Understanding Functional Form Misspecification in Regression Analysis
What is functional form misspecification in regression analysis?
Consider the following regression equation: y = Bo + B,X1 +u. Which of the following indicates a functional form misspecification in E( y/x)?
a. Ordinary Least Square estimates are positive while Weighted Least Squares estimates are negative.
b. Ordinary Least Squares estimates exceed Weighted Least Squares estimates by a small magnitude.
c. Ordinary Least Squares estimates equal Weighted Least Squares estimates.
d. Weighted Least Squares estimates exceed Ordinary Least Squares estimates by a small magnitude.
Answer:
Functional form misspecification refers to situations when the model's assumed form does not adequately match the actual relationship between variables.
Model misspecification takes place when the set of potential distributions considered by the statistician does not include the distribution that generated the observed data.
Misspecification of functional form can result from the omission of important variables from the regression or the use of incorrect data forms in the regression.
This can be due to failure to transform variables that are non-linear, leading to bias in the final parameter estimators. Inconsistency in coefficient estimations can also occur.
Detecting functional form misspecification involves plotting the estimated regression function and the data, as well as choosing the appropriate functional form to improve model fit.
Discrepancies in Ordinary Least Squares (OLS) and Weighted Least Squares (WLS) estimates do not necessarily indicate a misspecification. Misspecification is typically indicated by low R-squared values, residual patterns suggesting nonlinearity, or empirical evidence pointing to a nonlinear relationship.