Questions tagged [deviance]
Deviance is a measure of distance between two probability distributions. In the case of GLMs, (total) deviance is twice the difference in log-likelihood between the full model and the restricted model.
233
questions
2
votes
0
answers
27
views
Proportion deviance explained by a predictor in a GAM fitted using mgcv with 'select=TRUE' (variable selection using double penalty)
Objective: To calculate proportion deviance explained by a predictor.
Approach: Following this post by Simon Wood, the deviance explained by a predictor x1 is the ...
- 21
1
vote
1
answer
26
views
How to interpret dispersion estimated for a Poisson model?
Suppose I have the following data: $(N_i, x_i, \nu_i)$ for $i=1,\dots,n$. I motivate this quickly from car insurance pricing. $N_i$ represents the number of claims, $x_i$ are some features I know and $...
- 113
5
votes
1
answer
217
views
F-test for nested GLM
Assume we are given two nested GLM models $M_0 \subset M_1$ with $q$ and $p$ parameters respectively. We also know that dispersion parameter in both models is estimated as the same value, denote it $\...
- 51
0
votes
0
answers
39
views
Questions regarding the definition of the deviance in the context of GLMs
I've been self-studying GLMs and I have some questions regarding the deviance in the context of GLMs. In Generalized Additive Models An Introduction with R, the author defines the deviance of a model ...
- 21
0
votes
0
answers
15
views
Comparing GLMs with different fitted distributions
I have a scenario where I need to compare some generalized liner models (with same link function, target variable, but not necessarily nested) with k fold cross validation, using a cost function to ...
- 25
1
vote
0
answers
58
views
Rel. contribution of each term to deviance explained (in GAM)
I have seen this and similar questions all over the place, but no really satisfying answers: How can we quantify the contribution that each term in a GAM (using mgcv package) adds to the total ...
4
votes
1
answer
81
views
How Do I Calculate the Scaled Deviance of a GLM with Gamma(Exponential) Distributed Dependent Variable?
I'm fitting a generalized linear model to a theoretically exponentially distributed dataset. The exponential distribution has PDF
$$
f(y;\lambda) = \lambda e^{-\lambda y}
$$
This question Deviance for ...
- 103
1
vote
1
answer
89
views
Manual variable selection in GAM model based in deviance explained
I'm fitting a generalized additive model (GAM) to predict bottlenecks in a manufacturing process of a company. They have data of the bottlenecks that occurs in their process of making hot steel rolls. ...
2
votes
0
answers
21
views
Logistic Regression Pattern in Deviance Variance Across Variables
I fitted a Logistic Regression model for a Customer Churn dataset with the following results
I tested this model with a validation set and calculated the ROC AUC score, which was approximately 0.85 – ...
- 21
3
votes
0
answers
134
views
How can we justfify the assumption of equal scale/variance in the definition of R-squared from Deviances in GLMs?
If we take the R-squared to be the comparison of Deviances between models (the model of interest, the saturated model, and the constant model), we can write it as (see this answer CC BY-SA 4.0):
$$R_{...
- 19.4k
3
votes
1
answer
100
views
Prove that the Deviance and the Generalised Pearson Statistic are asymptotically equivalent
I am reading the paper Exponential Dispersion Models from Jørgesen and at page $137$ I have encountered a claim that I don't know how to prove.
The author claims that the Generalised Pearson Statistic,...
- 202
1
vote
1
answer
119
views
Solution for Overdispersion in Poisson Regression
I have run poisson regression in SPSS (Generalized Linear Model), where BMI is my IV and length of stay (LOS) in hospital for certain disease is my DV (and it's a count variable).
When I run poisson, ...
- 151
3
votes
1
answer
63
views
Should Kullback-Leibler as an R2 value be large or small for better goodness-of-fit
I am trying to use the Kullback-Leibler as an R2 value for goodnes-of-fit for GLM models.
The R package performance defines their function as:
...
- 133
1
vote
0
answers
93
views
Is there a justification for the Bernoulli deviance in the R stats package?
Using the standard glm(...) function in R for Bernoulli regression, it appears that the residual deviance has the same value as the binomial deviance where each ...
- 11
1
vote
0
answers
85
views
Hierarchical partitioning for GAM model?
I am fitting a gam model with multiple environmental factors as predictors (actual evapotranspiration, climate water deficit, wind speed, etc).
My goal is to understand how each one of them contribute ...
- 31
3
votes
1
answer
448
views
Pearson chi squared test vs deviance test in GLM
From my understanding, both Pearson chi squared test and deviance test can be used to assess the goodness of fit for GLM, but they have different alternative hypotheses. For the Pearson chi-squared ...
- 363
0
votes
0
answers
42
views
Is Pearson's chi-squared appropriate for models with low deviance explained?
I'm working on fitting a binomial GLM using LASSO in R (package glmnet). My response variable is a proportion which is generated using count data (successes and failures). The main purpose of my model ...
- 37
3
votes
1
answer
195
views
Gam using mgcv is giving negative deviance explained
I run a null binomial generalized additive models (gam) using mgcv and it gives negative deviance explained!
As far as I know deviance explained is analogue of R^2 ...
user369390
4
votes
3
answers
2k
views
How to extract the residual and null deviances from a glmmTMB object (to calculate D2, the deviance explained)?
The context is about the use of a given model deviance (often referred to as “Residual deviance” in R) and that of its “Null deviance” to calculate D2, the deviance explained for models with non-...
- 181
4
votes
1
answer
938
views
Is unit deviance (statistics) equivalent to the loss function (machine learning)
In this page from scikit learn, about GLM, the notion of unit deviance is introduced as loss function (from the machine learning perspective).
I want to know if there is equivalence between these two ...
- 250
0
votes
1
answer
63
views
Testing the interaction of B:C on a glm using the analysis of deviance in R
A glm, where the response is Poisson distributed, is tested by using the analysis of deviance.
In R the model looks like this:
...
- 61
0
votes
0
answers
34
views
How to fit a nested glm model using deviance for selectio?
I have weight as response variable which is continuous variable. And 3 explanatory variables viz; Parity(Count), Age(continuous) and Sex(Factor).
I want to fit a glm model using deviances analysis to ...
- 21
0
votes
0
answers
344
views
Why are the deviance residuals in my binomial GLM all zeroes?
I am currently trying to run a binomial GLM to investigate the influence of temperature (factor: 5 levels 20, 23, 26, 29, 32 degrees Celsius) and species (factor: 2 levels HA and AP) on the likelihood ...
- 441
0
votes
1
answer
194
views
Null deviance vs deviance of null model
In GLM analysis, is the null deviance of a model the same thing as the deviance of a null model?
- 33
2
votes
1
answer
150
views
Discrepancy between model selection based on REML score vs explained deviance in GAMs
Will be grateful for insights into the issue below!
I have two explanatory GAMs below (in this example implemented with mgcv), where the effects of x1 and x2 are of interest. x1 is air temperature, x2 ...
- 361
1
vote
0
answers
29
views
Deviance vs Predictive Power of a variable in Logistic Regression
I have a question. I have a logistic regression model with two variables a & b. In the analysis of deviance table (type = 2) seems that variable b is more significant than a. But when I plot the ...
- 139
3
votes
1
answer
448
views
Understanding KL divergence in chapter 7 of Statistical Rethinking
I'm having a hard time understanding McElreath's explanation of how the KL divergence allows us to decide whether one of two models is closer to the 'real' model.
Here is what McElreath writes on p. ...
- 551
2
votes
1
answer
66
views
Intuition behind the null distribution of the deviance statistic in survival models
I am reading Tutz & Schmid "Modeling Discrete Time-to-Event Data" (2016) chapter 4 Evaluation and Model Choice section 4.2 Residuals and Goodness-of-Fit. A goodness-of-fit statistic ...
- 68.8k
4
votes
2
answers
356
views
Why null deviance is different from my manual calculations?
Let's consider this very simple example with Poisson regression:
...
- 203
3
votes
1
answer
125
views
F statistic for 3 nested models
Given models M1 and M2, the first with q parameters and the second with p>q parameters, and assuming that M1 is nested in M2, then we can test the hypothesis that the smaller model is adequate by ...
- 1,511
0
votes
0
answers
209
views
Deviance statistic vs Wald test
I have a question. I have run a logistic regression model with 5(X1,..., X5) continuous predictors. The predictor with the highest coefficient is X2, but the predictor that reduces the most deviance ...
- 139
0
votes
0
answers
138
views
H2O Deviance - Negative Binomial
I'm hoping to get some clarifications on the deviance calculation of negative binomial.
From H2O documentation, the deviance formula for negative binomial regression is expressed as:
$$D=2\sum_{i=1}^{...
- 1
2
votes
1
answer
360
views
In Poisson models with an offset, should performance metrics (such as deviance) be calculated in terms of raw counts or counts per exposure?
For context, I need some metrics that can compare a standard Poisson regression (with population offset) to a random forest regressor with Poisson criterion.
The test predictions for both methods are ...
- 143
3
votes
0
answers
1k
views
Is the F test in ANOVA a likelihood ratio or Wald's one?
I'm trying to figure out, if the F test in ANOVA is the Wald's test or LRT?
I learned, that the LRT compare nested models and "assess" the reduction in residual variance. This would justify ...
- 71
1
vote
1
answer
462
views
Discrepancy in degrees of freedom from R svyglm vs glm
I fitted a Poisson model using svyglm in R. The null and residual deviances from the svyglm model are as expected. For the degrees of freedom however, I get confusing results. With a sample size of n=...
- 11
1
vote
0
answers
123
views
How to compare the goodness of fit between linear and logit? Why linear deviance is less than logit?
How can I evaluate which model - between linear and logit - determine the best fit to the data?
The models use the same input variables and I thought that comparing the deviances was the proper choice ...
- 43
0
votes
0
answers
718
views
How to implement logistic regression deviance from scratch
As a learning exercise, I'm trying to implement the deviance for logistic regression from scratch.
I understand the deviance to be:
$\mathcal{L}_S - \mathcal{L}_M$, where $\mathcal{L}_s$ is equal to ...
0
votes
0
answers
105
views
Deviance of a larger model is much larger than the deviance of the reduced(nested) model
I am doing a logistic regression with 8 variables but for some reason the model with the second degree of interaction has a much larger deviance than the nested model without interaction. Because of ...
1
vote
0
answers
255
views
How is that possible that SAS and R can test for main and interaction effects for the GEE if it has no likelihood?
I was taught, that GEE, being not likelihood based, has no way to compare models. That we cannot assess the main and interaction effects the way we do with ordinary GLM, OLS, GLS, mixed models and so ...
- 91
5
votes
1
answer
1k
views
GLM tests involving deviance and likelihood ratios
I'm a little confused about the different common tests for GLMs.
There is the null deviance, which is similar to a likelihood ratio for the difference between the saturated model and the model with ...
- 555
5
votes
1
answer
404
views
Why is deviance $\neq -2\times$logLik for logistic regression in R?
Just tried to compute McFadden's $R^2$ from hand in R from a fitted logistic regression, but stumbled accross the problem that the reported deviance is not equal to -2 times the reported log-Liklihood:...
- 5,430
3
votes
2
answers
2k
views
Overfitting, but why is the training deviance dropping?
The test set values increase over iterations signaling overfitting, but why is the training set deviance continuing to drop at the same time? This seems to indicate to me that the training set is ...
- 47
1
vote
0
answers
70
views
Is deviance a relevant metric for non-linear (neural) model?
Is deviance a relevant metric for non-linear (e.g. neural network) models?
$$
D(y,\hat\mu)=2\left ( log((p(y|\hat\theta_{s})) - log(p(y|\hat\theta_{0})))) \right )
$$
For example, when we model ...
- 111
2
votes
0
answers
482
views
For Poisson GLMs, when does the residual deviance follow a chi square distribution?
According to Generalized Linear Models by McCullagh and Nelder (I am looking at the 2nd edition, 1999), the deviance function is defined as
$$D(y; \hat{\pi}) = 2[l(\tilde{\pi}; y)- l(\hat{\pi}; y)]$$
...
- 121
1
vote
0
answers
353
views
Interpretation of Multinomial Logistic Regression model fit in R
I have fitted a multinomial logistic regression model in R. The data has 35 independent variables and the dependent variable has 3 levels.
I do not find information on how to interpret the outcome of ...
- 21
2
votes
2
answers
5k
views
What is null hypothesis in the deviance goodness of fit test for a GLM model?
To test the goodness of fit of a GLM model, we use the Deviance goodness of fit test (to compare the model with the saturated model).
In many resource, they state that the null hypothesis is that &...
0
votes
0
answers
285
views
How the deviance residual of a GLM model is actually calculated
The deviance residual of a GLM model is defined to be:
$2 (log L_{Saturated Model} - log L_{GLM Model})$
where Saturated model is the model that has as many parameter as the number of data points.
As ...
1
vote
2
answers
560
views
Bit confused on the concept of Deviance
So, I understand what the deviance is; the deviance is simply the residual sum of squares. However, what I don't really get is the decomposition of the total sum of squares. That is $\sum_{i=1}^\infty ...
- 381
3
votes
1
answer
2k
views
How to calculate the percentage deviance explained wiith glm.nb?
I’ve observed that when I fit a Negative Binomial regression with glm.nb, the null deviance I get from the model differs from the deviance of the null model. I ...
- 31
0
votes
1
answer
144
views
Is the residual deviance / residual dof equivalent to reduced Chi^2?
Question:
I'm using a poisson fit; is the residual deviance = $ \chi^{2}$, and residual deviance / residual degrees of freedom = $\chi^{2}_{reduced}$?
Does this method provide a valid tool comparable ...
- 149