# Tagged Questions

Refers to the property of a random process to have non-constant variance along some continuum. This most commonly presents in regression where the error variance increases as a function of one or more predictors, but also commonly refers to a time series whose variance changes over time.

781 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 ...
657 views

### Homogeneity of variance in regression

I have carried out simple linear regression and I am now checking the models meets the assumption of homogeneity of variance: • am I correct in concluding that the Levenes tests which gave a ...
136 views

### Comparing model fit with heteroscedastic data

I am developing a physiological test using R that requires some parameters optimised. In comparing the new method against the existing method, the values of individual readings correlate in a linear ...
1k views

### Comparing the means of two time series

I have data sets of the returns of two indexes in the same market (two different sets of stocks constituting each index), with 496 observations for each. I want to compare if the means are ...
251 views

### Checking assumptions of regression - homogeneity of variance

I have made 9 models using simple linear regression. I'm now checking that each of models meets the assumption of homogeneity of variance. Each of the models used either categorical or numeric (year ...
431 views

### Do these residual plots indicate that my least squares regression coefficient estimates may be biased?

Lets say I have a linear regression: $$y \sim 1 + x_1+x_2$$ where the range of $x_2$ is $[0,10]$. I fit this model using lm or ...
667 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 ...
844 views

### Non-normal and heterogeneous data with repeated measures ANOVA

I have run a repeated measures ANOVA using 3 groups and one factor with two levels. I have discovered that the data are not normally distributed (but not badly), nor is the variance homogeneous in ...
127 views

### Modelling both mean and dispersion of count data

I have a model of the following form: $P(Y \mid X) = \,D(\mu,\sigma^2) ~~\text{where}$ $\mu = f(X) ~~\text{and}~~ \sigma^2=g(X)$ where $y$ is the response vector of count data, $X$ is the predictor ...
172 views

### Linear regression with shot noise

I'm looking for the right statistical terminology to describe the following problem. I want to characterize an electronics device that has a linear response $Y = \beta_0 + \beta_1 X + \epsilon$ ...
263 views

### How to check and correct heteroskedasticity in a multilevel model?

I've conducted an experiment in which we have registered a physiological measure (FR) of 30 participants in two different conditions. In each condition, I registered the measure in 20 time points, ...
506 views

### Are significance tests for the assumption of constant variance too strict when sample size is large?

My question is regarding linear regression and non-constant variance. I've heard that even though a large data set fails a normality test, this does not necessarily mean the data is not normal. This ...
111 views

### Estimating standard error of related regressions in R

I am working with regressions to understand the price creation of certain future contracts for commodities and try to explain it with other commodity pricese. These future contracts have different ...
7k 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 ...
846 views

### I want to do an nested ANOVA but my variances are very unequal

I have data that were collected at a number of sites, and each site was located within one of three zones (Lake Ontario, Erie and the St. Lawrence), so I was hoping to do nested ANOVAs to compare ...
680 views

### Understanding the homoscedasticity assumption

I can't understand how this works: $e$ is the error term and $x$ is the explanatory variable. $$Var(e|x) = E(e^2|x) - [E(e|x)]^2$$ I know that $[E(e|x)]^2$ = 0 because $E(e|x) = 0$, and squaring 0 ...
232 views

### Heteroskedasticity-consistent Standard Errors for Difference Between Two Populations?

This is a homework question, so I am looking for help in getting the right idea so that I can execute the rest of the work on my own. I have some data regarding military veteran status and ...
363 views

### Does a stationary process implies a normal distribution of the data?

My understanding is 'no', a stationary process does not imply a normal distribution of the data. However I haven't found a clear indication in my library or online. I am interested in other resources ...
441 views

### Heteroskedasticity, autocorrelation robust standard errors for SPSS

Is there a way of performing HAC robust standard errors in SPSS?
184 views

### Isn't a test for cointegration the same as testing for heteroskedasticity in the residual error terms?

Testing for cointegration tests to see if the residuals from a regression between the two variables is a stationary process. So wouldn't a test on those residuals for heteroskedasticity be the same ...
2k 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 ...
559 views

### Can I use generalised least squares with a binomial distribution and a nested structure?

I'm trying to fit linear models to my data in R. I need to use a generalised least squares method as I have heterogeneity of variance in one of my variables. I was planning to use varIdent, as the ...
1k 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: ...
1k views

### On testing for heteroskedascity, some questions on the White test & Breusch-Pagan test

Isn't the test statistic for both tests identical? The only difference I see is that the alternative hypothesis is different. Since you don't need to know the function h in the Breusch-Pagan test, ...
861 views

### Heteroskedasticity in linear regression model & data transformation

pls correct me if i'm wrong. of the econometrics' literature i've read so far, most mentioned heteroskedasticity is not a major problem empirically but multicollinearity would pose a greater concern ...
563 views

### Help using maxFratio() in R (Hartley's test)

I found documentation at: http://hosho.ees.hokudai.ac.jp/~kubo/Rdoc/library/SuppDists/html/maxFratio.html I am not sure how really to use this though and am coming up short finding help online. If ...
432 views

### Why does the Breusch-Pagan test fail?

How Breusch-Pagan can't reject the null for a series like that? ...
118 views

### How to test homoscedasticity when the errors are DEPENDENT?

I have done a linear regression and plot the residuals. I noticed that the errors are dependent(autocorrelated), how could I test homoscedasticity of this series? I read that Breusch-Pagan test only ...
128 views

### How should I fit heteroskedasticity by group?

I am trying to fit panel data to a model of the form $$y_{t,i} = \sum_{j} X_{t,i,j} \beta_j + \sum_k Z_{t,i,k} \gamma_{i,k} + \sigma_i \epsilon_{t,i},$$ where the regressors $X$ and $Z$ are observed ...
106 views

### Why to use fixed regressor in Breusch-Pagan?

I need to use Breusch-Pagan to check heteroscedasticity of my timeseries. I found the explanation of the function, here: http://hosho.ees.hokudai.ac.jp/~kubo/Rdoc/library/lmtest/html/bptest.html ...
287 views

### Are HAC estimators used for estimation of regression coefficients?

The references I can find on HAC procedures (like Newey-West) in regression focus on the standard error of the estimated regression coefficients and hypothesis testing involving the same. I cannot ...
201 views

### Is there a method to check the homogeneity of variance of a single time series?

I have a data frame with prices/dates, is there a method that checks if the variance is homogeneous during all the series? I know there are many test like fligner.test, bartlett.test but I need to ...
97 views

### Does it make sense to regress the residuals with rep(0, N) vector?

I need to use Breusch-Pagan test, to check whether two series are homoscedastic. First I calculate the residuals of two lists of prices after [...] and then I test residuals for homoscedasticity. My ...
501 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 ...
343 views

### Heteroscedastic test does not solve the problem

As my previous questions I'm trying to solve a problem with my stocks tests. I tried Breusch-Pagan test for heteroscedasticity but some residuals still pass these tests. My procedure is: Get two ...
2k views

### Testing homoscedasticity with Breusch-Pagan test

In these days I'm working with Breusch-Pagan to test homoscedasticity. I've tested the prices of two stocks with this method. This is the result: ...
399 views

### Why the Breusch-Pagan test fails if I set the intercept to zero?

I'm using bptest function of lmtest package to use Breusch-Pagan test. I get a strange result, doing the follow: ...
9k views

### Autocorrelation and heteroskedasticity in panel data

In the research, both autocorrelation and heteroskedasticity are detected in panel data analysis. I can solve them separately in stata with command "xtregar" and "robust", respectly. However, I cannot ...
1k views

### Kruskal-Wallis or Fligner test to check homogeneity of variances?

I have a doubt, I need to check the homogeneity of variances on the residuals of a linear regression. I read that Kruskal is also good without assuming a normal-distribution. But I don't know if it's ...
430 views

### Model errors, residuals and heteroscedasticity

I have a quick question about the correct way to describe variance functions when seeking to cope with heteroscedasticity. As I understand it the statistical error of a model represents the departure ...
427 views

### How can these residuals have homogeneity of variances?

I'm testing the Homogeneity of Variances with Fligner-Killeen test using the function fligner.test in stats On the chart below I have plotted the residuals that pass this test ...
196 views

### Inference in linear model with conditional heteroskedasticity

Suppose I observe independent variable vectors $\vec{x}$ and $\vec{z}$ and dependent variable $y$. I would like to fit a model of the form: y = \vec{x}^{\top}\vec{\beta_1} + \sigma ...
3k views

### Why is the Breusch-Pagan test significant on simulated data designed not to be heteroscedastic?

I'm testing the residuals of a linear regression using Breusch-Pagan Test to detect Heteroscedasticity. This is the plot of the residuals: and this is the R code: ...
266 views

### ANOVA for non-normal heterogenous unequally replicated data

I need some advice on how to proceed with my data analysis. I have 3 groups (Archaea, Bacteria and Eukarya). Each group has unequal number of individual species (70, 651, and 244 respectively). Each ...
189 views

### Two-sample t-test / ANOVA on functions, with unequal variances

Suppose $N$ experiments can be made in varying conditions. Each of them yields an estimate $f_i$ of a continuous (and, if necessary, positive) function of x over some interval. Experiment $i$ is ...
6k views

### Linear regression, heteroscedasticity, White's test interpretation?

I am trying to test whether my regression has an issue of heteroscedasticity. After running a regression, I can clearly see that the residual plot has a pattern. After taking a log of the dependent ...
5k 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 ...
261 views

### Measuring homogeneity across different spatial aggregations of data

I'm working with dataset of individual households that I aggregate into 'areas' using several different spatial configurations, from smaller to bigger. These areas are then characterized by four ...