Linked Questions

28
votes
4answers
53k views

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 ...
6
votes
2answers
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 ...
7
votes
1answer
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 ...
3
votes
1answer
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 ...
5
votes
1answer
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}^\...
2
votes
1answer
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 ...
1
vote
0answers
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 ...
2
votes
2answers
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 ...
4
votes
0answers
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: ...
0
votes
0answers
100 views

Comparing goodness of fit of quasi-Poisson regression model predictions vs. unknown forecast

I have built a quasi-Poisson regression to predict sales of different products based on a number of explanatory variables, with an offset term for the number of days each product was on sale. To ...
1
vote
1answer
38 views

Scoring rules for count models on: training data vs. validation data

In order to evaluate and compare count models (e.g. Poisson regression), we can calculate scoring rules (e.g. Brier Score, Dawid-Sebastiani score, etc.) which are explained here: Error metrics for ...