Indirect effect and spuriousity

  • Context: Graduate 
  • Thread starter Thread starter monsmatglad
  • Start date Start date
  • Tags Tags
    Ols Regression
Click For Summary
SUMMARY

The discussion centers on the impact of adding a new variable (Z) to an Ordinary Least Squares (OLS) regression model, particularly its effect on the coefficients of existing independent variables (X). When Z is introduced, it can either reveal a spurious relationship between X and the dependent variable (Y) or indicate an indirect effect. The addition of Z can lead to a decrease in the size and significance of X's coefficient, depending on the correlation between Z and X. This outcome is not definitive; the relationship between the variables can vary based on their correlations and the signs of their coefficients.

PREREQUISITES
  • Understanding of Ordinary Least Squares (OLS) regression analysis
  • Familiarity with concepts of spurious relationships in statistics
  • Knowledge of indirect effects in regression models
  • Basic statistical significance testing
NEXT STEPS
  • Explore the implications of adding variables in regression analysis
  • Study correlation coefficients and their impact on regression outcomes
  • Learn about multicollinearity and its effects on model interpretation
  • Investigate methods for detecting spurious relationships in statistical models
USEFUL FOR

Statisticians, data analysts, and researchers involved in regression modeling and interpretation, particularly those examining the relationships between multiple variables.

monsmatglad
Messages
75
Reaction score
0
Say one has a regression result (ols) with significant coefficients for all independent variables. Then a new variable (Z) is added. This new variable is either something that reveals a spurious relationship among one of the initially included variables (x) and the dependent variable (y), or represents an effect that is "between" the independent variable (z) and the dependent (z) - an indirect effect. Will both these situations cause the size (and significance) of the independent variable (x) to decline? I have a statistics course, and from what I remember, my lecturer told me that adding an additional independent variable which results in one of the original variables to have a smaller coefficient, is a sign of either an indirect effect or a spurious relation. Is this correct?

Mons
 
Physics news on Phys.org
I wouldn't say that any situation forces one to conclude that one of the variable effects is indirect or spurious. Both X and Z variables may have a component showing an effect on Y that is not reflected in the other variable at all.

If the new variable, Z, is correlated with a variable, X, already in the model, then if it is added, the coefficient of X will change.
If the correlation between Z and X is positive, and Z is added with a coefficient of the same sign as the X coefficient, then the magnitude of the coefficient of X will decrease. Likewise if the ZX correlation is negative and have the same sign of coefficient. The statistical significance of X may be decreased to the point where it should be removed from the model.
Other combinations would make the coefficient of X increase in magnitude.
 

Similar threads

Undergrad Linear regression, feature scaling, and regression coefficients
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Nonlinear Least Squares or OLS for Nonlinear Models?
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad Linear regression and random variables
  • · Replies 30 ·
2
Replies
30
Views
5K
Undergrad What Are the Key Differences Between OLS and GLM Models in Statistical Analysis?
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad What are the commonly used estimators in regression models?
  • · Replies 23 ·
Replies
23
Views
4K
High School Limitations of Multivariate Linear Regression
  • · Replies 6 ·
Replies
6
Views
3K
Graduate Using standard deviation values as independent variables
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Centering variables, linear regression
  • · Replies 1 ·
Replies
1
Views
2K
Graduate R2 Addition in OLS Regression: Unrelated Variables?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Coefficient sign flip in linear regression with correlated predictors
  • · Replies 13 ·
Replies
13
Views
5K