Heteroscedasticity Type 1 Error
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CFA Forums CFA General Discussion CFA Level I Forum CFA Level II Forum CFA Level III Forum CFA Hook Up Heteroskedasticity Tweet Widget Google Plus One Linkedin Share Button Facebook Like by mohammad.belaal on Dec 1st, 2011 Heteroskedasticity occurs when the variance of the errors differs accross observations i.e. variances are not constant. Heteroskedasticity could of be two types: 1. Unconditional Heteroskedasticity: When variance does not systematically increase or decrease with changes in how to correct heteroskedasticity the value of independent variable. It is violation of assumption 4 but does not upholds any serious problems with regression. 2. Conditional Heteroskedasticiy: It exists when error variance changes with the value of independent variable and it is more problematic. Consequences of (conditional) Heteroskedasticity: It does not affect consistency but it can lead to wrong inferences. Coefficient estimates are not affected. It causes the F-test for the overall significance to be unreliable. It introduces bias into estimators of the standard error of regression coefficients; thus t-tests for the significance of individual regression coefficients are unreliable. When Heteroskedasticity results in underestimated standard errors, t-statistics are inflated and probability of Type-1 error increases. When Heteroskedasticity results in overestimated standard errors, t-statistics are deflated and probability of Type-2 error increases. Testing for Heteroskedasticity: Heteroskedasticity can be tested by Plotting residuals on a graph and judging a relationship with respect to observations on the x-axis. A more stringent measure is the Breush-Pagan Test which involves regressing the squared residuals from the estimated regression equation on the independent variables in the regression. Null Hypothesis = No conditional Heteroskedasticity exists. Alternative Hypothesis = Conditional Heteroskedasticity exists. Test statistic = n x R2Residuals Critical value can be calculated from chi-square distribution table with degree of freedom = no. of independent variables (k) If test statistic > critical valu
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Interpret a Sequential One-Way Discriminant AnalysisMathematical Expectation[ View All causes of heteroscedasticity ]Regression AnalysisAssumptions of Linear RegressionTwo-Stage Least Squares (2SLS) Regression AnalysisUsing Logistic Regression in how to fix heteroskedasticity Research[ View All ]CorrelationCorrelation (Pearson, Kendall, Spearman)Correlation RatioMeasures of Association[ View All ](M)ANOVA AnalysisAssumptions of the Factorial ANOVAGLM Repeated MeasureGeneralized Linear Models[ http://www.analystforum.com/article/cfa/heteroskedasticity View All ]Factor Analysis & SEMConduct and Interpret a Factor AnalysisExploratory Factor AnalysisConfirmatory Factor Analysis[ View All ]Non-Parametric AnalysisCHAIDWald Wolfowitz Run Test[ View All ] CloseDirectory Of Survey InstrumentsAttitudesEmotional IntelligenceLearning / Teaching / SchoolPsychological / PersonalityWomenCareerHealthMilitarySelf EsteemChildLeadershipOrganizational / Social GroupsStress / Anxiety / Depression http://www.statisticssolutions.com/homoscedasticity/ Close CloseFree ResourcesNext Steps Home | Academic Solutions | Directory of Statistical Analyses | Regression Analysis | Homoscedasticity Homoscedasticity The assumption of homoscedasticity (literally, same variance) is central to linear regression models. Homoscedasticity describes a situation in which the error term (that is, the “noise” or random disturbance in the relationship between the independent variables and the dependent variable) is the same across all values of the independent variables. Heteroscedasticity (the violation of homoscedasticity) is present when the size of the error term differs across values of an independent variable. The impact of violating the assumption of homoscedasticity is a matter of degree, increasing as heteroscedasticity increases. A simple bivariate example can help to illustrate heteroscedasticity: Imagine we have data on family income and spending on luxury items. Using bivariate re
Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site About Us Learn http://stats.stackexchange.com/questions/133272/how-bad-can-heteroscedasticity-be-before-causing-problems more about Stack Overflow the company Business Learn more about hiring developers or posting ads with us Cross Validated Questions Tags Users Badges Unanswered Ask Question _ Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can how to answer The best answers are voted up and rise to the top How bad can heteroscedasticity be before causing problems? up vote 6 down vote favorite I have two questions about heteroscedasticity in multiple regressions. According to my trusty textbook (Using Multivariate Statistics 2007, p.127), it says that deviations from heteroscedasticity only reduce that statistical power of a test, rather than inflating the type I error rate (is this true?) heteroscedasticity type 1 I wanted to know if there were any guidelines about how to judge effect sizes for heteroscadisticity and how much is a bad effect size for it to matter (with N=187). Because I use two categorical variables, luckily my residual/predicted plot is in two distinct clumps that I can analyse (see below): regression heteroscedasticity assumptions type-i-errors type-ii-errors share|improve this question edited Jan 13 '15 at 19:18 gung 74.1k19160309 asked Jan 13 '15 at 19:05 user3084100 669 1 In real life problems heteroscedasticity could be the symptom of a more serious misspecification issue. For instance, it may indicate that you should be using unit root process instead of trend stationary. –Aksakal Jan 13 '15 at 19:24 I don't have time to post this as an answer but point 1 is not necessarily true. Try this R code: x <- c(rep(0, 9), 1); y <- c(rnorm(mean=0, n=9, sd=1), rnorm(mean=0, n=1, sd=100)); summary(lm(y~x)). The conditional mean of y is 0 everywhere but the variance is much higher when x=1. I only put one point at x=1, you can see the results! –Silverfish Jan 13 '15 at 19:37 add a comment| 1 Answer 1 active oldest votes up vote 4 down vote It is true that heterosce
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