Questions tagged [heteroscedasticity]

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

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18 views

Can we objectively determine whether assumptions have been violated in R?

I'm testing statistical assumptions in R and so far I've been using plot(model, which = c(1:6)), which produces six graphs for linearity, normality of errors, ...
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39 views

Is there a way to think about conditional vs unconditional heteroskedasticity graphically?

I find I understand concepts much better with the aid of charts/visualizations. I'm struggling to intuitively understand how one would be able to see whether error terms are correlated or not to the ...
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30 views

Residual standard error in GLS models

I am conducting a "residual analysis" in R (essentially an adapted Event Study), where I aim to use the RSE to construct a residual confidence interval to identify "outlier" ...
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1answer
29 views

White-Test: Use F-Statistic or LM-statistic?

to interpret the White-Test, it is recommended to use the LM-statistic = N*R-squared of the auxiliary regression which follows a Chi-squared distribution with df = number of restrictions. But I ...
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9 views

Which comes first: missing value imputation or homogeneity adjustment?

I am analyzing several rainfall timeseries with less than 5% missing values. I performed Standard Normal Homogeneity Test (SNHT) while ignoring the missing values. However, the rainfall timeseries are ...
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1answer
35 views

Modelling conditional coefficient of variation

Suppose we have 10,000 test tubes containing variable concentrations of some chemical. The aim is to use measurements of their chemical contents to characterise the measurement imprecision of a ...
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11 views

Which test to use to test for heteroscedasticity in a non linear model/fit?

I would like to test for heteroscedasticity in a non linear fit. I have a explanatory vector x and an explained variable y and ...
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18 views

Heteroscedasticity or not

I run a GLM model with a body condition as a continuous response variable. I included in the model on the explanatory side Pb concentrations (logged continuous variable), Age (2 levels), Sex (2 levels)...
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1answer
29 views

Additive Mixed Models: residual check for count response variable

Hi, The response variable is the count of daily number of physician visits of one specific disease.(y usually has the value for example of 4,5,6,10...,26). A standardized residual plot is produced ...
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Linear regression to predict both mean and SD of dependent variable

Imagine we were to investigate the relationship between people's annual income and daily food expenditure in a fictional population. The following example is not meant to be realistic, but hopefully ...
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9 views

Quantify heteroscedasticity of variances

I have a large dataset (101952 data points) where the response variable is sound pressure level (SPL) and the explanatory variables are mean number of boats (continuous) and frequency (Fc; categorical)...
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10 views

Weighted clustered standard errors

I am thinking about a weighted clustered standard error with heteroskedasticity. The estimate can be calculated as follows: \begin{equation} \begin{split} \hat{\beta} &= \left(\sum_g X_g'W_gX_g\...
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How to use the gamma distribution to induce heteroskedasticity in the errors of a linear model

Suppose for $Y\in\mathbb{R}^n$, $X\in\mathbb{R}^{n\times p}$, $\beta\in\mathbb{R}^p$ and $\epsilon\in \mathbb{R}^n$, we have the linear model \begin{equation} Y=X\beta +\epsilon,\quad \epsilon\sim N(0,...
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For residual vs. fitted plot in mixed Anova, do I include random effect?

I am doing a mixed ANOVA with one dependent variable: species richness one within-subject factor: Years (dry/wet year) one between-subject factor: Grazing intensity (no/little/moderate grazing) I am ...
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15 views

What kind of parametric test to use to find difference in distribution for two Heteroskedastic sample?

I was analysing Titanic Dataset, and I have to answer this question: Is there a significant difference in Age distribution between those who survived and those who did not? Given: N1=865, N2=430 Both ...
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1answer
24 views

Properties of OLS estimator for overlapping observations' regression

I am running regressions of long-horizon gross financial returns $$R_{t+k} = \prod_{i=1}^{k} R_{t+i}$$ where $R_t=1+r_t$, on current dividend-price ratios $DP_t=\frac{D}{P}_t$: $$R_{t+k}=\alpha +\beta ...
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1answer
34 views

How to perform F-test in R for checking equality-of-variance (homoscedasticity/heteroscedasticity) if raw data is not given?

In a typical two-sample problem scenario, I possess the sample mean, variance, and size, but not the raw data for samples drawn from two populations. I wish to perform the F-test to check equality of ...
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1answer
112 views

Unbiasedness of Covariance Matrix Estimator in OLS

I want to prove that $V$ is an unbiased estimator of the covariance matrix $$(X'X)^{-1}(X'DX)(X'X)^{-1},$$ where $D=diag(\sigma^2,...,\sigma^2)=E(ee'|X)$ in a linear model. $$V = \frac{n}{n-k}(X'X)^{-...
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Citing levene's test statistic for 1-way ANOVA with likert-scale variables

I am running a 1-way ANOVA on a set of two variables where the d.v. is a survey output with the satisfaction scale from 1-4 and i.v. is the education level of respondents on a similar 4 category scale....
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1answer
28 views

ANCOVA by SPSS with outliers and non-homogeneity

I’m working on ANCOVA to compare post- vs. pre-treatment percentage change of a blood test value, L, between 10 groups (10 dosages from 3 drugs all of which can lower L), with the pre-treatment (...
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19 views

Should I check if the problems(i.e. autocorrelation and heteroskedasticity) were overcome by using "NeweyWest()"?

Please help me, because I can't resolve the following problems by myself. Model: reg_lm <- lm(Y~A+B+C, data=Data1) In the above model, there are two problems to ...
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1answer
57 views

Heteroskedastic time series outlier analysis using machine learning

Is anyone aware of machine learning models that are able to deal with heteroskedasticity in time series, when trying to detect outliers? There are a lot of anomaly detection tools out there (like k-...
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24 views

Generalised least squares regression when variance and regression is heteroscedastic

I am trying to model a continuous response variable using a categorical grouping variable and a continuous covariate. The data looks like this, and there are the same number of data points in each ...
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28 views

Difference between Welch's and Satterthwaite's approximations

Stata's ttest command has two options for approximating the degrees of freedom when performing t-tests between two groups with unequal variances. One uses Welch's 1947 approximation, the other using ...
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2answers
74 views

is there any non parametric Welch's ANOVA?

I need to test for differences between non-normally distributed and heteroscedastic data. I know that I can use the Kruskal-Wallis test to assess significant differences between groups but one ...
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15 views

Calculating Generalised Least Squares Manually

I would like to know how to estimate the error-covariance matrix in order to manually calculate a Generalised Least Squares model. Based on Wikipedia and this paper: https://www.uh.edu/~bsorense/...
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26 views

Autocorrelation Correction to Covariance

This is a follow-up to my previous question about autocorrelation impact on estimation of statistical quantities. I want to estimate covariance matrix and Pearson's correlation matrix for stationary ...
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1answer
75 views

How does data that violates linear regression assumptions (of the residuals) look?

Linear regression has two assumptions about the residuals : The residuals should have constant variance (for every level of the predictor). The residuals should follow a normal distribution. Is it ...
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24 views

Weighted least square regression - different ways of estimating weights

Newbie here. I have a question regarding WLS regression. Specifically, I've come across different ways of estimating weights in WLS regression, the most frequent ones being: ...
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2answers
20 views

Heteroscedasticity in synthetic control methods

A reviewer asked me: to what extent the empirical method (Syntethic Control Method) controls for potential heteroskedasticity problems according to the problem under analysis? The problem under ...
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2answers
51 views

Linear mixed effect model - heteroskedascity interpretation

I have a dataset with speed difference between men and women on several race distance. The data structure look like this. ...
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45 views

Heteroskedasticity: conditional or unconditional - a (critical?) distinction yet adjective ignored

In non-time series, regression models when we say "heteroskedasticity" we almost always refer to "conditional heteroskedasticity". For example, the Breusch-Pagan test is a test for ...
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How do I confirm that HC3 has fixed Heteroscedasticity?

My data is heteroscedastic and cannot be remedied with transformations (I tried boxcox to no avail). I've recently found out about HC3 but am unsure about its effectiveness, as I've run a breusch-...
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23 views

Heteroskedasticity test R()

I am a bit confused after doing 1 exercise in R where it was required to perform a heteroskedasticity test on the estimated model. For completeness after doing the bptest and ncvTest I made a plot of ...
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26 views

Heteroscedasticity due to skewness of predictor(s)

I read that in a linear model skewness of one of the independent variables can be the reason for heteroscedasticity in the model but I can't think of (or create) an example where this would be the ...
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1answer
84 views

Implications of fitting an ARIMA model with constant variance to a process with nonconstant variance

Hamilton (page 657) in Time Series Analysis warns that a variance that changes over time has implications for the validity and efficiency of statistical inference about the parameters in an AR(p) ...
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2answers
89 views

Calculating parameters from non linear regression of sum of exponentials

I am attempting to fit some data that seems to follow an equation that is the sum of two exponentials. When fitting with a single exponential the residual histogram is not normally distributed. The ...
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1answer
71 views

Interpretation of the Breusch-Pagan bptest () test in R

I am a little confused regarding the interpretation of the Breusch-Pagan bptest () test in R. Thus, a p-value below 5% would mean that homoskedasticity is present and thus in turn reject null ...
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22 views

Which design one-way ANOVA or 2-way ANOVA using SPSS?

I have 2 drugs A & B with different 6 concentrations and for both drugs, at a specific concentration, the result is recorded (3 replicas), so I am confused. I have tried 2-way ...
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13 views

Heteroskedasticity in Survey-Weighted Linear Probability Model

I am estimating regression models with data of a complex-design survey in R. I understand that I have to use survey weights for this in order to adjust standard errors, or at least compare the results ...
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29 views

Correcting for Heteroscedasticity in multiple imputed datasets

I have a question regarding the homogeneity of variance in three regression models of diffrent datasets belonging to the same multiple imputed data. As I used multiple imputation I have to check ...
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22 views

Problems with VAR: Autocorrelation when imposing restrictions, ARCH effects and non-normality at all times

I am estimating a VAR model for log-returns of: copper prices, USD/local currency exchange rate, and the local stock market index. Using VARselect I estimated a VAR(...
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Analyzing heteroscedasticity in linear model with a residual and probability plot?

I'm analyzing the residual of a linear regression that I did and when plotting the residual it shows a funnel, but I'm not sure if this funnel is due to heteroscedasticity or because I have fewer ...
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66 views

heteroskedasticity of surrogate residuals for ordinal logisitic regression

I am fitting a ordinal logistic regression. The real model is multivariate, but I am using a bivariate version for simplicity in this question. Most references I have seen do not list ...
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1answer
60 views

Crossed-random effects model: linear heteroscedasticity

we conducted a study in which two groups from different populations (both n = 25) were instructed to rate the symmetry (visual analogue scales, 0 to 100) of 50 different faces in randomised order each....
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1answer
73 views

Do my results suggest the assumption of homoscedasticity was violated?

I ran a multiple regression with 16 predictors and did assumption testings. I am not sure if my graph shows homoscedasticity, I googled and the information that I have gathered suggests that my data ...
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25 views

Better to solve heteroskedasticity by diffing time steps or by adding variables?

Trying to learn stats on my own and I came across a problem that asked if it better to solve heteroskedasticity by taking the difference between time steps, by adding a variable, or by adding a lag. ...
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18 views

Improving clusters with little observations

I am trying to cluster a small dataset of nearly 400 observations. For this, I first tried kmeans. After tunning the number of clusters I got: Then, in order to account for noise, I tried DBSCAN. ...
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29 views

What statistical tests should i use if both normality and homogenity of distribution assumptions were violated?

my (quantitative) data are divided into 4 groups: T0, n = 415 T1, n = 93 T2, n = 74 T3, n = 51 *NOTICE THE DIFFERENT GROUP SIZES! I wish to compare between the groups. Usually ANOVA would fit, however,...
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22 views

How do I write the Jeffreys prior for error variance in stan? p(mu, sigma1^2, ... , sigmaC^2) propto Prod{ sigmai^-2 }

I need to model the Jeffreys prior for error variance in a heteroscedastic ANOVA design in rstan. That is to say, $\pi(\mu,\sigma_1^2,\dotsb,\sigma_C^2)\varpropto\Pi_{i=1}^{C}\sigma_i^{-2}$. Is the ...

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