Questions tagged [heteroscedasticity]

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

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13 views

How to handle violation of Homoscedasticity

It seems that my model doesn`t follow the assumption of Homoscedasticity(simple linear regression). How should this issue be handled?
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Heteroskedasticity tests: heavy-tailedness of squared estimated errors

I have a time series model and obtain the following distribution of estimated errors: I suspect that the errors are heteroscedastic in the sense that their variance depends on the level of one or ...
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Is a nonlinear regression model valid even if it not Homoscedastic?

I have a couple of experimental datasetsa where I am trying to determine if there is, for each data set, a particular linear/nonlinear regression model that correlates both variables. To this end, I ...
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25 views

Is assumption of residual normality and Homoscedasticity in nonlinear regression

I am still learning a lot about nonlinear regression and I have some questions about residual normality and Homoscedasticity: 1) From what I could find here (Consequences of violating assumptions of ...
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11 views

How to do a levene's test without a grouping variable?

I have a list of people who did a test before and after an intervention. And I want to compare their pre- and post-scores. Now before I do t-tests, I have to check for heteroscedasticity with a levene ...
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31 views

Is this Residual-vs-Fitted-Plot showing homoscedasticity or heteroscedasticity?

I have a regression model. I checked it with hettest (test for heteroscedasticity) in Stata and it gave me an insignificant result; thus no heteroscedasticity. But ...
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1answer
19 views

Contradictory results between Breusch-Pagan test and Goldfeld-Quandt test in Python

I am reading Python regression diagnostic for statsmodel in Python. Under the heteroskedasticity tests, they introduced two test: the Breusch-Pagan test and the Goldfeld-Quandt test. From my ...
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Generalized Least Squares for linear regression with continous and categorical predictors

I have a linear regression model in R studio with a continous and a categorical predictor, where the assumption of homoscedasticity is violated: ...
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How to fit the data with both Ridge and Robust regressions

I have a set of data that has multicollinearity and heteroscedasticity. I understand if the data only have multicollinearity we can use ridge regression or I can use the VIF indicator and remove the ...
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Heteroskedasticity testing with Breusch-Pagan in R, two functions — very different answers?

I am currently testing two different functions in R to determine heteroskedasticity in a regression model with 4 predictors, 2 continuous and 2 categorical. One function is telling me there is a high ...
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23 views

Gauss- Markov Efficiency?

if I have a ragression model $y_i = x_i\beta + u_i$ were I know that the square of error have this $u^{2}=\gamma w^2_{i}+\epsilon_{1}$, where I know only that $E(\epsilon_{i}|w_{i})=0$, $E(u_{i}|w_{i}...
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Question about notation for constant variance

In the context of linear regression where there is an assumption of "constant variance" I have read this: $$\mathbb{V}(\epsilon_i \mid X_i)=\sigma^2$$ But there are two ways I can read this. Either $...
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Testing for homoscedasticity using the Breusch Pagan Test

I am trying to figure out how to test for homoscedasticity. But run into a small issue. I am using this r-bloggers article as a learning resource. According to this article there is no ...
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Adjusting standard errors for *both* heteroskedasticity and clusters in MATLAB?

My data is not exactly a panel, so I can't use the Panel Data Toolbox. It is over time (years) but not for the same industries. For example I have multiple rows with same industry in one year, and ...
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Why do heteroscedasticity-robust standard errors in logistic regression?

I am following a course on R. At the moment, we are working with logistic regression. The basic form we are taught is this one: ...
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Dealing with Heteroskedasticity in Estimated Dependent Variable model

I work on my research in finance concerning pricing of green bonds and I am running a two stage model. Stage 1 regression is an unbalanced panel fixed effects estimation. For each of my 100 green ...
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why arima uses differencing transform not the log transform to make data stationary?

I am currently working on time series project and i am naive. I would like to ask, there exist strict stationary, differencing stationarity. If i understood correct the first order differencing ...
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Heteroscedasticity in GLMM

I'm after some advice regarding heteroscedasticity in a residuals vs predicted plot. I have measured the length of a group of animals at birth and then at five subsequent time points into the future. ...
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variance of beta 1 OLS homocedastic v/s OLS robust

Hi i would like to demonstrate this but I could not. firstly we know that $var(\hat{\beta}_1^{homo})=\frac{\sigma^2}{\sum(x_i-\overline{x})^2}$ in the homoskedastic model. Secondly, we also know that ...
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26 views

Variance stabilizing transformation for time series

I differenced the time series and got this plot. I think I'm supposed to use a variance stabilizing transform because variance is increasing over time but I'm a bit confused as to which one I'm ...
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238 views

Is there ever a statistical reason NOT to use Satterthwaite's method to account for unequal variances?

Two related questions: 1) From what I've read, using Satterthwaite degrees of freedom does not assume equal variances, which allows it to be used on datasets that would be inappropriate for, say, a ...
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Algorithm for dynamic linear regression with stochastic volatility?

Is there any paper or textbook on how to estimate dynamic linear regression model with stochastic volatility? The observation equation and state equation, $$Y_t = \beta_t'X_t + \epsilon_{t}$$ $$\...
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Weak stationarity with conditional heteroskedasticity

The standard definition of weak stationarity is constant mean, and the covariance is shift-invariant - which I read to imply constant variance? But I've seen GARCH processes described as weakly ...
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57 views

Dealing with violation of OLS assumptions

I am currently writing my Master's thesis in economics. I am analyzing the second home rate in Swiss municipalities in R. The second home rate for municipality $j$ is defined as the share of the ...
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Comparing means with unequal variances

I have a dataset (n = 451) of integers split into six uneven groups and was hoping to run a version of a one-way ANOVA to compare means, but I'm struggling with meeting the normality and equal ...
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Why is homoscedasticity (homogeneity of variance) important in neural network layers?

I'm studying the famous Xavier initialization paper (Understanding the Difficulty of Training Deep Feedforward Neural Networks (Glorot and Bengio, 2010)) and had a question. When they explain the ...
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How much heteroscedasticity need to be present in order to justify the use of robust standard errors?

Im trying to figure out if my data is heteroscedastic and if I need to use robust standard errors (Huber-White standard errors). The dataset contains 70 000 rows and 5 columns. Y is a numeric ...
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1answer
43 views

How does taking the log of the variable solve our problem of heteroscedasticity?

I have been taking online classes on linear regression, and in that the instructor told that heteroscedasticity can be solved by taking log of the variables, I was not much acquainted with the ...
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2answers
51 views

Analysis of variance for nonnormal data with unequal variance

I would like to ask whether it is possible to perform an analysis of variance on data that is not normally distributed and has unequal variance, but I have large enough sample size. I have read that ...
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1answer
24 views

Residuals and Homoscedascity in SEM with lavaan

I intend on investigating longitudinal effects through a cross-lagged panel design, facilitating the lavaan package in R. Currently, I have set up a simple Model given the scheme and code below, in ...
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How to split residuals into groups for the Brown-Forsythe test

I have the following data id: 1 2 3 4 5 6 7 8 9 10 11 12 num. responses(predictor): 16 14 22 10 14 17 10 13 19 12 18 11 cost(response): 77 70 85 50 62 70 55 63 88 57 81 51 I fitted the linear ...
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Breusch-Pagan Test for Heteroskedasticity, what is the correct form of the null hypothesis?

For the Breusch-Pagan Test, under pg. 4 of this resource It claims that the null is $$ H_0: E(u\mid X) = \sigma^2 $$ But here it is stated that the null can be written as $$ H_0: \delta_1 = \...
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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 ...
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1answer
55 views

Do these graphs show that the regression assumptions are met?

Is there any concern regarding this plot, specifically that it meets the homoscedasticity assumption? May I continue with multiple linear regression? How can I fix this? My research is on household ...
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1answer
115 views

Breusch and Pagan Lagrangian multiplier test for random effects for Random effect heteroskedasticity

I'm really confused about Breusch and Pagan Lagrangian multiplier test for random effects. The command in stata is xttest0. Some say it is a test to choose between random and fixed effects and ...
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1answer
41 views

Heteroscedasticity test for random effects model in (Stata) [closed]

I'm using panel data in my study. So far, already done the analysis with xtreg, for re and fe, and Hausman test yielded that I should use re. However, when I wanted to test for Heteroscedasticity, ...
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1answer
36 views

Using GLS to fix heteroscedasticity

I have a dataset of global solar irradiance (ghi), diffuse solar irradiance aka solar radiation bouncing of trees, clouds, etc (dhi), and cloud cover. I theorize that I can estimate the dhi given ghi ...
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GLS models: how to interpret results and how to run predictions [closed]

I have data that is quite heteroscedastic, and therefore decided to try fitting a GLS model in python with the statsmodels package in python. The data has two continuous feature variables with skewed ...
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KPSS test and heteroscedasticity

I am trying to transform a time series to make it stationary. After two differencings it looks like this: KPSS test value is 0.01075801 with p-value=0.1, so the stationarity is not rejected. But just ...
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35 views

Minimizing the expectation value of least-squares loss when data and model are randomly distributed with known normal distribution

How do you minimize the stochastic robust least-squares problem $$ \min_x \mathbb{E}\left\{||A x - b||^2\right\} $$ in which both the parameters $b$ and the model $A$ are normally distributed with ...
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One-way ANOVA or Kruskal Wallis in SPSS for non-normal data that shows no homogeneity of variance?

I have fisheries catch data that I need to analyse for my thesis. I already did meta-analysis in Excel, and got some main trends and percentiles out of it. For other stats I am using SPSS. I was ...
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96 views

Does homoscedasticity imply that the regressor variables and the errors are uncorrelated?

By OLS regression equation: $$Y = a + bX + e$$ My thoughts are that homoscedasticity by definition imply that $Var(Y|X) = Var(e|X)=$ constant, then this would imply that $Var(e|X) = Var(e)$ which ...
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57 views

How to fix heteroscedasticity (funnel shape)?

I am running a mlr in python on a dataset with 2D feature vectors, X1 and X2 on a single response, Y. The data ends up being funnel-shaped, as below: X1 v Y, with the colors being X2. It was ...
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1answer
46 views

Interpreting Residual Plots

I was hoping to get some input on people's thought process when looking at residual plots of a linear regression to assess the fit / whether assumptions are met. I included a plot of a model I'm ...
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1answer
27 views

Different ANOVAs by subgroup

I am analysing data which I generated using a simulation model. Due to the stochasticity of the model, the output is also stochastic. I have several dependent variables (let's say X and Y) and vary ...
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About heteroskedasticity form

While studying Heteroscedasticity, I got a question about its form. Usually it is written by $$ Var(\epsilon_i | x_i) = \sigma^{2}_i = \sigma^{2}h_i^{2} = \sigma^{2}\exp(z_i' \alpha) $$ where $z_i$ ...
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26 views

(G)LM prediction interval with heteroscedasticity

I am trying to get prediction intervals from some non-linear data which also exhibits heteroscedasticity. ...
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22 views

Multiple linear regression and model build in light of regression diagnostics

I have a dataset of approx. 200 observations, consisting of Profit which is my dependent variable and is continuous, and the independent variables are Turnover (also continuous), and 3 additional ...
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1answer
35 views

Comparision of mixed effect models via likelihood ratio test and assumption of homogeneity of variance

I would like compare different models with increasing complexity, since I would like to check the impact of each predictor (and the combination of both predictor variables) on the independent variable ...
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1answer
29 views

How does the violation of the homogeneity of variance assumption affect statistical test results?

in university modules it is almost ritualistically taught that variances must be equal in different groups when performing, for example, a t-test or an ANOVA. I understand that the empirical p-value ...

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