# 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.

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### Implementing Pettitt test in R

I'm trying to implement Pettitt test in R following papers like this pdf (pp. 5 & 6), or this pdf. But, I'm misunderstanding something, because having tested it with some data, I think that output ...
59 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 ...
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### Finding structural breaks in heteroskedastic time series

I'm trying to identify structural breaks in the movement of reserve currencies. I'm not yet all that versed in the finer details of time series, but I've been reading up on ARCH and GARCH estimators. ...
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### Does the sandwich estimator in GEE protect against both correlation misspecification and heteroscedasticity?

The relative merits of GEE with exchangeable correlation or GEE with independence and the sandwich estimate have been discussed, but I couldn't find a post specifically addressing my question. I have ...
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### Inspecting assumption of homoscedasticity

Using a Fligner test to infer about the respect of the assumption of homoscedasticity is not very smart given that the Fligner test tests to the null that there is no difference of variance between ...
25 views

### Fligner.test with R

Why does this: fligner.test(a ~ b + c + d, data=df) and this fligner.test(a ~ b + d, data=df) always equal for whatever ...
26 views

### Assumption violations with heteroscedastic data and OLS regression

I'm trying to model the typical performance of an experimental approach I've developed. I have a total of 3000 observations for 72 different case studies. My observations consist of a reading for ...
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### Anova. Homoscedasticity not respected

I'd like to perform an ANOVA with a normally distributed response variables and several explanatory variables. Some of the explanatory variables are continuous and some are categorical (factor(..)). ...
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### Correcting for heteroskedasticity in Logit fixed-effects model

I found out that my panel data 'suffers' from heteroscedasticity by doing the test described on Stata FAQ, Testing for panel-level heteroskedasticity and autocorrelation. I understand that the $H_0$ ...
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### Examples of Hetero- and Homoscedasticity with the Same Dependent Variable?

What are good examples to show that, even if a regression of $Y$ on $X$ is heteroscedastic, a regression of $Y$ on a different independent variable $Z$ could be homoscedastic? More formally, what are ...
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### Heteroscedasticity in the context of general additive model

For my given data (identity link), my target is to check a political variable, i.e., I intend to check, if a certain impact, given by some treatment at a certain time, affects the intercept and slope ...
8k 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 ...
113 views

### Compare means - heterogeneous variance, non-normal

I would like to perform some basic means comparisons (3 conditions, balanced, n = 21 for a total of 63 observations). The main dependent variable is total task completion time, i.e., the experimental ...
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### Fligner test in R, with several variables indicating the grouping

I have to run an multiple way Anova and want to test the assumption of homoscedasticity. How can I run a Fligner.test with several independent variables (variables indicating the grouping) with R? ...
38 views

### Negative Binomial Regression and Heteroskedasticity test

I am running a negative binomial regression in Stata and would like to know if I need to include the vce(robust) option in the model. I know the negative binomial ...
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### Quantifying homogeneity

I am hydrologist and I am looking for a solution for the following problem: Suppose that I have $k$ regions each yielding a sample of the same variable (e.g., annual peak flow) drawn from different ...
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### Forecasting in ARCH(1) models

I read this definition of an ARCH(1) model: $$r_{ลง}=\sigma_{t|t-1}\epsilon_{t}$$ $$\sigma^{2}_{t|t-1} = \omega + \alpha r_{t-1}^{2}$$ However, when it comes to forecasting the h-step-ahead variance, ...
435 views

### Heteroskedasticity, autocorrelation robust standard errors for SPSS

Is there a way of performing HAC robust standard errors in SPSS?
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### Heteroscedasticity-consistent F-test

Why is the F-test for overall significance (OLS regression analysis) invalid when residuals are heteroscedastic? Is there a way to calculate it in a consistent way under heteroscedasticity? Is there ...
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### How to do Univariate Heteroscedasticity Test

I just wanted to know how to do Heteroscedasticity Test on a Univariate Model? ex: an univariate autoregressive model ex: an univariate ARCH/GARCH model If it is possible, how does one do that in ...
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### if standard error that is heteroskedastic is corrected using E-views, does it become homoskedastic?

I am confuse to either use a t-statistic or white-robust-t test as t-statistic is for homoskedastic and white-robust-t is for heteroskedastic error. Which test should i use after data with ...
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### 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 ...
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### Does inference from a heteroskedasticity-consistent covariance matrix follow the t-distribution or the normal?

Background I'm currently looking into how reliable confidence intervals are on bounded scores (EQ-5D) and I compare regular asymptotic, robust and botstrap-based confidence intervals. The robust ...
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### How to detect heteroskedasticity for logit panel regression in Stata?

I am currently conducting research with binary logistic regression of panel data. For now, I am planning to conduct the specification test with linktest, goodness ...
101 views

### Weighted least squares to correct for heteroscedasticity

I would like to use a weighted least squares (WLS) regression to perform tests on heteroscedastic spatial data. Each data point represents the mean of some variable over an area, and the sample sizes ...
49 views

### Using GLS and weights to solve heterogeneity of variances?

Iโm fairly new to scientific significance testing and getting into the topic more and more. I have a multifactorial dataset with Respiration rate as response variable and Temperature and CO2 partial ...
188 views

### Heteroskedasticity - residual plot interpretation

I am plotting a residual plot to test for heteroskedasticity. The Breusch-Pagan test is significant and therefore I am suspecting there is evidence on heteroskedasticity. The question is: (a) How ...
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### Alternatives to ANCOVA when assumptions are violated

I am doing research on organisational change and looking at how certain types of change (e.g. closures of offices, layoffs, investment on activities/functions) have affected seven psychological ...
186 views

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

I have an example data set as follows: ...
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### Do methods based on trimmed means require homoscedasticity?

I understand (from Wilcox' book [1]) that methods using the trimmed means are robust to distributional assumptions. Do the methods (e.g. bwtrim, from the ...
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### Testing for equality of variance - with repeated measures?

I have 40 "subjects", each of them did 5 types of exams. The question I wish to test is if there is a difference in variance between the exams. That is, I would like to run something like a ...
563 views

### Newey-West t-statistics

I have a time-series which is autocorrelated by construction, and might be heteroscedastic. I have calculated the sample mean of this time-series, and would like to calculate the t-statistic ...
41 views

### Stationarity and homoscedasticity in break tests

Let me start by saying that I'm really not an expert in statistics/econometrics. Now to my questions: I have a data set containing weekly prices of a stock. I want to check whether a structural break ...
82 views

### Quantifying heterogeneity

I have been trying to quantify the heterogeneity of a given variable. I'd like to say that the distribution in calcite concentrations, for example, is more heterogeneous in one rock formation than ...
147 views

### Bootstrapped confidence intervals for the parameters of a linear model applied to multiply imputed data

I would like to construct CIs for $\beta$ in the linear model $Y = X\beta + \epsilon$ I observe $\{X', Y'\}$ which is $\{X,Y\}$ contaminated with values missing at random. $\epsilon$ is not Gaussian ...
426 views

### Several intraclass correlations (ICC) when modeling heterogeneous variances?

In a nested design (e.g., students in schools, ants in colonies, individuals in a species, leaves in a tree), ICC is defined as the proportion of variance among observations from the same subject ...
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### How to recover the underlying observations from the noisy ones using gaussian processes

I have some simulated experiments where I generate some samples with an exponential correlation function. I am assuming a spatial grid whose variables form a multivariate gaussian distribution with an ...
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### Confusion related to Gaussian Markov Random field

I was reading this paper related to Gaussian Markov Random field. I didn't get how they derived this equation from the standard multivariate gaussian distribution equation The multivariate gaussian ...
185 views

### Crises: ANOVA? Or: how to analyse non-normal, non-Homogeneity data with different group sizes?

I'm somewhat new the world of statistics, or at least it has been years since I last used it and basically the only program I know generally how to work with is SPSS. However, for my Master thesis I ...
130 views

### Questions on standard deviation of a time series

If the standard deviation of a economic time series is approximately proportional to its level, that is, the standard deviation is well expressed as a percentage of the level of the series, then the ...
37 views

### How to test for mean and variance both affected by a variable?

Suppose you observe $\left(x_i,y_i\right)$, where $y_i \sim \mathcal{N}\left(\mu_i,\sigma_i^2\right)$. There are a number of ways that the $\mu_i, \sigma_i$ might vary with $x_i$: If one suspected ...
145 views

### Hypothesis testing a location shift in heteroscedastic and non-normal data

How do I test for a "location shift" in something like the mean or median if the shape of the distribution has changed quite significantly between groups? Often an experimental intervention seems to ...
28 views

### What is the best way to control for within-group heterogeneity?

I have panel data with repeated measurements from households. There's likely heterogeneity within panels that I need to account for. I'm planning on using a Poisson regression, but I am not sure the ...
1k 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 ...
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### 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 ...
150 views

### Normality test and heteroskedasticity test violated in panel data

I have a panel data with 140 observations included from 280 and I want to perform a VAR analysis in Eviews. My data seems to fail the normality and the heteroskedasticity test and I am not sure if ...
128 views

### Nonlinear regression: heteroskedasticity and correlated residuals

I'm performing regression analysis of some data. I believe I have to use a non-linear model with the form $y = at^b + c$ where $t$ is time. A log transform won't linearize the data here because of the ...
32 views

### MCMC with heteroscedastic errors

I carried out an MCMC sampling using a Gaussian likelihood function:  -2\times\left\{-n \times \ln\left(\sqrt{(2 \times 3.14169)} -(n \times 0.5 \times \ln(sig_e)) -\frac {0.5} {sig_e} \times ...
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### Parametric segmented or piecewise regression with heteroscedastic errors

I am fitting longitudinal data with an increase in variance over time. The standard physiological model is a bi- or tri-linear model with variable breakpoints. The estimated parameters are used to ...
290 views

### Can I justify performing a two-way anova where data is normally distributed but has heterogeneous variances?

I'm an undergraduate psychology student currently finishing up my dissertation, but a few days ago, while going through my SPSS output, I realized my Levene's test is significant, but my data is ...