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Questions tagged [heteroscedasticity]

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

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Assessing heteroscedasticity in residuals vs. fitted values graph [duplicate]

I am running a mixed model regression with 3 levels (schools, groups and students). I applied robust standard errors with the R function ...
Elena García's user avatar
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Two Way Anova with Heteroscedasticity

I'm trying to run a two way anova test but the homoscedasticity condition is not met. My analysis is not balanced and I have over 3000 observations in my sample. Is it okay to proceed even if the ...
computer_goblin's user avatar
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Coefficient of determination in a linear regression model with a covaring predictor

Given a model: \begin{align}Y_{i}=Z_{i}*\beta * X_{i} + Z_{i}\tag{Eq. 1}&\end{align} I am interested in a closed formula for the proportion of variance explained by the predictor variable $X$, ...
CafféSospeso's user avatar
2 votes
1 answer
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Assumption in multiple linear regression

The principles of multiple linear regression are widely described, however there are still some aspects I don't truly understand why. Specifically speaking I don't understand why heteroscedasticity ...
Javier Hernando's user avatar
5 votes
1 answer
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Very basic questions about choosing weights for WLS

Hi all – very new to stats and ML here (though with plenty of math experience – I’m not a student looking for homework help, I’m 58, know plenty of math, and am looking to expand my skills).

I ...
Steve Lane's user avatar
1 vote
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Does "residualising" out the effect of a covariate on the response variable achieve similar results to including the covariate as a predictor?

Sorry - the question itself is wordy! I am running a Welch ANOVA, but want to account for the effects of a covariate on this Welch ANOVA. I am unaware of any ways that I could conduct a Welch ANCOVA. ...
Cam_stats's user avatar
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Determining when two slopes are different or not, given heteroskedasticity

My current experiment investigates substrate consumption at two different substrate concentrations. My question concerns whether the slope of consumption is equal. However, I obtain an F-value ...
simon vandenberghe's user avatar
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Testing for Homoscedasticity - should Levene's and Brown-Forsythe use Welch's t-test/ANOVA?

This question just came up and I haven't seen any literature on the subject. Background: When testing homoscedasticity for, say, a two-sample t-test, the F-test for equal variances is deprecated due ...
Steven Ouellette's user avatar
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Trying to construct Response surface involving unequal variance for the data mentioned using Minitab [closed]

I'm new to Minitab and I never learned statistics as a proper subject. I need to get a response surface and CI for a factorial experiment for my thesis. I'm faced with what looks like unequal and ...
Ladislav Révay's user avatar
1 vote
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Potential heteroskedasticity in maximum likelihood

I've created a bad loan classifier model using logit regression and maximum likelihood. The actual v expected comparison of the result is shown below. In order to create the chart, we binned the ...
user11209442's user avatar
1 vote
1 answer
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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. ...
Mattia's user avatar
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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 ...
Pau Colom Montojo's user avatar
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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?
user409978's user avatar
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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 ...
user409978's user avatar
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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 ...
Taoufik7789's user avatar
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1 answer
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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 ...
mbp's user avatar
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1 vote
1 answer
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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 ...
Richard Hardy's user avatar
1 vote
0 answers
31 views

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 ...
pluke's user avatar
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3 votes
2 answers
367 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 ...
hilberthotel's user avatar
1 vote
0 answers
36 views

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 ...
David Wang's user avatar
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32 views

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 ...
virtuolie's user avatar
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120 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 ...
flâneur's user avatar
1 vote
0 answers
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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, ...
Nick's user avatar
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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 ...
spencergw's user avatar
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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 ...
krauuuus's user avatar
1 vote
0 answers
156 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 ...
basementGenius's user avatar
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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, \...
user346624's user avatar
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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) ...
Nimas Pertiwi's user avatar
1 vote
0 answers
27 views

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 ...
cfp's user avatar
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0 answers
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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
1 vote
1 answer
70 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 ...
Brett Cooper's user avatar
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0 answers
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 ...
guharup's user avatar
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0 answers
45 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 ...
Tim's user avatar
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6 votes
1 answer
117 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^{\...
StaEx_G's user avatar
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4 votes
1 answer
142 views

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 ...
user356816's user avatar
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0 answers
20 views

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 ...
Marlon Brando's user avatar
1 vote
0 answers
40 views

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 ...
kissmemiau's user avatar
6 votes
1 answer
367 views

Difference between heteroskedasticity and overdispersion

Are both terms equivalent? They seem very similar to me. Or does one imply the other?
sitems's user avatar
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1 vote
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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 ...
user356816's user avatar
3 votes
1 answer
29 views

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
1 answer
40 views

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 ...
user356816's user avatar
3 votes
1 answer
48 views

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 ...
user356816's user avatar
0 votes
0 answers
39 views

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
1 answer
53 views

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
1 vote
0 answers
20 views

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
239 views

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 ...
feetwet's user avatar
  • 1,148
1 vote
1 answer
158 views

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
230 views

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
  • 151
3 votes
1 answer
162 views

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
  • 151
0 votes
0 answers
43 views

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 ...
NeuroPanda's user avatar

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