Questions tagged [heteroscedasticity]

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

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55
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2answers
116k views

What does having “constant variance” in a linear regression model mean?

What does having "constant variance" in the error term mean? As I see it, we have a data with one dependent variable and one independent variable. Constant variance is one of the assumptions of linear ...
47
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7answers
32k views

When conducting a t-test why would one prefer to assume (or test for) equal variances rather than always use a Welch approximation of the df?

It seems like when the assumption of homogeneity of variance is met that the results from a Welch adjusted t-test and a standard t-test are approximately the same. Why not simply always use the Welch ...
42
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1answer
41k views

Alternatives to one-way ANOVA for heteroskedastic data

I have data from 3 groups of algae biomass ($A$, $B$, $C$) which contain unequal sample sizes ($n_A=15$, $n_B=13$, $n_C=12$) and I would like compare if these groups are from the same population. One-...
35
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5answers
7k views

Why are there two spellings of “heteroskedastic” or “heteroscedastic”?

I frequently see both the spellings "heteroskedastic" and "heteroscedastic", and similarly for "homoscedastic" and "homoskedastic". There seems to be no difference in meaning between the "c" and the "...
29
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5answers
26k views

What are the dangers of violating the homoscedasticity assumption for linear regression?

As an example, consider the ChickWeight data set in R. The variance obviously grows over time, so if I use a simple linear regression like: ...
27
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2answers
61k views

How do you find weights for weighted least squares regression?

I am a bit lost in the process of WLS regression. I have been given dataset and my task is to test whether there is heteroscedascity, and if so I should run WLS regression. I have carried out the ...
24
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1answer
31k views

Why Levene test of equality of variances rather than F ratio?

SPSS uses the Levene test to evaluate homogeneity of variances in the independent group t-test procedure. Why is the Levene test better than a simple F ratio of the ratio of the variances of the ...
23
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3answers
16k views

Regression modelling with unequal variance

I would like to fit a linear model (lm) where the residuals variance is clearly dependent on the explanatory variable. The way I know to do this is by using glm with the Gamma family to model the ...
23
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4answers
35k views

Best way to deal with heteroscedasticity?

I have a plot of residual values of a linear model in function of the fitted values where the heteroscedasticity is very clear. However I'm not sure how I should proceed now because as far as I ...
23
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1answer
12k views

Sandwich estimator intuition

Wikipedia and the R sandwich package vignette give good information about the assumptions supporting OLS coefficient standard errors and the mathematical background of the sandwich estimators. I'm ...
22
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2answers
27k views

Transforming proportion data: when arcsin square root is not enough

Is there a (stronger?) alternative to the arcsin square root transformation for percentage/proportion data? In the data set I'm working on at the moment, marked heteroscedasticity remains after I ...
21
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4answers
13k views

Practically speaking, how do people handle ANOVA when the data doesn't quite meet assumptions?

This isn't a strictly stats question--I can read all the textbooks about ANOVA assumptions--I'm trying to figure out how actual working analysts handle data that doesn't quite meet the assumptions. I'...
21
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6answers
55k views

Always Report Robust (White) Standard Errors?

It has been suggested by Angrist and Pischke that Robust (i.e. robust to heteroskedasticity or unequal variances) Standard Errors are reported as a matter of course rather than testing for it. Two ...
18
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2answers
36k views

How to run two-way ANOVA on data with neither normality nor equality of variance in R?

I am working on my master thesis at the moment and planned on running the statistics with SigmaPlot. However, after spending some time with my data I came to the conclusion that SigmaPlot might not be ...
18
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1answer
7k views

MLE vs least squares in fitting probability distributions

The impression that I got, based on several papers, books and articles that I've read, is that the recommended way of fitting a probability distribution on a set of data is by using maximum likelihood ...
17
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2answers
37k views

How do I interpret this fitted vs residuals plot?

I don't really understand heteroscedasticity. I would like to know whether my model is appropriate or not according to this plot.
17
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2answers
13k views

Explanation for non-integer degrees of freedom in t test with unequal variances

The SPSS t-Test procedure reports 2 analyses when comparing 2 independent means, one analysis with equal variances assumed and one with equal variances not assumed. The degrees of freedom (df) when ...
16
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3answers
37k views

Alternative to One-way ANOVA unequal variance

I would like to compare the means across three groups of equal sizes (equal sample size is small, 21). The means of each group are normally distributed, but their variances are unequal (tested via ...
16
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5answers
4k views

Checking ANOVA assumptions

A few months ago I posted a question about homoscedasticity tests in R on SO, and Ian Fellows answered that (I'll paraphrase his answer very loosely): Homoscedasticity tests are not a good tool ...
16
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2answers
5k views

Measures of residuals heteroscedasticity

This wikipedia link lists a number of techniques to detect OLS residuals heteroscedasticity. I would like to learn which hands-on technique is more efficient in detecting regions affected by ...
16
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2answers
28k views

How to perform residual analysis for binary/dichotomous independent predictors in linear regression?

I am performing the multiple linear regression below in R to predict returns on fund managed. reg <- lm(formula=RET~GRI+SAT+MBA+AGE+TEN, data=rawdata) Here ...
15
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1answer
8k views

Is bootstrapping standard errors and confidence intervals appropriate in regressions where homoscedasticity assumption is violated?

If in standard OLS regressions two assumptions are violated (normal distribution of errors, homoscedasticity), is bootstrapping standard errors and confidence intervals an appropriate alternative to ...
15
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1answer
3k views

Comparison between Newey-West (1987) and Hansen-Hodrick (1980)

Question: What are the main differences and similarities between using Newey-West (1987) and Hansen-Hodrick (1980) standard errors? In which situations should one of these be preferred over the other? ...
15
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3answers
1k views

Predicting variance of heteroscedastic data

I am trying to do a regression on heteroscedastic data where I'm trying to predict the error variances as well as the mean values in terms of a linear model. Something like this: $$\begin{align}\\ y\...
14
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2answers
14k views

Why does sphericity diagnosed by Bartlett's Test mean a PCA is inappropriate?

I understand that Bartlett's Test is concerned with determining if your samples are from populations with equal variances. If the samples are from populations with equal variances, then we fail to ...
13
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1answer
8k views

Calculate Newey-West standard errors without an lm object in R

I asked this question yesterday on StackOverflow, and got an answer, but we agreed that it seems a bit hackish and there may be a better way to look at it. The question: I would like calculate the ...
12
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2answers
15k views

Heteroskedasticity and residuals normality

I have a linear regression that's quite good, I guess (it's for a university project so I don't really have to be super accurate). Point is, if I plot the residuals vs. predicted values, there is (...
12
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2answers
12k views

Bartlett's test vs Levene's test

I am currently trying to address violations to ANOVA assumptions. I have used Shapiro-Wilk to test normality, and have dabbled with both Levene's test and Bartlett's test of variance equality. I have ...
12
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1answer
9k views

Conditional homoskedasticity vs heteroskedasticity

From Econometrics, by Fumio Hayashi (Chpt 1): Unconditional Homoskedasticity: The second moment of the error terms E(εᵢ²) is constant across the observations The functional form E(εᵢ²|xi) is ...
12
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1answer
586 views

Visualizing many left-skewed distributions

I have a series of left-skewed/heavy tailed distributions that I would like to show. There are 42 distributions across three factors (labeled as A, ...
11
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2answers
4k views

What is the Bayesian counterpart to a two-sample t-test with unequal variances?

I am looking for the bayesian counterpart of the two-sample t-test with unequal variances (the Welch test). I am also looking for a multivariate test, like Hotelling's T statistic. References ...
11
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3answers
36k views

Interpretation of the p-values produced by Levene's or Bartlett's test for homogeneity of variances

I have run Levene's and Bartlett's test on groups of data from one of my experiments to validate that I am not violating ANOVA's assumption of homogeneity of variances. I'd like to check with you guys ...
11
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2answers
6k views

How to get ANOVA table with robust standard errors?

I am running a pooled OLS regression using the plm package in R. Though, my question is more about basic statistics, so I try posting it here first ;) Since my regression results yield ...
11
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2answers
15k views

Test of independence vs test of homogeneity

I am teaching a basic statistics course and today I will cover the chi-squared test of independence for two categories and the test for homogeneity. These two scenarios are conceptually different, but ...
11
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2answers
9k views

Residual Diagnostics and Homogeneity of variances in linear mixed model

Before asking this question, I did search our site and found a lot of similar questions, (like here, here, and here). But I feel those related questions were not well responded or discussed, thus ...
11
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2answers
171 views

Estimate The Rate At Which Standard Deviation Scales With An Independent Variable

I have an experiment in which I am taking measurements of a normally distributed variable $Y$, $$Y \sim N(\mu,\sigma)$$ However, previous experiments have provided some evidence that the standard ...
10
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3answers
16k views

What are the consequences of having non-constant variance in the error terms in linear regression?

One of the assumptions of linear regression is that there should be a constant variance in the error terms and that the confidence intervals and hypothesis tests associated with the model rely on this ...
10
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3answers
26k views

Linear model Heteroscedasticity

I have the following linear model: To address the residuals heteroscedasticity I have tried to apply a log transformation on the dependent variable as $\log(Y + 1)$ but I still see the same fan out ...
10
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2answers
7k views

When to use (non)parametric test of homoscedasticity assumption?

If one is testing assumption of homoscedasticity, parametric (Bartlett Test of Homogeneity of Variances, bartlett.test) and non-parametric (Figner-Killeen Test of ...
10
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2answers
9k views

Simulate linear regression with heteroscedasticity

I am trying to simulate a dataset that matches empirical data that I have, but am unsure how to estimate the errors in the original data. The empirical data includes heteroscedasticity, but I am not ...
10
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3answers
350 views

What is this bias-variance tradeoff for regression coefficients and how to derive it?

In this paper, (Bayesian Inference for Variance Components Using Only Error Contrasts, Harville, 1974), the author claims $$(y-X\beta)'H^{-1}(y-X\beta)=(y-X\hat\beta)'H^{-1}(y-X\hat\beta)+(\beta-\hat\...
10
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3answers
47k views

Spearman's or Pearson's correlation with Likert scales where linearity and homoscedasticity may be violated

I am wanting to run correlations on a number of measurements where Likert scales were used. Looking at the scatterplots it appears the assumptions of linearity and homoscedasticity may have been ...
10
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2answers
12k views

What is the difference between these two Breusch-Pagan Tests?

Using R on some data and trying to see whether or not my data is heteroscedastic, I've found two implementations of the Breusch-Pagan test, bptest (package lmtest) and ncvTest (package car). However, ...
10
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2answers
22k views

How do I interpret the results of a Breusch–Pagan test?

In R I can perform a Breusch–Pagan test for heteroscedasticity using the ncvTest function of the ...
10
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3answers
8k views

Conceptual distinction between heteroscedasticity and non-stationarity

I'm having trouble distinguishing between the concepts of scedasticity and stationarity. As I understand them, heteroscedasticity is differing variabilities in sub-populations and non-stationarity is ...
9
votes
2answers
11k views

Will log transformation always mitigate heteroskedasticity?

Will log transformation always mitigate heteroskedasticity? Because the textbook states that log transformation often reduces the heteroskedasticity. So, I want to know in which cases it won't lessen ...
9
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3answers
4k views

Advice on explaining heterogeneity / heteroscedasticty

I am looking for any help, advice or tips in how to explain heterogeneity / heteroscedasticity to biologists in my department. In particular I want to explain why its important to look for it and deal ...
9
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2answers
314 views

How do residuals relate to the underlying disturbances?

In the least squares method we want to estimate the unknown parameters in the model: $$Y_j = \alpha + \beta x_j + \varepsilon_j \enspace (j=1...n)$$ Once we have done that (for some observed ...
9
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3answers
16k views

statistical test to see if relationship is linear or non-linear

I have an example data set as follows: ...
9
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2answers
1k views

Is OLS Asymptotically Efficient Under Heteroscedasticity

I know that OLS is unbiased but not efficient under heteroscedasticity in a linear regression setting. In Wikipedia http://en.wikipedia.org/wiki/Minimum_mean_square_error The MMSE estimator is ...

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