Using External Information for More Precise Inferences in General Regression Models

Area of Science:

• Statistics
• Psychological Research

Background:

• Empirical research often utilizes external information like study results, meta-analyses, and expert knowledge.
• Psychological research can leverage external data for theory building and hypothesis generation.
• Existing statistical techniques, such as Bayesian prior distributions, incorporate external information into the estimation process.

Purpose of the Study:

• To introduce and discuss the benefits of generalized method of moments with external moments (GMEM) in empirical research.
• To provide analytical formulas for estimators and their variances in multiple linear regression using GMEM.
• To introduce a robustification method for GMEM against external moment misspecification using imprecise probabilities.

Main Methods:

• Derivation of analytical formulas for estimators and variances in multiple linear regression.
• Implementation of these formulas in an R function for applied use.
• Simulation study to analyze the effects of various external moments.
• Development of a robust approach using imprecise probabilities to address misspecification of external moments.

Main Results:

• Analytical formulas for GMEM in multiple linear regression were derived.
• A simulation study demonstrated the effects of different external moments.
• A novel robustification technique against external moment misspecification was introduced.
• Application to a dataset showed reduced variances and narrower confidence intervals for predicting premorbid intelligence quotient.

Conclusions:

• Generalized method of moments with external moments offers a valuable technique for enhancing empirical and psychological research.
• The proposed robustification method improves the reliability of GMEM when external information is imprecise.
• GMEM leads to more precise estimations, as evidenced by reduced variances and narrower confidence intervals in predictive modeling.