking for the sum of their squares, $$\sum_{k=0}^\infty p_k^2,$$ as a function ...
1k views

### How to calculate model error (like MSE) for a multivariate proportional response?

I have data where the response is multivariate and proportional (rows [observations] sum to 1). I am modelling this response using a Dirichlet regression via the DirichletReg R package where the ...
386 views

### Sum of squared Negative Binomial probability masses

Let $(p_k)_{k=0, \dots, \infty}$ denote the probability masses of a Negative Binomial distribution with parameters $r>0$ and $p\in]0,1[$. I'm looking for the sum of their squares, \sum_{k=0}^\...
901 views

### Count data model validation

I'm using different models to model count data, the purpose of modelling is prediction. Values vary from 0 to 7. I try to use cross-validation method to assess out-of-sample predictive perfomance, but ...
303 views

### Why is R2 not reported for GLMs based on last iteration of IRLS weighted least square regression with which it is fit

Given that GLMs are generally fit using iteratively reweighted least squares (based on a Fisher scoring algorithm to maximize the max likelihood objective, which is a variant of Newton-Raphson, see ...
77 views

### How do we compare count models for prediction and inference?

I have estimated a number of count models on a data, including Poisson, Zero-Inflated Poisson (ZIP), mixed-effects Poisson, mixed-effects ZIP and, a few different versions of each of these based on ...
104 views

### Is the ALRE method of standardization/rescaling appropriate for proportion data?

I have data in which groups of experts make proportion estimates. I've been encouraged to use the ALRE method of scoring the error of these estimates. I found an article which describes this method: ...