# Questions tagged [heteroscedasticity]

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

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### Weighted least squares estimator variance using noisy weights

I have a linear system with uncorrelated, heteroscedastic noise, $Y \propto \mathcal{N}(Xβ,Σ)$ where $Σ$ is a diagonal matrix with elements $σ_{ii}^2$. The MLE is given by weighted least squares (WLS) ...
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### Heteroskedasticity-robust standard errors computation by hands

Consider the following multiple linear regression model \begin{equation} y=\beta_0 + \beta_1 x_1 + ... + \beta_k x_k +u \end{equation} If the variance of the error is not constant for any value of the ...
1 vote
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### Why does heteroskedasticity not affect $R^2$ and why does it make estimated regression more statistically significant?

I am studying what the consequences of heteroskedasticity are. And i found that assuming that the model is linear in the parameters (i.e $Y=X\beta+\epsilon$), is identifiable, has no perfect ...
1 vote
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### Include variance change at point in ARIMA model estimation in R

I have a series which I am trying to model through ARIMA approach. However, when checking the residuals, there appears to be a change in variance at a specific point. This is, given the residuals $e_t$...
29 views

### I am using Stata to perform my statistics for a paper. What should I do if a sample is normally distributed but don't have equal variances? [duplicate]

I am using Stata for my analysis. I am analysing a numerical variable over a categorical one (with 3 groups). After confirming they are normally distributed, I did a one way ANOVA test. But Bartlett's ... 28 views

### Regression analysis and time series data

I'm trying to model the effect of flow at entry and flow at exit on the produced energy in a thermal power plant ,The data is collected every 2h for two years,in my internship they want me to model ...
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### time series with heteroskedasticity in the lagged series

Dear members, I am researching time series data with heteroskedasticity. I have an R code that acts on stock data, call it F(), which returns a time series. The time plot of F() is not problematic and ...
37 views

### Order of independent and dependent variable in Breusch-Pagan test

I've been working on my master thesis, and I've been using R to test heteroskedasticity with Breusch-Pagan test. The code is rather simple: ...
13 views

### Violated Residual Linearity/Homoscedasticity Assumptions in X13 Time Series Decomposition: How to Interpret and Resolve?

I have been working on decomposing a monthly time series of the country's exports using JDemetra+ with the X13-ARIMA-SEATS model. My aim is to break down the series into its Trend, Seasonal, and ...
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### heteroscedastic uncertainty

I am majoring in economics and I am reading this paper by Crossley & Kennedy (2002). It discusses the reliability of self-assessed health status (that is "In general, would you say that your ...
1 vote
79 views

### Heteroscedasticity still present after Box-Cox transformation

I just started to learn regression and I'm trying to fit a linear regression model to some data with one continuous independent variable x1, one categorical variable x2, and the dependent variable y. ...
21 views

### How should I proceed with a one-way ANOVA if homogeneity of variance is violated, I have unequal sample sizes, and I want to control for covariates?

I'm using SPSS. I have a multi-level categorical IV and a few continuous DV's. My main analysis goals are to test the effect of the IV on the DV, and then to follow-up with pairwise comparisons of ...
1 vote
56 views

### Transforming Data for Linear Models

I am relatively new to statistics and need some help understanding some concepts relating to linear models and their assumptions. My question refers to one assumption, but I am using this as an ...
34 views

### Two-way ANOVA but normality and homogeneity violated

I have a 2x3 between-subjects design. I want to run two-way ANOVA but have no normality and no homogeneity. I have 3 variables and 103 observations in total. Factor 1 - attentional bias (CFT): G0 n....
36 views

### How to address the heteroskedasticity and non-normality of my residuals in my model?

My study is about the influence of board diversity (gender and age) and fund size on the voting behavior of pension funds. I have also included control variables that concern the board type, board ...
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### What does it mean when dots on a residual vs fitted graph are clumped like a shotgun result? How do I fix it if it needs to be fixed?

Here's the code for these graphs ...
147 views

### Heteroscedasticity problem violating assumptions for lm and glm

I’ve been trying to fit some data for a manuscript to a model for the past two days and I keep running into problems with violation of assumptions for the lm and <...
85 views

### How to compare more than two groups of continuous, not-normally distributed values?

I'm currently analyzing the age variable in a dataset of all italian phyisicians (~470,000 obs) and I'm trying to check if age is significantly different between three groups defined by another ...
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### Estimating heteroscedasticity in linear mixed effects model?

I have a dataset with columns: (subject, method, recordingDate, side), which I am modelling in R using lme4: ...
1 vote
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1 vote
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### Variance stabilization of Scaled Noncentral Chi-squared

For an integer $k > 0$, $\mu_i \in \mathbb{R}$, and let $\zeta_i \sim \mathcal{N}(0, 1)$, $1 \leq i \leq k$. In the background we are taking $k \to \infty$. Then the random variable $T$ has a ...
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### Which one (conditional or dispersion model) is the final result in glmmTMB? [closed]

Please help me to figure out the final result in a glmmTMB. I used this code model1<-glmmTMB(ctmax ~ lat+ (1|site), dispformula=~lat,data=data) summary(model1) ...
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### Should I use OLS robust standard errors with FGLS or PSCE?

My sample size is 8 banks over 10 years. There is heteroskedasticity but no serial autocorrelation. I use stata 13.
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### Breusch Pagan R test which function is correct

So I have a model: $log(y)= \beta_0 + \beta_1dog +\beta_2cat$. I want to test for heteroskedasticity using a Breusch-Pagan test and the variables cat and dog. Should by formula be ...
1 vote
41 views

### How to calculate heteroskedastic standard errors

I'm doing curve fitting, but my error is non-stationary. The variance decreases: I'm looking for a signal in the noise (In this case at x=90, y=50). I'd like to calculate the "standard error&...
22 views

### Paired Data collected; one condition is non-homogenous; Paired t-test possible?

I collected data on language attitudes to three languages in two moments of time, so the responders were the same. For two languages, the Bartlett test approved the homogeneity of variances, so then I ...
1 vote
43 views

### Feasible GLS estimator

I'm approaching for the first time GLS estimators. Suppose that $\operatorname{Var}(u|x)=\sigma^2 h(x)$, where $h(x)$ is some function of the explanatory variables that determines the ...
221 views

### Relevance of the homoscedasticity assumption

I understand that the homoscedasticity assumption is one of the Gauss Markov assumptions to get a BLUE estimator. Why is homoscedasticity crucial for justifying the usual t and F statistics?
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### How do coefficients change in a weighted least squares regression?

We regress $Y$ on categorical data $X_i,\ i=1,\ldots,\ p$. Suppose this is a large dataset and many of the rows of the design matrix are duplicated. We minimize the dataset as follows: We average $Y$ ...
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### How to perform a multifactor ANOVA with heterocedastic data

I am analyzing a set of data of two factors, one at three and other at seven levels, to check how they influence my response variable. However, when testing the ANOVA assumpions it results it follows ...
855 views

### Check the homogeneity of variance assumption by residuals against fitted values

I am studying this source about One-Way ANOVA Test in R. We know that ANOVA test assumes that the data is normally distributed and the variance across groups are homogeneous. In the source the claim ...
1 vote
66 views

### Why would bootstrap OLS standard errors differ from ML estimate?

Let's say I have a regression dataset (paired x and y) such that the response variable (y) has an unknown distribution (but definitely not Gaussian) and is large enough such that the central limit ...
128 views

### Dealing with violation of linear regression assumptions

I have a data set where some extreme, but not nonetheless important observations are present which prompts violation of the linear regression assumptions of normality and constant variance. The ...
49 views

### Testing assumptions for repeated measures ANOVA

I was wondering how to assess residual normality of a repeated measures ANOVA. In some threads, users refer to Venables and Ripley: Residuals in multistratum analyses: Projections and recommend to ...
61 views

### Can't fix non-normality and heteroskedasticity

I am attempting, via linear regression, to model a dataset.I've tried various transformations on the response/ and predictors, as well as WLS but the assumptions are not met. I'm looking for the ...
1 vote
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### How to produce a synthetic dataset demonstrating heteroskedasticity?

Consider a hypothetical world in which only three variables exist: X, Y and Z. X causes Y, but Z also causes X and Y (refer below). Assume that this model is complete, and no others factors exist in ...
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### Disagreement between studentized Breusch-Pagan test and the plots "residuals vs fitted" and "scale location"

Given the model: > Durée <- c(6, 5, 3.5, 3, 5, 3, 2, 8, 2.5) > Note <- c(18, 16, 14, 10, 15, 13, 8, 19, 12) > model <- lm(Note ~ Durée) I was ...
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### Testing for Homoscedasticity and Independence of Residuals

I ran a multiple linear regression model for a study where I try to predict different companies' emission levels using a few predictors. Two of my predictors are categorical and I performed one hot ...
21 views

### Why are standard errors smaller when spread of the residuals is larger at higher values of the predictor variable

I learned that heteroskadiscity causes the standard errors to be biased and if the residuals are larger at higher values, then the standard errors will be underestimated. But I am still having a hard ...
1 vote
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### How to interpret scatterplot to test linearity b/w covariate and DV?

I'm doing an ANCOVA on a fictitious dataset of math test results (DV) by group (n1 = 50 online training; n2 = 50 no training) with previous math ability as a (covariate) to see if there is a ...
1 vote