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Questions tagged [heteroscedasticity]

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

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Stationarity of ADL(p, q) with heteroskedasticity

Suppose I have the model $$y_t = \alpha_0 + \alpha_1 y_{t-1} + ... + \alpha_p y_{t-p} + \beta_0 x_t + ... + \beta_q x_{t-q} + \epsilon_t,$$ where $\{x_t\}$ is a stationary process and $\epsilon_t$ has ...
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24 views

How would heteroskedasticity look like with negative correlation?

I hope I formulated the question correctly, but I am purely interested in heteroskedasticity: cov($e_i$,$e_j$) and not in autocorrelation with the dependent variables. So positive correlation of the ...
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7 views

Generating multivariate heteroskedastic data

I am trying to estimate a VAR model with heteroskedastic error terms. $e_{it}$ is given by $η_{i,t} √h_{ii,t}$, where $η_{i,t}$ is iid, N(0,1). I am trying to get $e_{it}$ Does anyone have any ...
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8 views

Appropriate method to assess scatter or variation in groups with dramatically different means

I am working on a product fabrication process, and I want to demonstrate the consistency of my product. To do this, I am trying to measure the variation in the extent to which a biological material is ...
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3 views

Wide variety of results in Breusch-Pagan Tests on simulated data?

I wanted to see how the results of the BP-test would come out. This stemmed from a debate with someone who claimed that the BP-test would start rejecting the null hypothesis of homoskedasticity even ...
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23 views

why do residuals of the model show heteroscedasticity when plotted against time

Following up on question Dealing with heteroscedasticity in mixed models I collected crop yield data for many years across multiple locations, which are nested under provinces and some associated ...
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15 views

Lagrange Multiplier Statistic When Testing for Heteroskedasticity

I had a debate with another student and wanted to get some more perspective. She brought up a fascinating point for when we test for heteroskedasticity through the Breusch-Pagan Test. Recall, $$LM = ...
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46 views

Dealing with heteroscedasticity in mixed models

I collected crop yield data for many years across multiple locations, which are nested under provinces and some associated weather data. I am interested in making a model and then using new weather ...
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7 views

Why does the Breusch Pagan test use unstandardized residuals and predicted values?

If I understand correctly, there are different ways to test for heteroscedasticity. I first learned to do it by looking at a scatterplot of standardized residuals vs. standardized predicted values. I ...
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1answer
36 views

Breusch–Pagan test: what exactly is the z-variable

I want to perform a Breusch-Pagan-Test. I did calculate some very small examples following the procedure described below, just to understand what the test does: found here: (https://ipfs.io/ipfs/...
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1answer
28 views

Implement VAR model in R with HAC corrected standard errors [closed]

I have fitted a VAR model in R (with function VAR) and would like to use HAC corrected standard errors. How is that possible?
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2answers
47 views

What are the assumptions of a Gamma GLM or GLMM for hypothesis testing?

What are the assumptions when doing hypothesis testing using a Gamma GLM or GLMM? Are the residuals suppose to be normally distributed and is heteroscedasticity a concern like the Gaussian (normal) ...
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31 views

Use of supportive inferential statistics (e.g. Levene's and normality tests) in underpowered samples

We know that underpowered statistics greatly increase the probability of a type II error (by definition), meaning a greater chance of failing to reject the null hypothesis despite the existence of a '...
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2answers
49 views

Do these standardized residuals show heteroskedasticity?

I'm practising in the individuation of heteroskedasticity from the standardized residuals. I know that, if the time series is homoskedastic, the spread of the residuals should be constant and random ...
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53 views

Unable to remove heteroscadasticity

This is my model: lm(PCTUI~year+statefips+factor_agecat+factor_sexcat+factor_racecat+factor_iprcat, data = train) I have factorized the categorical variable. ...
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45 views
+50

How to perform over-dispersion test where null is quasi-Poisson

If I understand correctly, a quasi Poisson regression assumes roughly that $$ \mbox{E}\left[y\left|x\right.\right] = \exp{\left(x^{\top}\beta\right)}, \quad \mbox{VAR}\left(y\left|x\right.\right) = \...
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30 views

Testing for Heteroscedasticity of Multivariate Multiple Regression [closed]

I want to test for heteroscedasticity on a regression model with multiple dependent variables using R. I want to see if the indenpendent variable has an effect on the variance of all of the dependent ...
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37 views

Which one of these is correct for linear regression?

Only one of these is supposed to be the correct one for simple linear regression. Which pair of plots would you say has constant variance and normal distribution? I feel like none of them have both ...
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37 views

Heteroskedasticity robust confidence interval

I have used Chebyshev's Inequality to construct confidence intervals. I know that Chebyshev's Inequality works for any distribution as long as the second moment exists. But I have got a comment that ...
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17 views

Heteroskedasticity testing

Im estimating the carhart 4 factor model. Im testing for heteroskedasticity to see whether i need to use adjusted standard errors, but i am finding conflicted results. All but one test (ARCH) are ...
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1answer
18 views

why homogeneity test is used for ANOVA not for t test?

Why the homogeneity test must be curried out for ANOVA test but not for t-test when sample size is more than 30 ?
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19 views

Heteroscedasticity and non-normaility in VAR(3) model

After specifying my VAR model, I run several diagnostic tests. While the serial.test indicates that there is no Autocorrelation, ...
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1answer
78 views

Jarque-Bera test for Normality

Which test should I consider if by JB-test result I have heteroscedasticity and by the result of two others no. $JB JB-Test (multivariate) data: Residuals of ...
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19 views

heteroskedasticity and quantile regression

I am working on a quantile regression. I saw that there are tests for heteroskedasticity like a test by machado and silva (MSS) and a KB test. However, i have also read that having errors with ...
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31 views

Intuition behind White's Estimators/ Heteroscedasticity-consistent Standard Errors

For a medical study I am trying to understand the intuition behind heteroscedasticity-consistent standard errors. I know that it can be used, when in OLS regression residuals are heteroscedastic. By ...
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22 views

Heteroskedasticity correction

After I ran a bptest and I detected heteroskedasticity, I want to correct for it. What is the difference between the functions HC1, HC2 and HC3 in R? bptest(model2) model3 <- coeftest(model2, ...
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1answer
31 views

Without testing: when are error terms possibly homoscedastic?

I am facing the following study: In the 1980's, Tennessee conducted an experiment in which kindergarten students were randomly assigned to regular and ...
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84 views

Difference between OLS and GLS linear Regression in data with heteroscedasticity

I have a cross sectional model which displays heteroscedasticity. I've tried a GLS regression and an OLS with heteroscedasticity-consistent standard errors linear regression. They give significantly ...
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1answer
42 views

Introducing random slopes in nested model improves model fit but residuals variances become unequal

I have measured boldness scores (continuous variable) across time (trials) for individuals (ID) within colonies (colony). The data is coded such that individuals 1-30 belong to one colony, 31-60 to ...
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24 views

R - Heteroskedastic robust errors with `bife` package

I'm using a fairly new R package called bife for binary choice fixed effects model. It looks like vcovHC in the ...
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0answers
43 views

ANOVA with post hoc for non-normal data with unequal variance

I have 200-some variables with 25,000 observations in each of 4 categories. For each variable individually, I need to identify where we have variability between categories. Therefore, I need an ...
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2answers
295 views

Why use OLS when it is assumed there is heteroscedasticity?

So I'm slowly going through the Stock and Watson book and I'm a bit confused on how to deal with the issue of homoscedacity/heteroscedacity. Specifically, it is mentioned that economic theory tells ...
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1answer
26 views

Intuitive explanation for Studentized Residuals

I'm currently testing the homoscedasticity assumption of multiple linear regression. This can be done by plotting studentized residual plots. The problem with residual plots is even if the variance of ...
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23 views

What to do when there is heteroskedasticity in an ANCOVA model?

What to do when there is heteroskedasticity in an ANCOVA model? Is there a correction similar to Welch ANOVA? Or is better to use a OLS regression model? Should we try to solve heteroskedasticity by ...
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46 views

Exponential heteroskedasticity

Assume that the form of heteroskedasticity is exponential such that $u_{i} = e^{0.5X_{i}\gamma}\upsilon_{i}$ where it is assumed that $\upsilon_{i} \mid X_{i} \sim N\left(0,1\right)$ and $X_{i}$ ...
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1answer
32 views

WLS vs Dummy variable coding for heteroscedasticity

I am a beginner level stat learner (with graduate training in Applied Math) I have just read a sage book which states the following: "Dummy variables help address the issue of heteroscedasticity in ...
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1answer
44 views

How to use White-test to check if the heteroscedasticity has been effectively dealt with by a WLS?

Consider an OLS model with $n$ observations and $p$ explanatory variables (including an intercept term) $$y=X\beta + \epsilon$$ We may use a White test to (approximately) check for the presence of ...
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Standardizing Variable for a Regression of X on ratio Y/Z: What would you do?

I have a 3 variables X,Y,Z and I'd like to observe the effect of X on Y/Z. (If you're interested in the flavor text of this question: X is the capacity of air conditioners (BTU), Y is the price, and ...
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9 views

Estimate variance of next element in heteroskedastic time series

I have a time series $X$ of which I can reasonably assume the mean is constant at zero. However, I know it to be heteroscedastic. Given $X_1$ through $X_N$, I'd like to estimate the variance $\sigma_{...
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1answer
53 views

Heteroskedasticity-consistent standard errors

See https://en.wikipedia.org/wiki/Heteroscedasticity-consistent_standard_errors. Assume the model of interest is the linear regression model. If the errors are heteroskedastic, $\hat{\sigma}^2_i = \...
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1answer
68 views

In linear regression, data is highly skewed, transformation doesn't work..!

I have dataset with 9524 observations / 97 variables. Most of variables are numerical, and some of factor variables (Yes/no or several levels) I want to perform multiple linear regression with ...
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22 views

Construct Confidence Curve in R in Change Point analysis

I am trying to reproduce the journal article "Confidence distributions for change-points and regime shifts" (on page 16 top left hand corner) Firstly, I generated random sample using i) N(1,1) and ii)...
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70 views

Robust Regression in MATLAB's robustfit: what is the optimal weight function to tackle heteroskedasticity?

I'm currently performing a linear regression analysis and encountered a fair amount of heteroskedasticity. Increases in predicted values go along with decreases in residual variance. Otherwise, the ...
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12 views

significance testing of unequality of coefficient of variation in multiple samples

I'm performing a study on inter-doctor variation. For that, I'm studying a diagnostic instrument that has around 100 items that all have to be rated. Some are dichotomous, some ordinal. Several ...
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1answer
33 views

Assumptions of linear fit; linearity and homoscedasticity

I'm reading about the assumptions of taking a linear fit between two variables from here, and that source says: For diagnosing non-linearity: nonlinearity is usually most evident in a plot of ...
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1answer
53 views

Interpreting a plot about heteroskedasticity

Can anyone tell me whether this graph shows heteroscedasticity? If the graph shows heteroscedasticity, how can I solve it?
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21 views

Considering heteroskedasticity in Cp approach to adjusting training error rate in regression

I have been introduced to $C_p$ as a way to adjust the training error rate to account for bias due to overfitting regression models. $C_p$ is defined as such: $C_p = \frac{1}{n} (RSS + 2d\hat{\sigma}...
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66 views

Assuming heteroscedasticity produces terrible QQ plot

I created a model using the lm function and obtained a model with an AIC of 390516.1 and the following QQ-plot: However, the Breusch-Pagan Test returned a p-value ...
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1answer
272 views

Assumption of homoscedasticity/equal variance violated in a 2-way ANOVA

I'm analyzing results from an experiment where 56 samples were tested for a specific response to electrical stimulation. Electrical stimulation was done at 2 different stimulation frequencies, and at ...
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21 views

Estimation in case of data dependent noise

I am trying to estimate $a$ and $b$ in the below linear model $$y = ax + b + \epsilon$$ where $x \in R^n$ and $y \in R^n$ are given, and $\epsilon$ depends on the parameters and the $x$. Also, it is ...