# Questions tagged [heteroscedasticity]

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

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### Does there exist an analytical solution to the log-likelihood minimisation for a Gaussian model with linear variance?

I'm trying to model some data using the following distribution: \begin{align} r &\sim \mathcal{N}(\mu, \sigma^2) \nonumber\\ \mu &= m_0 + m_1 d \nonumber\\ \sigma^2 &= s_0+s_1 d\nonumber\\ ...
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### How to add weights in KNN and Decision Tree Regression

I am using a data that has multicollinearity and heteroscedasticity present in it. I am using KNeighbours Regression and Decision Tree Regression in sklearn to model the data and make predictions. I ...
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### Heteroskedasticity in R apart from bptest [closed]

I am trying to test a regression model for heteroskedasticity in R. The library(lmtest) and bptest for my studio generated an error. Which other code or test can I use to test for heteroskedasticity ...
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### consequences of using SARIMA on heteroscedastic data

If I were to run SARIMA on data that was heteroskedastic how would it affect my model? I know in OLS the heteroskedascity only changes my standard errors and not the coefficients themselves, is that ...
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### Autocorrelation test robust to heteroskedasticity

I'm testing the random walk hypothesises 1 and 3. I'm done with the first hypothesis but am struggling with the test distribution of the third one. I'm using the autocorrelationstest. For the first ...
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### ANOVA curve representation

I am researching the embodied cognitive intent exhibited by archeological assemblage, e.g., in ancient glass. I work out homogeneity by ANOVA so as to suggest a Levene's value. For both the real ...
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### Calculation of Olea and Pflueger's (2013) Effective F-statistic

I am trying to understand the calculation of Olea and Pflueger's (2013) test for weak instruments when the errors are not conditionally homoskedastic and serially uncorrelated, which is calculated as: ...
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### Checking the constant variance assumption for residuals vs fitted plots: What about for the same fitted values?

For a residuals vs fitted plot, we use the fitted values $\hat{Y} = \beta_0 + \beta_1 + \cdots + \beta_p x_p$ on the horizontal axis and the residuals on the vertical axis, and then compare the ...
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### Heteroskedasticity leads to inconsistent estimate in log-linear model

My question concerns the following paper. Silva, J. M., & Tenreyro, S. (2006). The Log of Gravity. Review of Economics and Statistics, 88(4), 641-658. doi:10.1162/rest.88.4.641 To summarize, ...
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### What does it mean if magnitude of the variance of each measurement is allowed to be a function of its predicted value?

To better understand Logistic Regression and why it is called regression still, I was reading about Generalized Linear Models on Wikipedia, and I came across the below statement: "The GLM ...
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### How to model variance of a heteroskedastic dataset

I have a dataset (scatter plot shown below) where x-axis corresponds to observed value and y-axis being the true value (yeah, sort of flipped from the convention where y is the observed value). I am ...
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### MANOVA for equal sample sizes, non-independent samples, and heteroskedasticity for time series data

I am looking for a MANOVA-like procedure testing for equal mean vectors for populations that allows for dependent samples (probably because the data are time series and the vectors are correlated), ...
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### Imprecision of coefficient estimates can lead to slightly larger errors?

I'm looking into how to diagnose homoscedasticity. In http://people.duke.edu/~rnau/testing.htm, it states "Because of imprecision in the coefficient estimates, the errors may tend to be slightly ...
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### Plotting residuals vs fitted values or vs independent variables?

I've seen posts where residuals were plotted against fitted values $\hat{y}$ and posts where they were plotted against the independent variable (assume simple linear regression for simplicity). When ...
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### Alternative to Mixed ANOVA without homogeneity of variances

As is tradition on these posts, I should say I'm relatively new to statistical analysis at this level so if I don't provide enough info off the bat bear with me. So I've conducted an experiment ...
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### how to check heteroskedasticity in pyhton?

After building model by using glm. How to check heteroskedasticity? are there any tests available to find or is it checked by using graphs??
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### When distributions are non normal and heteroscedastic, is it preferred to use ordinal logistic regression or permutation tests?

I am currently conducting statistical tests on my two independent samples (both with more than 1500 entries each). The sample sizes are no equal. My response variables are interval as well as quasi ...
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### Statistical analysis of data heteroscedasticity and non-normal residuals

I am dealing with a data set that contains a continuous positive response variable (weight of a beetle that feeds on plants) and two treatments (categorical variables with each 2 levels). It's a ...
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### Homoscedasticity and relationship to error/residuals

My understanding is that homoscedasticity is related to the unobserved error, e.g., $\epsilon$ in the model $Y = X\beta + \epsilon$, and not the residual, i.e., $r = Y - X\hat{\beta}$. If this is the ...
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### Why does PCA require/benefit from homoscedasticity?

Why does PCA specifically (and dimensionality reduction methods in general) require that the variance remains constant across the different values of the mean? An explanation not relying on strong ...
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### Calculating group-level mean with varying group sizes for micro-macro data structure

My study is designed in such a way that I have individuals with varying numbers of observations of the predictors, but only one observation of the outcome. Like a multilevel model, but with the ...
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### How can the below graph be interpreted

How can you interpret the scale location graph in terms of Homoscedasticity?
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### Neural Network Assumptions in a Time series

I was wondering whether an artificial neural network regression, like ARIMA, requires statistically insignificant residual autocorrelation -- and, if so, why? I presume that, if I am using the ANN ...
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### Difference between heteroscedasticity and ARCH effects?

What is the difference between heteroscedasticity and ARCH effects? For example in R you can do a Breusch-Pagan Test to test for heteroscedasticity, and a Lagrange Multiplier (LM) test for ...
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### What is the reason for using Fligner-Killeen test on non-normal data, if ANOVA requires more or less normality? What are the other applications of it?

Variance homogeneity tests like Bartlett or Levene assume approximate normality of the data among groups. That makes a lot of sense, if we the tests before running ANOVA, which wants the normality as ...
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### Lognormal GLM and variance estimation

I'm modeling an outcome with a positively-skewed distribution. I have chosen to use a GLM with a lognormal distribution and the identity link. Note: I am not log-transforming the outcome variable ...
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### I think my data is heteroscedastic but I would like another opinion if possible?

Thank you for looking at my question, I've been driving myself a little crazy over it today! I have run tests for the assumption of homoscedasicity however I have been deliberating whether the ...
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### Data transformation to deal with heteroscedacity

I am trying to build a linear regression model of the data which generally looks like this: Certainly due to the exponential (I guess) nature of the data, I have tried to do a logarithmic ...
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### How to use HAC errors in VAR model

I would like to use the Newey-West method for the standard errors in a VAR(p)-model (I use statsmodels.tsa.vector_ar). The VAR(p)-model assumes that the residuals ...
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### 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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### 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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### 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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### 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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### 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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### 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 ...