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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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Correlation coefficients, many realizations [on hold]

I'm doing an experiment to see the level of correlation between two variables $x$ and $y$. I simulated under the same conditions the set of data $x$ and $y$, and repeat it many times. After each ...
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0answers
35 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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0answers
10 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
33 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
101 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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0answers
19 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
46 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
35 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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43 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
33 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
35 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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0answers
8 views

Should I use weights in calculating the Coefficient of Variation for transformed proportions?

I have percentages of people having an event for 21 regions. Since I want to calculate a Coefficient of Variation, I took the arcsine of the proportions to normalize data. The problem is: every region ...
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1answer
233 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
289 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
51 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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0answers
9 views

dispersion of a sample where each item has its own error

I have a question relating the calculation of dispersion of a sample. A standard deviation is typically used, however in my situation each element in the sample has its own error prescribed (i.e. each ...
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0answers
18 views

Indicator of disproportion [closed]

What is the best way to report about dispersion of paramater? For example in situations where you know true values of parameter, but you also know that mean value is not very good representative of ...
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1answer
74 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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0answers
93 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
140 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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0answers
56 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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0answers
136 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
332 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
349 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
332 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
445 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
427 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
500 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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0answers
103 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
165 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
158 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
4k 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
215 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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0answers
63 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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0answers
93 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
51 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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0answers
275 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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0answers
82 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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0answers
59 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
581 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
577 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 ...
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1answer
145 views

Measures of clustering vs dispersal

I'm looking for metrics of the degree of grouping/clustering of spatial data. I'm not looking to formally cluster the data i.e. classify points within groupings. But rather an index such as from 0 for ...
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0answers
30 views

Is standard deviation always larger than mean deviation? [duplicate]

If yes why is it the case that it have this property? There must be some mathematical proof or intuitive understanding in that case.
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1answer
297 views

Why don't dispersions like median deviation and mode deviation exists on the lines of mean deviation?

Or to say in the formula MD=$\frac{1}{N}\sum_{i=1}^{N}|x_i-\overline{x}|$ why can't we have median or mode instead of mean($\overline{x}$) and as a result speak about additional possible measures of ...
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1answer
580 views

Is mean deviation the same as mean absolute difference?

Do both terms mean the same thing or are they different?
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1answer
262 views

Can variation ratio ever be 0?

I think that it can't since whenever we have data then we have mode and since we have mode it's frequency is at least 1. Therefore, variation ratio can't ever be 0. What do you think?
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1answer
1k views

Index of Dispersion - How to test its significance?

Starting from Poisson distribution and cluster analysis I am trying to find a statistical/empirical method in order to test if my Index of Dispersion (https://en.wikipedia.org/wiki/...
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1answer
110 views

Why iterative estimation of dispersion in negative binomial glm

If we do a negative binomial GLM with unknown deviance, a frequent strategy (used for example by glm.nb in package MASS in R) is ...
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1answer
100 views

Appropriate measure of dispersion for q-gaussian distribution data

I have financial data (prices) which are believed to be q-Gaussian. I want to measure the dispersion for fixed periods in the dataset. Which tool is better, the mean absolute deviation, the ...
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2answers
266 views

Testing for differences in distributions (medians AND dispersion) between groups with a Likert scale question

I am interested in testing for significant differences with a Likert scale question between three groups. There are plenty of questions about comparing medians here, but I am interested in differences ...