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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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Reference for Directional Statistics of Plane Orientation

I've got a project I'm working on where I've got the orientation (normal) vectors of planes. These vectors are all within a unit hemisphere where the $z$-coordinate is strictly positive. The ...
David G.'s user avatar
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0 answers
23 views

GLM dispersion based on Pearson residuals

In R's glm, the dispersion parameter can be automatically derived using a quasilikelihood model. When I manually compute it, the values are slightly different. The difference is very small and will ...
quibble's user avatar
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1 vote
0 answers
76 views

Estimating variance of a Gaussian distribution from the mean of absolute values of first differences in a sequential sample

Edited Question: This question is about estimating the variance (or $\text{SD}_0$) of a parent distribution from which a set of random independent samples is taken. The samples are taken in sequence ...
Maciej Tomczak's user avatar
0 votes
1 answer
35 views

Problems with a constant in regression analysis in Excel [duplicate]

I am using regression analysis in excel for a dataset. If I take into account the constant, then I get terrible r-squared values, but the indicators of t-statistics and p-values indicate that it is ...
Danil Molchanov's user avatar
0 votes
0 answers
36 views

GLM link function, variance Function, and dispersion for linear regression

we were recently introduced in class to GLM's and I am still trying to wrap my head around link functions, variance functions and dispersion paramters. In particular we were asked re-write the linear ...
Harry Lofi's user avatar
4 votes
1 answer
88 views

Unusual variance measure

I explore centrality measures for graphs and discretized regions. The data array (for given point) is all distances from this point to the boundary of region. At the beginning I used standard ...
lesobrod's user avatar
  • 253
2 votes
1 answer
137 views

Variance in set of different random variables

Imagine we have sample of values a_1, a_2,...a_n, with a_i value originating from a normal distribution with mean mu_i_a and variance var_i_a, thus each value is single realization of different random ...
GAMer's user avatar
  • 163
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0 answers
22 views

Distribution of the relative range ($R/\sigma$) [duplicate]

Let us assume a $n$-sized random sample $\{ X_1 , \dots, X_n \}$ from a random variable $X \sim N(\mu, \sigma)$. Let $X_\mathrm{min} = \mathrm{min}\{ X_1 , \dots, X_n \}$ $X_\mathrm{max} = \mathrm{...
Vicent's user avatar
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0 votes
0 answers
64 views

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 ...
Fiona's user avatar
  • 11
0 votes
0 answers
90 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. $n$ ...
Taylor Fang's user avatar
6 votes
1 answer
2k 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), ...
quibble's user avatar
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1 vote
1 answer
117 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, ...
user222456's user avatar
0 votes
0 answers
61 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 ...
Andrea Nerla's user avatar
5 votes
3 answers
118 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 ...
sruthipriya mahesh's user avatar
0 votes
1 answer
223 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 ...
dcoy's user avatar
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0 answers
72 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 ...
Chris's user avatar
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1 vote
1 answer
53 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 ... ...
user avatar
1 vote
1 answer
142 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 ...
AllDoe_1's user avatar
7 votes
1 answer
1k 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 ...
Kozolovska's user avatar
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0 votes
0 answers
55 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 ...
capewindow's user avatar
8 votes
1 answer
197 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 ...
J-J-J's user avatar
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10 votes
1 answer
554 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 ...
Galen's user avatar
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1 vote
1 answer
63 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
New Stats's user avatar
3 votes
1 answer
1k 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,...
Casey's user avatar
  • 33
2 votes
1 answer
447 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 ...
Giuseppe Biondi-Zoccai's user avatar
1 vote
1 answer
1k 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 ...
vegetabletina's user avatar
0 votes
1 answer
101 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 ...
norivotset's user avatar
3 votes
0 answers
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, ...
Rex Parsons's user avatar
0 votes
0 answers
85 views

Correlation frequencies with two different groups?

Have a dataset similar to this: ...
user326789's user avatar
0 votes
1 answer
593 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 ...
C.K.'s user avatar
  • 131
6 votes
1 answer
7k 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. ...
userpisquared's user avatar
0 votes
0 answers
235 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 ...
joshisanonymous's user avatar
1 vote
1 answer
304 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 ...
Fabio Carbone's user avatar
0 votes
1 answer
130 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 ...
Epideme's user avatar
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12 votes
0 answers
3k 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 ...
eab's user avatar
  • 121
2 votes
0 answers
789 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 ...
mon's user avatar
  • 1,548
0 votes
0 answers
32 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 ...
tcvdb1992's user avatar
  • 139
1 vote
0 answers
81 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 ...
user257053's user avatar
0 votes
0 answers
495 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....
Lochend's user avatar
  • 51
1 vote
1 answer
117 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 ...
spalan's user avatar
  • 13
3 votes
1 answer
563 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 ...
Sparsity's user avatar
  • 584
0 votes
1 answer
3k 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 ...
SvC's user avatar
  • 1
0 votes
1 answer
126 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?
user avatar
1 vote
1 answer
36 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 ...
carak's user avatar
  • 13
0 votes
0 answers
104 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 ...
SportcastJon's user avatar
1 vote
1 answer
214 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 ...
Alex Romer's user avatar
0 votes
0 answers
68 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 ...
Coder's user avatar
  • 23
2 votes
2 answers
105 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. ...
zkldi's user avatar
  • 21
0 votes
1 answer
503 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 ...
amd1972's user avatar
4 votes
2 answers
111 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 ...
ExcitedSnail's user avatar
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