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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16 views

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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1answer
29 views

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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35 views

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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22 views

DIspersion Parameter of Generalized Poisson Distribution [closed]

Could someone please explain how the dispersion parameter in a generalized Poisson distribution is calculated? I'm currently trying to write an EM algorithm for a zero-inflated generalized mixed ...
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32 views

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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28 views

What are the different ways to measure dispersion in a binary data?

I am working on a research project which requires finding dispersion from a bunch of 0/1 (binary numbers). The idea is to get several different measures and see whether different measures pick up ...
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15 views

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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53 views

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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1answer
58 views

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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6 views

Dispersion index and Cosine distance

I have different sets of vectors of dimension n and I want to measure and compare the dispersion index of each set. For my specific problem, each set contains vector representations of words (...
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1answer
48 views

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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9 views

Descriptive statistics for complementary random variables

I have two datasets, each one contains 157 images of microscopic field processed with a different preparation tecnique. My task is to show if there any differences like cells density, distribution and ...
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1answer
54 views

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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185 views

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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14 views

the importance of estimating correctly the dispersion parameter in hypothesis testing

I am reading an article, which is related to negative binomial model in estimating the dispersion parameter. https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0081415 The author ...
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1answer
128 views

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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2answers
549 views

Choosing the optimal theta / dispersion parameter for negative binomial regression (glm / glm.nb) in R

I am applying a negative binomial regression to my data in R. For this, I use the package MASS and have two different ways to calculate it: ...
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27 views

How to define a measure of dispersion of a group of points in a given area?

I'm working in a simple exercise in my current trining to data analyst. I need to define a measure (indicator) of how good or bad its an area according with two variables. The first variable is the ...
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1answer
234 views

Negative Binomial Regression: Offset Variable and Dispersion Parameter

My case is that previously it's assumed that the counts of events follows a negative binomial distribution, and the annualized exacerbation rate is 1 with a dispersion parameter of 1.5, and all 500 ...
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1answer
49 views

Measure of dispersion around the mode

I usually associate the standard deviation with the mean and the IQR with the median. Is there a measure of dispersion typically associated with the mode?
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54 views

Which measure dispersion would one use to evaluate ratio conservation?

I am wondering which would be the most appropriate dispersion measurement in the following situation: In my experiment I am measuring two proprieties of multiple objects (e.g. height and weight) in ...
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1answer
61 views

Pros and cons of using a median version for measuring dispersion?

If a data set is in the presence of some outliers, then the sample average could not be a "fair" measure of the centrality of that data set. Instead, the sample median could be a better choice. ...
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1answer
38 views

Uncertainty of the dispersion parameter

I am trying to retrace the steps that Gary King and colleagues suggest in their article "Making the most of statistical analyses: Improving interpretation and presentation" to calculate quantities of ...
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1answer
566 views

How to measure diversity (dispersion) of a categorical variable?

I have unemployment rates for 3 regions (North, Center, South). The unemployment rate is defined by (number of unemployed ($u$)/ active population ($pa$)). The unemployment rate by region ($r$) is $\...
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1answer
840 views

What are the differences of Standard Deviation, Variance, Co-variance, Coefficient of Variation when it comes to measures of dispersion or variation?

When we talk about measures of dispersion or variation(not sure if they are 2 different tools), then for what purpose we use what exactly? Where are we bound to use only Standard Deviation, not ...
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1answer
154 views

How to measure the spatial dipresion of multiple clustered data

Context: My data are binary maps that represent the spatial distribution of events. Whenever an event occurs at a location, the pixel representing that location is assigned with the value 1. Below are ...
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1answer
103 views

Interpreting dispersion for Inverse Gaussian GAM (log linked)

After reading Wood (2006), Zuur et al. (2009) and all questions related to GAMs here, I still haven't found the following: Should I calculate the dispersion for an ...
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137 views

Name of the test for over/under dispersion

When testing for over or underdispersion in a count variable there is a test (available for example in the glm.nb() function in the ...
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1answer
205 views

Dispersion value with glmmTMB versus mgcv::gam()

Assume we parametrize the variance in a negative binomial regression model as: variance = mu(1+mu/theta). Fitting the model with glmmTMB, I check theta from: <...
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84 views

Has the Weibull distribution got pseudovariance?

I have a scholar question about the Weibull distribution, which can be parameterised, among other options, like follow: $f(t)= \lambda \alpha t^{\alpha-1}{exp} \left \{ \lambda t^\alpha \right \}$ ...
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216 views

Bimodal distribution dispersion

what is the correct way to study the variability of a data set when all the observations are distributed like a bimodal distribution? For instance, here I identified the two modes as central index. ...
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5answers
548 views

How to measure dispersion in word frequency data?

How can I quantify the amount of dispersion in a vector of word counts? I'm looking for a statistic that will be high for document A, because it contains many different words that occur infrequently, ...
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1answer
674 views

Evaluating dispersion parameter and goodness of fit for binomial regression in r

First, I have looked at other posts but none address this specific question. I am trying to evaluate goodness of fit for a negative binomial regression, and what the dispersion parameter indicates in ...
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1answer
503 views

What is the best way of measuring the dispersion or concentration of categorical data?

Let me provide some background. I am writing a paper on the effectiveness of specialist vs. generalist software companies. I have data on the number of products of theirs that are being used across ...
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1answer
606 views

How does dispersion parameter affects results of gamma glm

I ran a log-linked gamma glm and noticed that the estimated coefficients and AIC did not change when I update the model with a dispersion parameter. However, I did noticed that the standard error of ...
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1answer
839 views

Why do we need coefficient of mean deviation?

Mean deviation can give us a sense of how much data is dispersed from one of the average measurements (mean,mode,median). Mean deviation depends on the difference between the data and the average ...
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1answer
648 views

Dispersion parameter in mass and PSCL package (zero-inflated negative binomial and negative binomial)

I have run Zero inflated negative binomial and negative binomial model with same data set in R. I get log(theta)= -2.47 for Zero inflated negative binomial and log(theta)= -5.149 for negative binomial ...
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142 views

Estimating dispersion parameters in GLMs

I've been working on implementing a glm library in python for my students to use (for various reasons, the existing implementations are not sufficient). My reference for the material is Marlene ...
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1answer
354 views

Clustering: measure of dispersion based on distances

I am having a set of strings, they have been alligned and I have a matrix of pairwise distances. Now the objects have to be clustered yet I do not know the number of clusters beforehand. I would like ...
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3answers
210 views

Which measure of dispersion is this function related to?

Consider a sample $x=\{x_1,...,x_n\}$. Define the average as $\bar x$. Consider the following formula: $$ \dfrac{\sum_{i=1}^n\left(\dfrac{x_i}{\bar x} \right)^c}{n} $$ or equivalently: $$ \dfrac{\...
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1answer
6k views

Why would someone plot variance normalized by the mean?

I'm reading a scientific paper where they plot the variance of particle intensity normalized by the mean of particle intensity. I'm a bit confused and don't have an intuition for how this should be ...
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1answer
351 views

Statistical test of dispersion difference with experimental treatment

The question: Is there an appropriate statistical test of a change in dispersion across a large number of variables as a result of experimental manipulation? Background: A manipulation has been made ...
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68 views

Is it valid to average IQR values?

I am interested in quantifying the dispersion of pixel values in one image. More specifically, I want to get an average value of dispersion of the image column-wise (i.e., compute the dispersion of ...
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117 views

Intuition behind Besel's correction for an unbiased estimate of the variance [duplicate]

We have two estimators for samples dispersion: $\frac{1}{n}\sum_1^n (X_i - \overline{X_n})^2$ and $\frac{1}{n - 1}\sum_1^n (X_i - \overline{X_n})^2$. The second estimator unbiased - it has ...
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1answer
55 views

Finding measure of dispersion

Given a data set as follows: $$\begin{array}{crrrrrrrr} Classes: & Less\:than\:20 & 20-30 & 30-40 & 40-50 & 50-60 \\ frequency: & 30 & 20 & 15 & 10 & 5 \...
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325 views

interpret dispersion parameter in gamma GLM

On p. 383, Fox writes that "[with a gamma GLM] the dispersion parameter is simply the inverse of the shape parameter." I am trying to understand for what distribution this applies to. Using an ...
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100 views

Estimating burstiness in a time series: Dependence on overall frequency?

I have a dataset of time series normalized for length. A working R example below. I am trying to estimate burstiness within the series, i.e. to compare series in the degree of clusteredness in these ...
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61 views

Fitting a GLM – whether to estimate mean or dispersion first

I'm trying to understand how fitting GLMs works. I asked before on math.SE but this community is probably more appropriate. My confusion is the following: The MLE for $\hat\mu$ uses $\phi$. My books ...
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1answer
809 views

Standard deviation non centered (normal) data

I'd like to get a prediction interval (or a good measure of dispersion) of my data but it seems like standard deviation is not the right way to do it because my data is not centered (or not normally ...
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2answers
790 views

What do the terms dispersion parameter - deviance - and variance of $y_i$ mean?

I am studying GLMs and I am struggling a bit with some of the concepts. I think mine is more of a theoretical issue. Basically I am a bit confused by the meaning of these three concepts: the variance ...