Questions tagged [heteroscedasticity]
Non-constant variance along some continuum in a random process, or varying between discrete groups
1,188 questions
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Bradley's liberal criterion
I'm reading an article where the authors utilized Bradley's liberal criterion to estimate the robustness of the F statistic in the context of post hoc tests.
The problem here is that they said the ...
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How to test for equal variances of correlated observations?
Let $r$ be a vector valued random variable with mean zero and variance $\Omega$.
Let $r_t$ denote a specific observation of $r$ at time $t$.
$\Omega$ is unknown but I have 2 estimates of it: $\Omega_a$...
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How to separate 2 variances from observed variance?
I have that I broke down to the following:
var(predicted_conc) = actual_conc*var1 + var2
Note that the random variable generators are independent, hence variance is added not standard deviation.
I run ...
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Variance-Covariance Matrix of the OLS Estimator vs OLS Estimator of the Variance-Covariance Matrix
Suppose a model $y = X\beta + e$ that is unbiased and consistent but has some sort of heteroscedasticity or autocorrelation, thus, $E(ee'|X)=\delta^2 \Omega$.
In the exercise that I'm currently trying ...
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How to correct for Hansen-Hodrick standard error as Campbell & Shiller (1991) using R?
I am trying to replicate the Campbell & Shiller (1991) paper using Brazilian data.
My data consists of the following. Each line is a triple $(n,m,t)$, where $n$ is the maturity of the bond, $m$ is ...
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How do you calculate the conditional heteroscedasticity $\mathrm{Var}\left( \epsilon |X=x \right) $in a logit model?
I am currently reading the book Nonparametric and Semiparametric Models, where it discusses conditional heteroscedasticity with the following formula. However, I'm not sure how this formula is derived....
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Heteroscedastic variance prediction constant where it should not be
I am trying to make predictions about the heterscedastic noise in my dataset. I have an FPN already set up, treating the variance as an additional class. My dataset is the aerial semantic segmentation ...
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The value of scale parameter σ in accelerated failure time model
my model follows Weibull distribution, my question about σ is when we could replace it with one and when we may consider it a scale parameter?
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Assumptions of Linear Regression (homoscedasticity and normality of residuals)
I am confused about some assumptions of linear regression: homoscedasticity and residuals are normally distributed. These two require residuals, but to get the residuals, we need to fit the model ...
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Residuals changes with Predicted values range in LGBM regressor
I am doing a regression problem where the target variable ranges between 0.01 to 0.15. The model gives the best value when the predicted value is around 0.1. Plotting the residuals seems to show ...
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Does this graph show heteroscedasticity or homoscedasticity?
So I am using stock data for certain stocks over a period of about 13 years and now i want to check for heteroscedasticity and auto-correlation on stata. residual vs. fitted value is shown below.
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Welch t-test p-values are poorly calibrated for $N=2$ samples
I am performing a large number of Welch's t-tests (t-test with unequal variance) on very small sample sizes, often with only two samples per condition. I am finding the p-values are poorly calibrated: ...
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I think standard deviation of y is related to size of x. How do I create a model for this / test this?
I have a sample of data $(x_i, y_i)$. I hypothesize that $y_i$ is not dependent on $x_i$, but the standard deviation of $y_i$ depends on $x_i$
More concretely, say I assume $\textrm{Var}(y_i | x_i) = ...
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What criterion to use to compare multiple correlations of binary variables?
I have $N$ definitions of certain properties of countries (for example, if the country is "democratic", "totalitarian" etc.), and want to test how consistently different people ...
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Understanding Volatility Clustering: Conditional or Unconditional Variance?
A stylized fact observed in financial time series is volatility clustering. Volatility clustering is commonly described as the fact that large changes in asset prices are followed by large changes, ...
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GLMM for not so gaussian data
I am having an issue with GLMM and hope you could advice me.
So basically I have data from microscopy experiment of three independent groups (variable: subfolder) nested within 4 experimental ...
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Question on ARCH effect Test
I try to conduct ARCH effect test.
I have a time series (Global price of Brent crude oil) which follows AR(3).
First of all, I estimate AR(3) model for the Oil price.
$$Y_t = \alpha_0 + \alpha_1 Y_{t-...
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Which analysis instead of linear regression?
I have collected data pertaining to suffering (scale from 0 to 8, higher is worse) and cognitive distortion (0 to 40, higher is worse) for a study with ~ 200 participants. My hypothesis is that there ...
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Unbiased test for homogeneity of means of exponenential samples
Given $K$ independent samples of $Y_{i1},\dots,Y_{in_i} \ \text{i.i.d.} \ \sim Exp(\lambda_i)$ with $i=1,\dots, K$ and $n_i$ the size of the $i$-th sample, is there any statistics with analytically ...
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Assessing heteroscedasticity in residuals vs. fitted values graph [duplicate]
I am running a mixed model regression with 3 levels (schools, groups and students). I applied robust standard errors with the R function ...
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Two Way Anova with Heteroscedasticity
I'm trying to run a two way anova test but the homoscedasticity condition is not met. My analysis is not balanced and I have over 3000 observations in my sample. Is it okay to proceed even if the ...
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Coefficient of determination in a linear regression model with a covaring predictor
Given a model:
\begin{align}Y_{i}=Z_{i}*\beta * X_{i} + Z_{i}\tag{Eq. 1}&\end{align}
I am interested in a closed formula for the proportion of variance explained by the predictor variable $X$, ...
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Assumption in multiple linear regression
The principles of multiple linear regression are widely described, however there are still some aspects I don't truly understand why. Specifically speaking I don't understand why heteroscedasticity ...
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Very basic questions about choosing weights for WLS
Hi all – very new to stats and ML here (though with plenty of math experience – I’m not a student looking for homework help, I’m 58, know plenty of math, and am looking to expand my skills).
I ...
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Does "residualising" out the effect of a covariate on the response variable achieve similar results to including the covariate as a predictor?
Sorry - the question itself is wordy!
I am running a Welch ANOVA, but want to account for the effects of a covariate on this Welch ANOVA. I am unaware of any ways that I could conduct a Welch ANCOVA.
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Determining when two slopes are different or not, given heteroskedasticity
My current experiment investigates substrate consumption at two different substrate concentrations. My question concerns whether the slope of consumption is equal. However, I obtain an F-value ...
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Testing for Homoscedasticity - should Levene's and Brown-Forsythe use Welch's t-test/ANOVA?
This question just came up and I haven't seen any literature on the subject.
Background: When testing homoscedasticity for, say, a two-sample t-test, the F-test for equal variances is deprecated due ...
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Trying to construct Response surface involving unequal variance for the data mentioned using Minitab [closed]
I'm new to Minitab and I never learned statistics as a proper subject.
I need to get a response surface and CI for a factorial experiment for my thesis. I'm faced with what looks like unequal and ...
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Potential heteroskedasticity in maximum likelihood
I've created a bad loan classifier model using logit regression and maximum likelihood. The actual v expected comparison of the result is shown below. In order to create the chart, we binned the ...
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Different estimates of conditional mean parameters from OLS vs ARCH
Consider the market model for security $i$:
$$
R_{i,t}=\alpha_i + \beta_i R_{m,t} + e_{i,t}.
$$
I estimated the parameters with the OLS method.
...
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Addressing Heteroscedasticity in Mixed Effects Models with glmmTMB and DHARMa in R [duplicate]
I am analyzing ecological data in R, where I aim to understand the impact of urbanization on species trends. My response variable is the coefficient of species trends (estimate), and my main predictor ...
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Heteroscedasticity in VECM residuals: consequences and solution
Does anyone know the consequences of heteroscedasticity in VECM residuals? For impulse reponse, standard errors and so on?
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Heteroscedastic residuals of a VECM estimated by MLE
I have estimated an VEC model in Matlab, and it turns out the residuals are heteroscedastic.
Now, does anyone know how to apply HAC errors to a VEC Model in Matlab?
Alternatively, given the model is ...
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how to identify the form of heteroskedasticity?
After having done the heteroscedasticity test, and having confirmed its existence, I want to correct the model. To correct it, and proceed with the transformation of the data, I must identify the form ...
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How critical/serious is the heteroscedasticity in my data (Breusch-Pagan test significant at p=.03)?
edit below
I am doing this analysis for the first time. How concerned should I be about heteroscedasticity in my data? Here's the scatterplot of predicted values vs residuals:
The Breusch-Pagan test ...
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Regression with single-observation dummies: F-test under heteroskedasticity
I have a linear regression model with an intercept and a few dummy variables. Each of the dummies indicate a single observation, so the fit is perfect for these observations. Having fit the model, the ...
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Trust the graphs or go with Breusch-Pagan and White's tests for Homoscedasticity on large datasets? [duplicate]
I have a large dataset (n > 500,000) which I'm building a linear model with lm(PV1READ ~ PV1MATH + PV1SCIE + ST004D01T). Tests for Normality, No ...
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Heteroscedasticity in linear mixed effects models (lmer)
I am computing the following model in R, using lme4::lmer:
m3 = lmer(e ~ (X*Y*Z) + (1|ID/R), data = data_transform)
e is a continuous variable. X, Y, and Z are ...
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Robust standard errors leading to false positives [closed]
I have an odd scenario in my data analysis and I'm not sure what is causing it. I have a large set of tuples $(Y_1, X_i) \dots, (Y_N, X_N)$ where $Y_i$ is a random vector from some arbitrary ...
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True or False: If the distribution of Y|X is normal, then the regression of Y on X must be both linear and homoscedastic [duplicate]
I'm trying to interpret an early and pretty dense (to me) paper on the theory of linear regression:
Bartlett, M. S. (1934). On the theory of statistical regression. Proceedings of the Royal Society of ...
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How to deal with Heteroskedasticity in a GAM model
I am running a set of GAMs (Generalized Additive Models) to model a smoothed effect. I have verified all the other necessary checks of my GAMs for the basis functions, etc. However, I find persistent ...
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Non constant Feature Importance [closed]
I have a financial dataset which has 10 years worth of data. The aim is to build a regressor capable of predicting next year sales. So, if I want to predict sales for 2024, I could use data from 2023, ...
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Conditionally conjugate prior in heteroskedastic model
I am researching a linear model where the noise is a function of the slope parameter as follows
$$y_i = \beta_0 + \beta_1x_i + \beta_1\epsilon_i$$
$$\epsilon_i \sim N(0, \sigma^2 g)$$
where $g$ is ...
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Heteroskedasticity Adjusted Correlation Coefficients
I've been reading Forbes & Rigobon (2002) "No contagion, only interdependence" article, in which they suggest to adjust the correlation coefficients for heteroskedasticity.
I can't ...
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MLE of Linear Regression with heteroskedasticity
Assume a linear regression model $y = X \theta^{*} + \epsilon$, where $X$ represents a feature matrix and $\theta$ represents a parameter vector.
Here we assume heteroskedasticity where $\epsilon \sim ...
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Advantages of GLS Estimator for OLS in the Presence of Violated Spherical Assumption
Let be the linear model given by:
$$y_i = x_i'\beta + \varepsilon_i$$
Using its matrix form, consider strictly exogenous assumption and spherical assumption, respectivelly:
$$E[\varepsilon | X]=0, \...
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What should I do when my data is normal, but not homogen?
My data is (n:43)genotypes with block as replication (n:2). the design is randomized complete block design. and I did normality test and the result said normal, but I did homogeneity test (levenetest) ...
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Optimal three parameter variable stabilizing transformation of a Poisson
In the paper: "On the classical choice of variance stabilizing transformations and an application for a Poisson variate", Shaul K. Bar-Lev and Peter Enis give an optimal two parameter ...
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Resolving heteroscedasticity in Gamma GLMM glmmTMB
I am investigating the effect of predictor variables population.size (continuous), farm.type (categorical) and control measure y.n (binary) on my response variable outbreak duration (continuous). I ...
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Homoscedasticity across different samples
I understand that homoscedasticity, constant variance of the error terms at each different X value, is a key assumption for linear regression. Assume we collected a single data sample $(X,Y)$. The ...
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