Questions tagged [heteroscedasticity]

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

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Different estimates of conditional mean parameters from OLS vs ARCH

Consider the market model for security $i$: $$ R_{i,t}=\alpha_i + \beta_i R_{m,t} + e_{i,t}. $$ I estimated the parameters with the OLS method. ...
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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 ...
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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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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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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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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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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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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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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 ...
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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 ...
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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 ...
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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 ...
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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, ...
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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 ...
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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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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, \...
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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) ...
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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 ...
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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 ...
Tamsin Harper's user avatar
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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 ...
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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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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 ...
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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^{\...
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Which Levene statistic do I report?

I am writing a paper comparing quantitative values across $5$ groups. I have performed an ANOVA in SPSS 29 and have requested from the software the Levene statistic to judge if there is homogeneity in ...
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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 ...
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Heteroscedasticity and Serial correlation test

Let’s consider linear regression model, estimated using OLS. According to information from Hayashi (Econometrics, Chapter 2) it must be the case of no serial correlation in errors to perform White’s ...
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Difference between heteroskedasticity and overdispersion

Are both terms equivalent? They seem very similar to me. Or does one imply the other?
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Could a study be considered to be underpowered if the effect size they detect is significantly below their predicted effect size? [duplicate]

I'm assessing a paper, the authors of which state that they recruited 3000 patients because that was what the power calculation suggested was necessary to detect a 5% difference at 85% power. They ...
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How can I tell if a clutser-randomised crossover trial has made a unit of analysis error?

I am studying the following paper: https://jamanetwork.com/journals/jama/fullarticle/2698491 This is a cluster randomised control trial with crossover. I want to ensure they have not made a unit of ...
user356816's user avatar
1 vote
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What would be the effect of assuming the wrong homoskedastic/ heteroskedastic spread of data?

If a cluster trial had homoskedastic data, but the regression model used by the authors used 'robust standard errors' intended for use with heteroskedastic data (or vice-versa), would the implications ...
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Does the use of "robust standard errors" in cluster randomized trials suggest heterskadistic data, implying there is high between-cluster variability?

Please bear with me. I am only recently familiar with some of these concepts. Please correct any poor assumptions. I am analysing a cluster randomized trial with crossover between intervention and ...
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How to visually check for homoscedasticity? [duplicate]

I want to know what to look for in a boxplot, when we want to check for homogeneity of variances among groups, which is an assumption in ANOVA. I used this codes to get a boxplot: '''boxplot(log(...
scholar101's user avatar
2 votes
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Anova model assumptions. How to go by?

I have a data frame that contains a continuous response variable measured on different species, at different elevation and month of sampling as explanatory variables. I want to analyze how the ...
scholar101's user avatar
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Understanding assumptions of equivalence of random effects variances; what to do when violated?

The random effects model is stated as: $Y_{ij} = \mu + \tau_i+\epsilon_{ij}$ Where, $\tau_i \overset{iid}{\sim} \mathcal{N} (0, \sigma^2_{\mu} ) \\ $ $\epsilon_{ij} \overset{iid}{\sim} \mathcal{N} (0, ...
Estimate the estimators's user avatar
4 votes
1 answer
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Hypothesis tests for Rayleigh variables

Given samples from two Rayleigh-distributed random variables with unknown parameters, $X \sim R(\sigma_x), Y \sim R(\sigma_y)$, what tests can we use to determine if and to what extent their ...
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Homoskedasticity and Collinearity

I am curious whether the property of homoskedasticity is more or less dependent on the correlation between independent variables. I assumed that if the $cor(x_1,x_2....x_n) \approx 0$, hence the ...
Tunay Sabri Yüksel's user avatar
3 votes
2 answers
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White's test interpretation

I am running a regression in python (a basic market model with just one index as regressor). After doing that I conduct the heteroscedasticity test on residuals using two tests, White and ARCH. I am ...
Mattia's user avatar
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1 answer
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What aspects should I test from a fitted GARCH model?

I estimated a GARCH(1,1) assuming that the residuals follow Student-$t$ distribution. ...
Mattia's user avatar
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Is it possible to fit (frequentionist) Gaussian model with known variance of residuals?

Is it theoretically possible to fit a Gaussian model if we already know variance, that is, variance of outcome is not inferred but is known a priori and is defined for every measurement of outcome ...
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BART with non-parametric heteroscedastic noise?

Is there a variant of BART that robustly captures noise that is both heteroscedastic and non-parametric (or has an a-priori unknown parametric form)? For example, a BART that could fit this test data: ...
Luke Gorrie's user avatar
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I am unable to relate the normal distribution dependency for regression . I need a mathematical intuition cum understanding for regression assumptions [duplicate]

What is the mathematical significance for the assumptions of linear regression to hold true for arriving at a single/multiple regression formula? Can anyone use the assumed normally distributed ...
ANKIT CHAKRABORTY's user avatar
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Using standard deviation of outcome variable as predictor in multiple linear regression

I am attempting to fit a multiple linear regression equation to a continuous, real-valued outcome variable, $Y$, using a number of predictive variables, $(X_1, X_2, ... X_n)$, i.e., $$ Y = \beta_0 + \...
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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 ...
Marlon Brando's user avatar
2 votes
2 answers
156 views

Do all GLM models not require equal variance?

I am trying to learn about generalized linear models (GLMs). For example, in a Poisson GLM: $\text{g}(\mu_i) = \text{log}(\mu_i) = \beta_0 + \beta_1*X1_i$ $E[Y_i|X_i] = \mu_i = \text{exp}(\beta_0 + \...
stats_noob's user avatar
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1 answer
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Transformations to meet heteroscedasticity

I have a dataset containing angles. They represent the bending angle that a seedling makes to go toward light. I have two factors: treatment and genotype, so I use a two way ANOVA. However, the ...
Marius Audenis's user avatar
2 votes
2 answers
139 views

Multiple linear regression homoscedasticity/linearity

My question is about the implications of the violation of homoscedasticity/linearity for multiple linear regression. I have tried to find the answer in multiple sources but could not figure it out. I ...
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Dealing with conditional heteroskedasticity in dynamic linear model

I'm working on a regression problem and am struggling to figure out how to deal with the conditional heteroskedasticity present in the error terms. I will try and work through what I have done so far, ...
Arron's user avatar
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3 votes
1 answer
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In multiple linear regression does heteroskedasticity need to be evaluated for each predictor or just for the overall model?

If we want to make valid inferences about a simple linear regression estimator with one term, then homogeneity of variance of the residuals is a common assumption for making valid inferences. However, ...
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