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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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 ...
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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 ...
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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 ...
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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
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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,...
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Is overdispersion possible in binomial logistic regression model that is not subsettable?

I’m creating a binomial logistic regression model with two variables: average tree height within a survey site and tree density within that same site. For each site, I only have one measurement for ...
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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 ...
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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 ...
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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 ...
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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, ...
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How to get variance-covariance matrix for dispersion part of hglm model

I'm wanting to fit a 2-phase model to assess whether there is a change in within subject variance due to experimental group in this pre-post study design. Therefore, I am interested in the interaction ...
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How to deal with dispersion and Zeroninflation in GLMM binomial models?

I am working with a GLMM (binomial family). I test my model for dispersion and ZeroInflation with the DHARMa package. Here is my code to show what I test : ...
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Correlation frequencies with two different groups?

Have a dataset similar to this: ...
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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 ...
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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. ...
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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 ...
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Comparing means and medians (with different dispersion indeces) from different studies

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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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....
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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 ...
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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 ...
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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 ...
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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?
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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 ...
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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 ...
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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 ...
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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 ...
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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. ...
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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 ...
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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 ...
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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 ...
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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 ...
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2 votes
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Mean and variance and special distribution of events

A hospital Accident and Emergency (A&E) department receives an average of 6 ambulances an hour. It can process patients in 30 minutes, but if it receives more than five patients in 30 minutes, ...
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Concept of a z-score for a gamma distribution

This is a somewhat general question. For the normal distribution we have the handy concept of the z-score that can be used to measure distance from the mean in a standardized way. I've encountered a ...
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Negative Binomial GLM confusing effect on p value of model by changing theta

I am interested in generating a p-value for two small groups of count based data that I believe to show overdispersion. The groups are for example: ...
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Metric for dispersion that corrects for sample size

I'm looking for a metric to measure dispersion of a set of points in 2D (or higher dimension) space. This post gives some examples, such as the sample mean of all points to be the center point and ...
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GLM Tweedie dispersion parameter

I am running a tweedie regression and I need to get the dispersion parameter(phi). Here a simple R code: ...
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Is "dispersion" a parameter in Gaussian glm?

Let do a simple glm in R: > y=rnorm(100) > gnul <- glm(y ~ 1) > gnul$coefficients (Intercept) 0.1399966 However, of course, as the distribution is ...
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Looking at two PDF plots, is it possible to guess which distribution has a greater Gini coefficient?

By observing the PDF of two different distributions over the same support (as in the image), is it possible to infer which PDF describes the distribution with the greater Gini coefficient? I assume ...
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Test or measure for "stability" of dispersion in many samples

I'm looking for a way to quantify if a variable has a "stable" dispersion over many samples. More precisely, I have approximately 1000 subjects, each with 50 observations of the variable. The mean ...
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High-dimensional dispersion statistic

I'm looking for a metric of dispersion for data in a high dimensional space (say, 70 or so components). The idea is that my data has several groups that I suspect are similar within some or many of ...
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Variance (maybe?) of categorical data

I don't really know the correct terminology to ask this question well. I have categorical data with counts and I want a measure of how "diverse" or "spread out" the data is. Variance comes to mind, ...
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Definition of exponential family with dispersion parameter

I was recently reading a discussion of generalized linear models that considered the response to come from an exponential family with a dispersion parameter so $$ f(y|\theta,\phi) = \exp\left(\frac{y\...
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Is the Coefficient of Variation valid for data which does not follow a normal distribution?

I am trying to compare the dispersion of several data vectors. As an example I have that via two methods produces one vector of data that fits a normal distribution and other one that follows an ...
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3 votes
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The use of the quantile regression

I would like your help regarding the quantile regression. I was wondering if it makes sense to use the quantile regression when the relation of the number of data between variable x and y is 1 to 1, ...
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Transfering the approach of GLM/GLM.NB to FEGLM in R to find the best dispersion parameter

I would like to analyze my dataset with around 1 million observations and 10 thousand fixed effects with a negative binomial regression model. Due to the high number of fixed effects I cannot apply '...
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