# Questions tagged [dispersion]

This tag is very ambiguous. Dispersion is a general term for how spread apart values are. For questions related to disease dissemination content, use the tag epidemiology. For other meanings of dispersion consider using a related tag or creating a new one.

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### Gamma GLM goodness-of-fit diagnostics and remedies for double glm

I’m looking for some help in diagnosing a gamma GLM. I am not sure whether the apparently poor fit is to do with the fact that my glm models dispersion rather than the mean, whether I am ...
80 views

### Testing zero-inflated negative binomial models using Anova function

I used the glmmTMB package to fit zero-inflated GLMMs with negative binomial error distributions (example below): ...
38 views

### How do I measure the "dispersions" of a group of time series

I have a group of time series $X_1, X_2, ... X_n$. I want to measure how much they have "dispersed" over time. i.e. are they moving "more together" in 2023, comparing to 2022. $n$ ...
341 views

### dispersion parameter in Poisson models

When using a Poisson GLM, its dispersion parameter can be estimated as "residual deviance/degrees of freedom". But when analyzing Poisson data with a Poisson model (i.e., not overdispersed), ...
34 views

### pros and cons of different robust measures of scale/ dispersion

I would very much appreciate some help regarding how to interpret different robust measures of scale (Inter-quartile range or IQR, biweight midvariance, and median absolute deviation or MAD). Thus, ...
54 views

### How to find the relative dispersion of a list of numbers over a number in it?

In the game of chess a white advantage is defined as a positive number, a black advantage is a negative number, an equal position is 0. A chess engine displays a list of the n best variations of a ...
29 views

### what do we mean by range in descriptive statistics?

The definition of the range has been given as the difference between the largest and the smallest value of the distribution. This, in my perception, tells us the discrepancy between the smallest and ...
70 views

### Best way for measuring dispersion in two dimensional, continuous data

I have a list of coordinates for where different people live over an eight-year period. They are repeat cross-sections of populations served by several county agencies for free workforce training for ...
58 views

### In getting to the standard deviation, why do we square d.f.?

this question is similar to another on this platform, but that one adresses the general question of rooting the variance, while this question is about rooting d.f. - furthermore, that question has an ...
47 views

### Are negative t-values important for pairwise betadisper results?

I am running the betadisper() function from the vegan package for an analysis of multivariate homogeneity of group dispersions. ...
40 views

### Converting dispersion to standard deviation in a beta regression

I'm unsure about the relationship between dispersion estimates (precision^-1) from beta regression models (log link) and the standard deviation. The left panel is from a glmmTMB model ... ... 19 views

### Does beta logit model assume dispersion like Poisson or in Binomial model?

I would like to know what are the assumptions of a beta logit model and more particularly does it assume certain dispersion. In other words, does one speak about over and under dispersion for beta ...
162 views

### How to handle triangle-shaped scatterplot of data?

Over the past year, I have tried to record my productivity in the following way: The first yellow mark is the time I "clock in", or start working for the day. For the five minutes of work ...
1 vote
98 views

### Absolute deviation from the mean using logarithms

I am calculating the absolute deviation from the mean of a strictly positive set $\{x_1, x_2, \ldots, x_n\}$ like: $$\left| x_i - \bar X\right|$$ My analysis makes it appropriate to work in logs ...
732 views

### Tweedie Dispersion Parameter Estimation Methods

In the book Generalized Linear Models with Examples in R - Dunn and Smyth, in Chapter 6.8, it is recommended to use the Pearson estimator of the dispersion - "This makes the Pearson estimator the ...
31 views

### General Closed Form and dispersion parameter of the Expected Maximum of i.i.d Gumbel Variables

I would like to know the general closed form of the expected maximum of i.i.d Gumbel variables. I found this onlie: Expectation of the Maximum of iid Gumbel Variables In the linked page, it shows the ...
171 views

### Why does log-linear analysis seem to ignore the Poisson regression equidispersion assumption?

As far as I understand it, log-linear analysis is based on the use of a Poisson regression. This is what I understood from various online resources, like this online tutorial or this text whose intro ...
433 views

### Median of the squared difference from the median of a Cauchy random variable

Motivation One of the classic challenges with Cauchy random variables is that their moments are not finite, and I even recently learned that Cauchy principal values of even moments of Cauchy random ...
1 vote
38 views

### How to find coefficient of variation [closed]

Suppose 2x−3y= 5 is the relation between the variables x and y .If the variance of x be 1.44 and y has mean 1, then calculate the coefficient of variation of x
690 views

### How to correct underdispersion in logistic regression

I created a logistic regression model with four continuous variables and a binary outcome. I divided the residual deviance by the residual degrees of freedom, which equaled 0.63. From my understanding,...
286 views

### A measure of variability/dispersion that captures only one direction of change

I am conducting a study trying to correlate changes in a biologic parameter (e.g., blood bilirubin concentration) with clinical outcomes (e.g., bleeding). I have found that variability in such ...
1 vote
831 views

### What is the dispersion parameter of binomial distribution?

Binomial distribution is a member of exponential dispersion models, but I can not find the dispersion parameter of it. Could anyone help me find it out? IMO the Binomial distribution only has an ...
81 views

### How to measure if a point of data is a deviation from other data points?

I have a data set that consists of many single data points. They are the measurements of network traffic, so they include e.g. '1403021', '1402341, '1399312'... values that are labeled as 'label1' and ...
76 views

### How to interpret a n-related change in coverage for model (simulation study)

I have repeated measures data from n_subjects where each has n_obs number of measurements before and after some intervention, ...
76 views

### Correlation frequencies with two different groups?

Have a dataset similar to this: ...
392 views

### How to compare the degree of dispersion of different distributions?

I don't know if it is a good question or a well-defined question, but I really need some suggestions! Any suggestion is valuable for me! Very much thanks! The question is: There are many attributions ...
5k views

### How does R find the dispersion parameter in a GLM?

I'm working on a problem involving fitting a GLM to data and I'm curious about how R calculates the dispersion parameter. For example, I have this output for the summary of my GLM. ...
164 views

### Significance test for the difference in Simpson's Diversity Index values?

I've taken several samples of categorical data and calculated the spread of each using Simpson's Diversity Index. I would now like to perform a significance test to see if these spreads are similar or ...
1 vote
285 views

### Comparing means and medians (with different dispersion indeces) from different studies [closed]

I'm doing a systematic search and I have a pool of articles that for each outcome report different central values (mean and median) and dispersion indices (SD, 95% CI, IQR). Is there a statistical ...
106 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 ...
2k views

### Varying dispersion parameter (=dispformula) in glmmTMB in R to account for heteroscedasticity that originates from one predictor

I struggle with understanding the dispersion model and dispersion parameter of glmmTMB , and could not find answers anywhere. I constructed a GLMM using ...
577 views

### Explanation on why SD is better than MD [duplicate]

Trying to understand why Standard Deviation (SD) is widely accepted as a measure of dispersion instead of Mean Deviation (MD) $\frac {1}{N}\sum|X-\mu|$. Revisiting a 90-year-old debate: the advantages ...
31 views

### Measuring variability in blood pressure in a repeated measures design with different time intervals between study visits

I have repeated measures on blood pressure for a lot of patients, measured at different intervals (table below). I want my standard deviation to reflect that a large deviation in blood pressure ...
1 vote
75 views

### PERMANOVA: removing dominant species to avoid dispersion effect

Dear StackExchange community, I have an ecological dataset that contains several species from different sample sites. One species is extremly abundant that contributes 80 - 90 % to the entire ...
391 views

### Continuous (not categorical) measures of diversity?

Which measures of diversity are used where? When I search for diversity indicators I find the Simpson and Shannon index, but these are both for categorical data. If I have data with some structure (e....
1 vote
103 views

### Testing for difference in distributions of Likert-scale data that differs only in a median-preserving spread

Assume that I have a Likert scale with five categories, coded as {1, 2, 3, 4, 5} and that I have two samples, the first of which is generated by drawing from a uniform distribution over these five ...
431 views

### When is the dispersion parameter estimated in a GLM?

I'm looking at some notes online and I can see that in the example given, the dispersion parameter is estimated when we have a Gaussian model, but not when we use a Poisson model. Why is this? Is ...
2k views

### Significant dispersion test

I used DHARMa for my residual diagnostics. For two models, the dispersion test is significant even though the rest of the diagnostic output looks good. I am wondering if both my models are correct ...
122 views

### Which is the right measure of dispersion to be used as a proxy for risk for a fat tail distribution?

Which is the right measure of dispersion to be used as a proxy for risk for a fat tail distribution ? Standard Deviation, Mean deviation, Value at risk, what else? 1 vote
35 views

### Finding the distribution of [F; X]

I need to find the distribution of \begin{bmatrix}F\\X\end{bmatrix} where = (F1, F2, X1, X2, X3)^T This is the solution to the problem: I don't really understand the part of $D([F; X])$. Why there ...
93 views

### Is it possible to perform negative binomial regression with known theta?

Is it possible to perform negative binomial regression (in python, R) where you can supply a known value of theta? Say I want to compare different negative binomial regression models, the changing ...
1 vote
198 views

### Test homogeneity of multivariate dispersion with regard to the Modified Raup-Crick Metric

Please find a citation for the modified Raup-Crick Metric below Modified Raup-Crick Metric (Chase et al. 2011 As an extremely brief review, this metric generates a dissimilarity matrix containing ...
49 views

### burstiness in time data

So i have time of arrival data like this: time of arrival = [1,1.5,1.6,1.7,1.8,3,4,6, 8, 9, 10] we can see that there is a burst between 1.5s and 1.8s. i have already tried to create a plot of ...
98 views

### Measuring "regularity" of musical timing

Apologies if the term regularity is improper, I cannot find what the actual term I am looking for is. I'm looking for a method for calculating how "regular" rhythms are for musical notes. ...
444 views

### Measures of spatial dispersion

I have a series of data points in R^3. I am considering different measures of the spatial dispersion of these points. I have noticed something interesting. I have considered two different measures ...
102 views

### Vector-valued estimators, intuitively why $var(\widetilde{\beta})-var(\widehat{\beta})$ being p.s.d. means $\widehat{\beta}$ more efficient?

For two scalar unbiased estimators $\widehat{\alpha}$ and $\widetilde{\alpha}$, we know that if one has smaller variance, then we say it is more efficient, which intuitively means that this estimator ...
1 vote
214 views

### Why do we need F test of two variances if we have the Ansari-Bradley test?

I just read that the Ansari-Bradley test is a test of stochastic equality of two variances regardless of any distributional assumptions. If it is so flexible, why do we even need the F test? I am ...
1 vote
36 views

### Check which parameter causes less dispersion in a sample set - When to use CV (Coefficient of Variation) or CD (Coefficient of Dispersion) etc

The overall goal is to extract/engineer features from approximately 100 segments (various lengths but always more than 80 data points) that are as similar as possible to each other and have a very low ...