Questions tagged [heteroscedasticity]

Non-constant variance along some continuum in a random process.

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Distribution of true value when measurement imprecision is non-constant

What I believe to have understood so far (I am not a mathematician or a statistician, so please correct me if I'm wrong.) Say we are making measurements of some phenomenon $X$, and we have a normally ...
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Bayes Factor for two groups comparison with unequal variances from bayes.t.test in bolstad R package [closed]

After asking for a bayesian version of Welch test in a stackoverflow previous thread: https://stackoverflow.com/questions/72171331/bayes-factor-for-two-groups-comparison-with-unequal-variances-is-...
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Scale location plot interpretation

I ran a regular OLS regression and wanted to check if the assumptions for OLS regression was meet. To do this I plotted a scale location plot, but I'm struggeling with the interpretation of the result....
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Kruskal-Wallis test on data with heterogeneous variance and small sample sizes per group

I've been trying to figure out how to test (in R) if there are significant differences between the group means of my data because it seems to violate the assumptions of tests that do this (ANOVA, ...
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Covariance matrix of errors for homoskedasticity/heteroskedasticity

I've seen homoskedasticty and heteroskedasticity defined as the following The error term of our regression model is homoskedastic if the variance of the conditional distribution of $u_{i}$ given $X_{...
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Extreme Heteroskedasticity - Multiplicative Model - Strange residuals

I absolutely need your help with my research. When I checked for heteroskedasticity I obtained a weird result from the white test (p value = 0). When I plot the residuals, these are the results: ...
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Why is there heteroskedasticity even though no relationship seems present in the residual plot?

I estimated a random effects panel model and performed the Breusch-Pagan (BP) test for heteroskedasticity. The test is significant, meaning that there is heteroskedasticity. However, the residual plot ...
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How to build a regression equation for a gamma GzLM and how to interpret it?

I am trying to analyze if referral programs (1/0) have an impact on the average monthly spending of a user. I am confident that the gamma GzLM is the best model for my distribution: According to ...
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How to optimize transform function to make the variance and mode of the variance roughly stable?

$ curl -s https://i.stack.imgur.com/rl1eT.gif | tail -c +43 | zcat x y x2 2030667 x2 2343967 ... I have data like the above. If you compute the mean and ...
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Heteroskedasticity in OLS which best: clustered SE or robust SE?

I am trying to estimate the effect of a change in minimum wage regulation with no control group. I computed a propensity score for the probability of being affected by the change in MW before the new ...
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homoscedasticity violated or not?

I was wondering if the homoscedasticity in these two figures has been violated or not? Best regards, Elise
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Have my assumptions been met?

I am running assumptions for multiple regression and scatterplots are a real bane of mine. Can anyone advise as to whether the following scatterplot provides a linear or non linear relationship ...
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Do I need to transform/standardise my dependent variable?

Attached are the results and the residual plot for my regression of control variables on CEO compensation (TDC1). When I look at the plot my main concerns are the outliers (which I checked to be ...
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Parametric bootstrap *prediction* interval with heteroskedasticity and sandwich parameter covariance matrix

The sandwich estimator for OLS regressions where heteroskedasticity is suspected is $$ var(\hat\beta) = (X'X)^{-1}X'ee'X(X'X)^{-1} $$ If I want confidence intervals on predictions, I can just take ...
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Calculating fixed effects in a mixed model with non-normality and heteroscedasticity with a 3-level time variable?

Due to non-normality and heteroscedasdicity, I use robustlmm and not lme4 for my mixed effects model. The variables look like this: ID: subject variable (random factor) var1: categorical between ...
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Is homoscedasticity an assumption for Pearson's correlation?

I'm running correlation analysis in SPSS between my variables and I'm starting by checking the assumptions to run Pearson's correlation (r). I'm confused as to whether or not homoscedasticity is one ...
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How can i check homoscedasticity for Level-2(between)-residuals in a twolevel model?

i have specified a random intercepts and slopes model with a Level 2-predictor for the intercepts on the between level. I have done the estimation with the lme4 package in R. Now, i want to plot the ...
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Heteroskedacity and non-normality - What to do?

I conducted an experiment in which I am trying to model the relationship between my response weed_coverage [%] and the predictors soil moisture [%] + treatment + distance. Weed_coverage and ...
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How to tell if there is a homoscedasticity of the model based on this plot?

I am building regression model of cholesterol predicted by 4 dietary components. I want to check if the assumption of Homoscedasticity is satisfied. I plotted Residuals vs Laverage plot. ...
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Heteroscedasticity in palaeolimnology with GAMs

I'm trying to understand heteroscedasticity and the influence this may have on GAMs fitted to palaeo data (or other time series). My understanding of heteroscedasticity is as follows (please correct ...
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Linear Regression of non-normally distributed data [duplicate]

I am trying to understand the relationship between royalties received (independent variable) and health expenditures (dependent variable) for each municipality through a linear regression. My ...
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Using WLS vs making the residuals homoscedastic to fit OLS regression

I'm convinced that homoscedasticity (of errors) is not an assumption (at least not explicit) for OLS regression. Also, even though WLS is advocated for heteroscedastic errors, OLS is not particularly ...
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Heteroskedasticity for i.i.d. variable

I got an assignment to solve, which states the following: Consider the model with heteroskedasticity: $$ Y_i = X_i'\beta + \epsilon_i $$ where $\epsilon_i$ is explicitly assumed as i.i.d. with $$ \...
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Should heteroscedasticity of "residuals" frighten?

I have a dataset with 10 variables. A couple of them are "Customers" and "Sales". I want to find what is the increase in sales with a unit increase in customers. That is, I want to ...
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Comparability of variance estimation of residuals of WLS solutions

I have a linear regression model with $p$ parameters $$ y = X \beta + \varepsilon $$ and multiple datasets for the same model $y_i \in \mathbb{R}^N$ with known weights for each data point $w_i \in \...
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Does this plot show heteroscedasticity?

I am running a multiple regression with a continuous DV and a mix of dichotomous and continuous IVs (but mostly dichotomous). This is the ZRESID vs ZPRED scatterplot, and I think there is ...
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How to prove equality of standard errors for two-sample t-test and linear regression?

Using classical linear model assumptions, we know that $$\frac{\hat \beta_j - \beta_j}{se(\hat \beta_j)} \sim t_{n-k-1}$$ meaning that the ratio of regression coefficients to their standard error ...
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Simple question about usage of the Breusch-Pagan test

Currently I understand the Breusch-Pagan test as the following test (for simplicity, below in the auxiliary regression the same explanatory variables are taken as in the main regression model). The ...
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How is my data stationary?

I did a quick Dickey-Fuller test, to test whether my time series is stationary, and the result gives a P value of 9.6*10^-15, or in other words stationary. How is this possible, my data clearly doesn'...
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Tried rectifying Heteroscedasticity and I don't know why I did not succeed

I am doing a regression on the influence on interest rates on marketing spending. I tried many different approaches to get my regression working. I have panel data and time series. I got a data set of ...
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Would this data be considered stationary?

Would this data set be considered stationary or are there too many anomalies around 60-120. If no, would I ignore the anomalies or would I attempt differencing to turn it stationary?
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Testing regression for Heteroscedasticity with different results (white test, Breusch_Pagan and gvlma)

The main question is do I have now heteroscedasticity and if so how can I fix it if the boxCox transformation was not effective? I testet for Heteroscedatiscity in my regression. For this I used ...
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Mitigating seasonality and conditional heteroskedasticity

I came across this question online that's from a math/stat challenge a while back. Would love to get some thoughts on what the correct answer should be: You're trying to assess transit usage trends in ...
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Equal Variance vs. unequal Variance for comparing Groups

I am a little bit confused about equal and unequal variances. I understand the definition and mathematics behind it, yet I don't know, for the purpose of my research, how to appropriately test that. ...
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Trying to use the white test in r

I am doing a regression on the influence on marketing spending. I have already tested for heteroskedasticity with the Breusch-Pagan Test and found that the test came out positive. Based on the ...
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Fitting a line to absolute value of model residuals to detect heteroscedasticity

I have a series of data sets that I've fit with non-linear models (same model with different parameters for each data set). I'm trying to model the residuals e so ...
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Bartlett Test in R: Independent or Dependent variable assumptions

I'm trying to understand the assumptions of bartlett test a bit better and I currently have this definition: "Bartlett's test of Homogeneity of Variances is a test to identify whether there are ...
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Why how to check heteroscedasticity of residuals in linear regression

Before asking the particular question, I want to know why is heteroscedasticity a matter of concern? How to portray it? Intuitively, I think it is plot of actual values of DV vs the residuals. This is ...
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Can we objectively determine whether assumptions have been violated in R?

I'm testing statistical assumptions in R and so far I've been using plot(model, which = c(1:6)), which produces six graphs for linearity, normality of errors, ...
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Is there a way to think about conditional vs unconditional heteroskedasticity graphically?

I find I understand concepts much better with the aid of charts/visualizations. I'm struggling to intuitively understand how one would be able to see whether error terms are correlated or not to the ...
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Residual standard error in GLS models

I am conducting a "residual analysis" in R (essentially an adapted Event Study), where I aim to use the RSE to construct a residual confidence interval to identify "outlier" ...
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White-Test: Use F-Statistic or LM-statistic?

to interpret the White-Test, it is recommended to use the LM-statistic = N*R-squared of the auxiliary regression which follows a Chi-squared distribution with df = number of restrictions. But I ...
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Which comes first: missing value imputation or homogeneity adjustment?

I am analyzing several rainfall timeseries with less than 5% missing values. I performed Standard Normal Homogeneity Test (SNHT) while ignoring the missing values. However, the rainfall timeseries are ...
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Modelling conditional coefficient of variation

Suppose we have 10,000 test tubes containing variable concentrations of some chemical. The aim is to use measurements of their chemical contents to characterise the measurement imprecision of a ...
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Which test to use to test for heteroscedasticity in a non linear model/fit?

I would like to test for heteroscedasticity in a non linear fit. I have a explanatory vector x and an explained variable y and ...
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Heteroscedasticity or not

I run a GLM model with a body condition as a continuous response variable. I included in the model on the explanatory side Pb concentrations (logged continuous variable), Age (2 levels), Sex (2 levels)...
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Additive Mixed Models: residual check for count response variable

Hi, The response variable is the count of daily number of physician visits of one specific disease.(y usually has the value for example of 4,5,6,10...,26). A standardized residual plot is produced ...
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Linear regression to predict both mean and SD of dependent variable

Imagine we were to investigate the relationship between people's annual income and daily food expenditure in a fictional population. The following example is not meant to be realistic, but hopefully ...
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Quantify heteroscedasticity of variances

I have a large dataset (101952 data points) where the response variable is sound pressure level (SPL) and the explanatory variables are mean number of boats (continuous) and frequency (Fc; categorical)...
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Weighted clustered standard errors

I am thinking about a weighted clustered standard error with heteroskedasticity. The estimate can be calculated as follows: \begin{equation} \begin{split} \hat{\beta} &= \left(\sum_g X_g'W_gX_g\...
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