Questions tagged [heteroscedasticity]

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

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27 views

Test for non-normal data with homogeneity of variance

I'm new to the platform and would like the following question to be answered: I have performed a latent class cluster analysis with 28 variables and 9000 observations, for which I am currently ...
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23 views

Please verify whether the calculating process of the WLS estimator and the variance is correct or not

There are two Heteroscedasticity regression models 1. $$ y_i = \beta x_i + \epsilon_i, \quad i=1, \ldots, n $$ where $\epsilon_i$'s are independent and distributed as $\epsilon_i \sim N(0, \...
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2answers
43 views

Chart indicates homoscedasticity but Breusch-Pagan test p<.001

I am writing my master's thesis and doing multiple regression analysis for hypotheses testing. I transformed the data using ln and use a sample with N = 15,000. As a result of the assumption test, I ...
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16 views

When the error term is heteroscedasticity, how to have the best linear unbiased estimator and the variance?

The regression is heteroscedasticity. Please give me the process to find the best linear unbiased estimator and its variance. Thank you.
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18 views

How to find the weighted least squares estimator and its variance in this regression?

Hi, Please give me the process of finding the weighted least squares estimator and its variance. And please tell me why ordinary least squares is not allowed to use under this heteroscedasticity ...
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28 views

Bootstrapping of data, in R, for improving the homogeneity of variance

I have a data collected on five point likert scale; aims at studying, the level of preference individuals gives to the different factors, (such as Tax Benefits, Maturity period, Rate of Returns ...) ...
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22 views

Homoscedasticity in regression model building example

In a linear model building example for a class, we are given a data set and told to use methods like forward, backward, and stepwise selection to choose predictors to include. I get to a combination ...
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8 views

Quasi-generalized least squares and model selection with SAS or R

I want to conduct a model selection (stepwise) on a linear model, in which the parameters are estimated using the quasi-generalized least squares (due to the presence of heteroskedasticity). Does a ...
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1answer
18 views

Heteroscedasticity - interpretation of residual plot and P-P plot

Could you please help me interpret the following residual plot and P-P plot from a multiple regression analysis? I'd say that this shows evidence of heteroscedasticity as the residuals are grouped ...
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13 views

Stationarity vs. Heteroskedasticity

I am reviewing a OLS regression model based on time series data. The variables have been transformed so they are stationary; however, the existence of heteroskedasticity was assumed and the Huber ...
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7 views

Automated high-dimensional comparison?

For example, I have a table of customer attributes (high-dim) for a e-commerce group, includes country age sex education level last purchase day (R for RFM) purchase frequency and percentile level(F ...
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25 views

Bootstrapping across residuals for heteroscedastic data

I have a highly heteroscedastic 2d dataset (x,y) where both x and y cover about 3 orders of magnitude; therefore, although the % error is roughly constant and normally distributed across x, the ...
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1answer
29 views

Unequal variance in randomized experiments to compare treatment with control?

Consider a randomized experiment to compare (one or more) treatment(s) with a control. Since groups are defined by random assignment, we should expect equal variances for a null-experiment (that is, ...
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1answer
86 views

How to eliminate the influence of heteroscedasticity

As I want to find an approximately linear relationship between $x$ and $y$, how to transform this scatter plot with heteroscedasticity into an approximately linear model? If this cannot be ...
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19 views

Seemingly Proof of Gauss-Markov without using homoskedasticity assumption

I am trying to proof the Gauss-Markov theorem, and have seemingly done so without using the assumption of homoskedasticity once. Now I am wondering where I went wrong. The point is to prove that ...
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1answer
27 views

Stratify the analysis if Levene's test fails

I have a question about the correctness of a statistical analysis. I have a variable called L, which is the log of the number of bacteria present in some foods. L is a function of the treatment T (...
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How do I appropriately control for a limiting/maximum value in regression?

I have a dataset where one variable is limited by the value of another. It is a study of participants with a particular disease. By necessity, therefore, age of disease onset, A, can be no larger than ...
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15 views

Conditional heteroscedasticity for the tobit model in Layman's terms

I have been using the crch package for modelling censored data with the tobit model. I noticed early on that the errors (by far) are not normally distributed by ...
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27 views

How can I use spatial heterogeneity within regions as predictors about those regions?

Please forgive if I am misusing the term "spatial heterogeneity". I am trying to predict county level crop productivity using satellite acquired vegetative health (NDVI). Since this is pixel data, I ...
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1answer
38 views

Why cannot the model $\frac {y_{i,j }} {N_{i,j } } = \beta_0 + \beta_1 X_i + e_{i,j }, \ y_{i,j}\sim B(N_{i,j},\pi_i)$ have constant variance?

The following example is taken from a book by Walter Stroup on Generalized linear mixed models, and are supposed to show some limitations on trying to write models in equation form. Let $y_{i,j } \...
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Can I use subset of a time series if OLS assumptions are failing?

My OLS model build on full data has heteroscedasticity of residuals. Is it allowed to use a subset of the time series to get around this issue? What are the possible implications?
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Dealing with Heteroskedasticity: when to use WLS vs Box-Cox/Box Tidwel Transformation

Suppose you are fitting a linear model which has heteroskedastic (non-constant) residuals. I have read that there are a number of ways of dealing with this situation, including Weighted Least Squares (...
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1answer
34 views

Multiple Regression - Heteroskedasticity? - Is this a linear model?

I am analyzing a multiple regression model in SPSS. I am checking whether the requirements for a linear model are met. The last requirement is homoscedasticity. In my survey, you can choose between 1-...
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2answers
121 views

Heteroscedasticity in Linear Regression

I implemented a linear regression model on some dataset. When I plotted the scatter plot of residual v/s predicted y (i.e., yhat), I observed heteroscedasticity in the plot. What can I do about it? x-...
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23 views

semiparametric index model with heteroskedasticity

I'm trying to estimate a semiparametric binary response model with index heteroscedasticity in R. That is, I have a model defined with $y_i = \mathbf{1}\{\beta_0 + \beta_1 x_{1i} + \beta_2 x_{2i} + \...
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Appropriate type of regression for evolution of relative tumor size over time in two groups?

I am looking into data from a cohort study with two groups of patients with melanomas. Group A is beeing treated while group B is not. The relative size of several melanomas (relative to the initial ...
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1answer
39 views

heteroscedasticity evaluation of residuals in linear LASSO regression model [closed]

I plotted residuals for linear LASSO model. Though tests for heteroscedasticity doesn't show any but i am seeing one some lines in residual plots depicting some heteroscedasticity might be present. I ...
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16 views

Coefficient sign flips after applying Fixed Effects

Good day everybody, I am currently writing my master thesis and I research whether family owned companies (FFF=1 if family owned, 0 otherwise) have a positive or negative effect on the performance of ...
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28 views

What are the differences between HC estimators and their small sample properties?

I am currently using R to run regression with the following code: ...
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1answer
38 views

How can I adress problems of heteroscedasticity in mixed model analysis?

I am analizing pupil size data using mixed model analysis in R. I use lme() from package nlme. However, I am encountering serious problems of heteroscedasticity and ...
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31 views

Regression with GARCH error term

Let's consider the following multivariate regression ($y_{t}$ and $x_{t}$ below are matrixes of appropriate size) where the error term is assumed to follow a GARCH process: $$y_{t}=\beta x_{t} + e_{t}$...
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137 views

Can I continue ARIMA model despite my time time series has heterodasticity?

I estimated ARIMA model with daily gold time series. The residuals' corelogram is flat but its squared is not flat. Already I tried eVİEWS heterodasticity >> arch effect and ı found prob value 0.00 so ...
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23 views

R-squared unbiased when F-test is biased in heteroscedasticity?

If R2 and F-statistic are in functional relationship, is it possible, that in case of heteroscedasticity F-test is biased but R-squared is not?
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1answer
77 views

Heteroscedasticity consistent (HC) standard error analysis and interaction effects in an OLS

I have made a model with several variables, and 8 of them interact with a dummy to find interaction effects. These are added stepwise, resulting in three models. Now, through a Breusch-Pagan test I ...
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21 views

Checking Heteroskedasticity in ANCOVA models : Breusch-Pagan test?

I would like to check the heteroskedaticity in an ANCOVA model : ...
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20 views

Marginal log likelihood for Tobit model heteroskedasticity link function

I am using a Tobit estimator for a demand model left censored at 0. To account for heteroskedasticity, I specify the standard error as follows (using the crch function in the R package crch): $log(\...
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37 views

How can analytical weights be used together with sampling weights?

I run a linear probability model (LPM) on survey data, which contains sampling weights. Say the predicted probabilities from the OLS regression are $\hat p_i$. Heteroskedasticity would make me ...
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33 views

Lee Carter mortality model - OLS (SVD) estimators if errors are heteroscedastic

In the classical Lee-Carter model, central death rates are modelled as follows: $\log(m(x,t)) = a(x) + b(x)\kappa(t) +\varepsilon(x,t)$ for some $x=0,\ldots,\omega$ and $t=1,\ldots, T$ and where $a(...
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Volatility Models: Does this model have a name?

I am looking at some volatility models and the following functional form pops up naturally $$ \xi_t ^2|x = \sigma^2 x^{2\beta} + u_t. $$ Here $\xi_t^2$ represents the square residual and the terms $\...
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how to remove the heteroscedasticity of latent variable in tobit model? by using SAS software

i have done a tobit model. when using white test to test heteroscedasticity of latent, the outcome is significant. after search related questions in stackexchange, i found "inverse hyperbolic sine" ...
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17 views

Why does the average linkage method put more emphasis on greater homogeneity then the Centroid Method?

at first i have to admit that i'am not an native english speaker. I hope i can articulate myself clearly. I read that the average linkage methode put more emphasis on greater homogeneity then the ...
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1answer
32 views

Evidence for heteroscedasticity from unordered values

I'm fitting a linear regression model on a dataset about how many upvotes a certain post will get based on its views, its author's reputation ecc. To satisfy the normality assumptions I performed a ...
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19 views

General forms of conditional heteroskedasticity

I am currently reading a paper published in the Journal of Finance: Rapach et al. (2013), 'International Stock Return Predictability. What is the role of the United States'. The authors quote they ...
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2answers
101 views

Multiple linear regression: homoscedasticity or heteroscedasticity

Regarding the multiple linear regression: I read that the magnitude of the residuals should not increase with the increase of the predicted value; the residual plot should not show a ‘funnel shape’, ...
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0answers
21 views

test for homogeneity and heterogeneity in clustering

I want to check if there is a way (or test) to verify homogeneity among and heterogeneity between clusters, besides the almost 30 clustering indices that are available (see NbClust). I am also aware ...
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1answer
157 views

ARIMA requires constant variance, so why can we use GARCH for its residuals?

According to what I have found so far, in order to implement ARIMA we need to have a stationary (constant mean and variance) transformed data set. In addition, I have also seen that the square of the ...
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22 views

Does $\mathbb E\epsilon^2 = const$ and $\mathbb V\epsilon = const$ are equivalent conditions for homoskedasticity?

Wooldridge states in his book that homoskedasticity requires $$\mathbb V[\epsilon\mid x] = const.$$ But I often encounter that $\mathbb E[\epsilon^2\mid x] = const$ is required for homoskedasticity ...
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1answer
52 views

Polynomial regression - non-constant residual variance

I have the following regression task. The dataset below is a list of costs for certain levels of a covariate variable. ...
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28 views

ARIMA stabilization process

Initially, before apply arma model stationarity conditions must hold. According to that,time series data must have same variance and mean with normal distribution. If raw data is not normal then box ...
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0answers
187 views

How does heteroskedasticity affect the validity of R squared and other metrics?

I apologise for the trivial question, but I have got myself confused about how heteroskedasticity affects OLS regression and would be very thankful for your help. In standard OLS, homoskedasticity is ...