Non-normal measurement error in linear regression

Click For Summary
SUMMARY

This discussion focuses on addressing non-normal measurement errors in linear regression, specifically when using ordinary least squares regression is not viable due to known error components. The recommended approach involves utilizing a maximum likelihood functional relationship (MLFR) along with iterative algorithms. Logarithmic transformations are applied to both variables to achieve even sample distribution and homoscedasticity, resulting in log-normal sample errors. The participants seek freeware programs capable of estimating parameter values and confidence intervals under these conditions.

PREREQUISITES
  • Understanding of linear regression and its assumptions
  • Familiarity with maximum likelihood estimation techniques
  • Knowledge of log-normal distributions and transformations
  • Experience with statistical software for regression analysis
NEXT STEPS
  • Research freeware options for regression analysis with non-normal errors, such as R or Python libraries
  • Learn about advanced maximum likelihood estimation techniques for log-normal data
  • Explore the use of instrumental variables in regression to correct for measurement error
  • Study the implications of homoscedasticity and how to test for it in regression models
USEFUL FOR

Statisticians, data analysts, and researchers dealing with regression analysis involving non-normal measurement errors, particularly those seeking to improve model accuracy and reliability.

e065331
Messages
2
Reaction score
0
Hi,

Complicated stats question, but maybe someone out there knows how to proceed. I am trying to perform regression on two variables, the samples of which have significant, but known error components. Ordinary least squares regression cannot be used as it is assumed that measurements are made without error. As I understand it, the normal way to proceed would be to assume a maximum likelihood functional relationship (MLFR) and use some of the widely available iterative algorithms. However, in order to ensure even sample distrubution (i.e. not skewed) and homo-scedasticity I performed logarithmic transforms on both variables. As a consequence the sample errors are log-normal. standard MLFR techniques assume normal error distributions. Is there any way of dealing with this problem. Specifically, is anyone aware freeware computer programs that would allow one to estimate parameter values and confidence intervals.
 
Physics news on Phys.org
hi,

i am also trying to perform non normal error dist in linear regression.. may i know what is your general equation for the error term?
 
As far as I am aware, one way to correct for measurement error is to look for instruments that are correlated with the original independent variable(s) but do not have the measurement problem. See, e.g. Greene, 2nd Ed. Sec. 9.5.3.
 

Similar threads

Undergrad Linear regression, feature scaling, and regression coefficients
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad What are the commonly used estimators in regression models?
  • · Replies 23 ·
Replies
23
Views
4K
Undergrad What Are the Key Differences Between OLS and GLM Models in Statistical Analysis?
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad How to propagate errors through a regression & non-linear model?
  • · Replies 8 ·
Replies
8
Views
3K
High School Comparing Approaches: Linear Regression of Y on X vs X on Y
  • · Replies 64 ·
3
Replies
64
Views
6K
Graduate Error estimation in linear regression
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Desirable estimator properties...
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad Linear regression with error term
  • · Replies 8 ·
Replies
8
Views
3K
Graduate Obtaining standard deviation of a linear regression intercep
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Panel study, multiple linear regression, assumptions
  • · Replies 1 ·
Replies
1
Views
2K