Model Selection Criterion for Cross Sectional Data

While doing research in cross sectional data set, first of all we should estimate OLS (ordinary least square) model then do the post regression diagnostics, based on the presence of problem use the appropriate model specified in the table below.

  Diagnostic Source Model / Solution
Cross Sectional Data Non Normal Residuals

(Jarque Bera Test)

Too many outliers (Kurtosis >> 3) Use Logarithm Model
Dependent is count variable Use Poisson Regression
 

 

 

Multicollinearity (Variance Infaltion Factor)

Sample Too small Use single variable regression
Variables too many Step-wise regression
Indirect independent variables Indexed variables using Principle Factor analysis
One independent is catalysis for another Moderator approach
Few independent variables Ridge Regression
 

 

Hetroskedasticity   (Breusch Pegan Test)

Nonlinear variances Use Logarithm Model
Dependent is binomial dummy Logit / Probit model
Dependent is multinomial dummy Multinomial logit model
Mis-Specification

(Ramsey RESET test)

Nonlinear form missing Incorporate nonlinear form or

Use Logarithm Model

Instability (CUSUM and CUSUMsq) Data might have two or more different qualities Use independent dummy variables
Autocorrelation

(Durbin Watson)

Some quality is interconnecting the cross sectional residuals Add more variables or use bootstrap approach or

use robust regression

Endogeneity

(Hausman Wu test)

Valid Regression is other way around Reverse the regression or use IV / GMM regression
Contemporaneous Correlation / simultaneity Regression is two way Use SEM
Two equations are interrelated Use SEM

By practice researcher can directly used the appropriate model as by construction he knows what kind of problem is there.

Note: This chart is under-development phase and open for suggestions and amendments.

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