Questions tagged [heteroscedasticity]

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

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Addressing Heteroscedasticity in Mixed Effects Models with glmmTMB and DHARMa in R [duplicate]

I am analyzing ecological data in R, where I aim to understand the impact of urbanization on species trends. My response variable is the coefficient of species trends (estimate), and my main predictor ...
-1 votes
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29 views

Question Regression Heteroscedasticity

I encountered this problem while studying introductory econometrics: Assume a LM: $Y = X'\beta + \epsilon$ For parameter estimation we assume $Y_{i} = X_{i}'\beta + \epsilon_{i}, i \in [n] \ (1)$ ...
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1 answer
504 views

Non-normal distribution and heterogenous variances

I have a data set in which I measured a continuous variable (positive, continuous data) in response to different treatments(15 different pathogens) and I am unsure how to statistically analyse the ...
66 votes
2 answers
159k views

What does having "constant variance" in a linear regression model mean?

What does having "constant variance" in the error term mean? As I see it, we have a data with one dependent variable and one independent variable. Constant variance is one of the assumptions of linear ...
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1 answer
342 views

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 ...
1 vote
1 answer
58 views

Regression with single-observation dummies: F-test under heteroskedasticity

I have a linear regression model with an intercept and a few dummy variables. Each of the dummies indicate a single observation, so the fit is perfect for these observations. Having fit the model, the ...
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1 answer
86 views

How critical/serious is the heteroscedasticity in my data (Breusch-Pagan test significant at p=.03)?

edit below I am doing this analysis for the first time. How concerned should I be about heteroscedasticity in my data? Here's the scatterplot of predicted values vs residuals: The Breusch-Pagan test ...
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Heteroscedasticity in VECM residuals: consequences and solution

Does anyone know the consequences of heteroscedasticity in VECM residuals? For impulse reponse, standard errors and so on?
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Effect of heteroskedasticity in hierarchical (non-)linear models

Unlike linear models estimated via OLS where heteroskedasticity lead to inconsistency of the variance estimator but not the coefficient estimates, heteroskedasticity causes inconsistency of both ...
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1 answer
37 views

how to identify the form of heteroskedasticity?

After having done the heteroscedasticity test, and having confirmed its existence, I want to correct the model. To correct it, and proceed with the transformation of the data, I must identify the form ...
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Heteroscedastic residuals of a VECM estimated by MLE

I have estimated an VEC model in Matlab, and it turns out the residuals are heteroscedastic. Now, does anyone know how to apply HAC errors to a VEC Model in Matlab? Alternatively, given the model is ...
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1 answer
446 views

Does this look heteroskedastistic?

I've got a continuous y (bounded between 0 and 10) and a 3 level categorical x (small, medium, large) and some other covariates (age, gender). After OLS regression, both the residual vs fitted plot ...
6 votes
4 answers
14k views

Does this graph support the assumption of homoscedasticity?

I do not quite understand when a graph shows homoscedasticity. Can someone please explain this to me with the help of the plot I provided?
1 vote
1 answer
121 views

Does this scatterplot indicate homoscedasticity?

Can anyone perhaps confirm if it is true that this scatterplot indicates that my data is homoscedastic? Since there are quite some more datapoints on the upper side, I was a bit hesitating. Thanks a ...
0 votes
1 answer
674 views

Is there any test to check variance stationarity in time series?

The question is straightforward: Is there any test to check variance stationarity (homoscedasticity) in time series? And, if it exists, which are its implementations in R or Python?
2 votes
4 answers
504 views

Why the OLS underestimates the variances of the coefficients

CONSEQUENCES OF HETEROSCEDASTICITY $\textbf{1}$. The presence of heteroscedasticity does not make the OLS estimates of coefficients biased, but it causes the variances of OLS estimates to increase. $\...
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Trust the graphs or go with Breusch-Pagan and White's tests for Homoscedasticity on large datasets? [duplicate]

I have a large dataset (n > 500,000) which I'm building a linear model with lm(PV1READ ~ PV1MATH + PV1SCIE + ST004D01T). Tests for Normality, No ...
3 votes
2 answers
258 views

Heteroscedasticity in linear mixed effects models (lmer)

I am computing the following model in R, using lme4::lmer: m3 = lmer(e ~ (X*Y*Z) + (1|ID/R), data = data_transform) e is a continuous variable. X, Y, and Z are ...
1 vote
1 answer
399 views

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. ...
1 vote
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Robust standard errors leading to false positives [closed]

I have an odd scenario in my data analysis and I'm not sure what is causing it. I have a large set of tuples $(Y_1, X_i) \dots, (Y_N, X_N)$ where $Y_i$ is a random vector from some arbitrary ...
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True or False: If the distribution of Y|X is normal, then the regression of Y on X must be both linear and homoscedastic [duplicate]

I'm trying to interpret an early and pretty dense (to me) paper on the theory of linear regression: Bartlett, M. S. (1934). On the theory of statistical regression. Proceedings of the Royal Society of ...
3 votes
3 answers
1k views

ANOVA for non-normal, heteroskedastic response

I have a network data set on which I am running product diffusion simulations. I have three factors - A (10 levels), B (10 levels) and C (2 levels) producing 200 factor level combinations. For each ...
3 votes
1 answer
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On the characterization of heteroskedasticity in our tag description

Our tag description for heteroskedasticity says Heteroscedasticity refers to the property of a random process that has non-constant variance along some continuum. This most commonly presents in ...
2 votes
3 answers
778 views

Appropriate test for comparison of 50+ groups

I am currently working with a data set containing several hundreds of thousands of instances for which I am trying to find the most appropriate analysis. The goal is to determine whether there are ...
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88 views

How to deal with Heteroskedasticity in a GAM model

I am running a set of GAMs (Generalized Additive Models) to model a smoothed effect. I have verified all the other necessary checks of my GAMs for the basis functions, etc. However, I find persistent ...
1 vote
1 answer
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Interpretation of plots of residuals vs independent variables in multiple regression?

I know that to check the homoscedasticity assumption in OLS regression, we plot residuals vs predicted values. However, Excel provides plots of residuals vs each independent variable. What is the ...
1 vote
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Non constant Feature Importance [closed]

I have a financial dataset which has 10 years worth of data. The aim is to build a regressor capable of predicting next year sales. So, if I want to predict sales for 2024, I could use data from 2023, ...
0 votes
1 answer
251 views

Heterogeneity in residuals

I am very new in here, but I will try my best to create a good question. First of all I am doing some regression on Fama and French 3 factor model and an asset. Thus I am doing a OLS regression, using ...
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28 views

Conditionally conjugate prior in heteroskedastic model

I am researching a linear model where the noise is a function of the slope parameter as follows $$y_i = \beta_0 + \beta_1x_i + \beta_1\epsilon_i$$ $$\epsilon_i \sim N(0, \sigma^2 g)$$ where $g$ is ...
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Heteroskedasticity Adjusted Correlation Coefficients

I've been reading Forbes & Rigobon (2002) "No contagion, only interdependence" article, in which they suggest to adjust the correlation coefficients for heteroskedasticity. I can't ...
1 vote
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138 views

MLE of Linear Regression with heteroskedasticity

Assume a linear regression model $y = X \theta^{*} + \epsilon$, where $X$ represents a feature matrix and $\theta$ represents a parameter vector. Here we assume heteroskedasticity where $\epsilon \sim ...
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29 views

Advantages of GLS Estimator for OLS in the Presence of Violated Spherical Assumption

Let be the linear model given by: $$y_i = x_i'\beta + \varepsilon_i$$ Using its matrix form, consider strictly exogenous assumption and spherical assumption, respectivelly: $$E[\varepsilon | X]=0, \...
3 votes
2 answers
388 views

What does the asymptotic heteroskedastic variance-covariance matrix of beta look like?

I don't really understand the variance-covariance matrix of beta when there is heteroscedasticity. Can someone explain what the matrix looks like? I am talking about: $$V_\beta=Q_{xx}^{-1}\Omega Q_{...
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What should I do when my data is normal, but not homogen?

My data is (n:43)genotypes with block as replication (n:2). the design is randomized complete block design. and I did normality test and the result said normal, but I did homogeneity test (levenetest) ...
1 vote
1 answer
567 views

games-howell test with multiple independent variables

my data doesn't meet the homogeneity of variances criterium. After a welch one way test I wanted to perform a post hoc games-howell test since it doesn't require the homogeneity of variances criterium....
1 vote
1 answer
1k views

VAR, test for normality, autocorrelation and heteroskedasticity- should I use stationary first differences for these tests?

I am checking thhe long-term relationship between unemployment and labor force participation rate. I have a integration order I(1) and I want to run VAR. As far as I understand I need to use first ...
0 votes
1 answer
146 views

ANCOVA by SPSS with outliers and non-homogeneity

I’m working on ANCOVA to compare post- vs pre-treatment percentage change of a blood test value, L, between 10 groups (10 dosages from 3 drugs, all of which can lower L), with the pre-treatment (...
1 vote
0 answers
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Optimal three parameter variable stabilizing transformation of a Poisson

In the paper: "On the classical choice of variance stabilizing transformations and an application for a Poisson variate", Shaul K. Bar-Lev and Peter Enis give an optimal two parameter ...
0 votes
1 answer
462 views

Help on GARCH-X model theory

I need to understand how a GARCH-X model (GARCH with explanatory variable) works. What I've understood so far is: we have a simple GARCH(1,1) model: If I add to the conditional variance equation an ...
3 votes
1 answer
286 views

How to test homoscedasticity when the errors are DEPENDENT?

I have done a linear regression and plot the residuals. I noticed that the errors are dependent(autocorrelated), how could I test homoscedasticity of this series? I read that Breusch-Pagan test only ...
0 votes
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Resolving heteroscedasticity in Gamma GLMM glmmTMB

I am investigating the effect of predictor variables population.size (continuous), farm.type (categorical) and control measure y.n (binary) on my response variable outbreak duration (continuous). I ...
2 votes
1 answer
5k views

Dealing with heteroscedasticity and non-normality in a mixed model

I am trying to fit a mixed model (person as random effect) on data which has heteroscedasticity and non-normality. I log-transformed the Y-variable but it did not ...
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Aggregated Regressors and standard errors

Suppose we have some aggregated regressors and some that vary across all individuals. E.g. individual data on workers and aggregated data on the level of the US-states. We could either account for ...
1 vote
1 answer
64 views

Homoscedasticity across different samples

I understand that homoscedasticity, constant variance of the error terms at each different X value, is a key assumption for linear regression. Assume we collected a single data sample $(X,Y)$. The ...
6 votes
1 answer
107 views

Is there a model for both mean and variance?

Currently we have models where $y^{pred}_{i} \sim N(\beta_1 x_i + \beta_0, \sigma^2)$. Is it possible to create a model with non-constant variance $y^{pred}_{i} \sim N(\beta_1 x_i + \beta_0, e^{\...
0 votes
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27 views

Heteroscedasticity

I am trying to build a regression model to explain variations in mortgage volumes using variations in different mortgage rates. To account for the drastic change in macroeconomic environment: from ...
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44 views

Poor fitted vs. actual values

I'm using a BART model (Bayesian additive regression tree) to predict the relative risk of an outcome (21,384 observations) controlling for 388 features and I'm getting a really poor actual vs. fitted ...
3 votes
3 answers
951 views

Papers About Permutation Version of Welch's t-test

Permutation tests seem to provide a promising alternative for the unpaired t-test, requiring fewer assumptions. However, the core assumption of the permutation test, exchangeability, implies ...
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1 answer
268 views

Test of homogeneity for Odds Ratios in conditional logistic regression analysis SPSS

I'm doing a case-control study, and I have made stratified analyses based on two age groups, as well as subtype of the type of cancer I'm doing my research on. My exposure of interest seems to be ...
1 vote
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Heteroscedastic Asymptotic Variance Simple Transformation

Let's denote the asymptotic variance under heteroscedasticity as: $$\hat{\text{Avar}}(\hat{\beta}) = 1/N * \left(\frac{1}{N} \sum_{i}{x_i x_i'}\right)^{-1} \left(\frac{1}{N} \sum_{i} \hat{u}^2_i x_i ...

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