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SPSS macros to compare any two fitted values from a regression model.

Bruce Weaver¹, Sacha Dubois

¹Human Sciences Division, Northern Ontario School of Medicine, Thunder Bay, ON, Canada, P7B 5E1. bweaver@lakeheadu.ca

Behavior Research Methods

|May 22, 2012

Summary

Researchers can now compare any two regression model fitted values using new SPSS macros. These tools provide standard errors, confidence intervals, and p-values for complex models, enhancing statistical analysis.

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Area of Science:

Statistics
Econometrics
Psychometrics

Background:

Regression coefficients typically represent the change in Y for a one-unit increase in a predictor, holding others constant.
These coefficients capture only a limited subset of potential fitted value comparisons.
Existing statistical software often lacks standard errors for non-standard fitted value comparisons, especially in complex models.

Purpose of the Study:

To introduce two SPSS macros, !OLScomp and !MLEcomp, for comparing any two fitted values from regression models.
To provide standard errors, confidence intervals, and p-values for these comparisons.
To facilitate statistical inference for a broader range of fitted value comparisons.

Main Methods:

Development of two SPSS macros: !OLScomp for ordinary least squares (OLS) and !MLEcomp for maximum likelihood estimation (MLE).
Implementation of a matrix algebra approach to calculate differences between fitted values.
Integration of standard error calculation for these differences.

Main Results:

The macros successfully compute the standard error of the difference between any two fitted values.
Output includes a 95% confidence interval for the difference.
A statistical test with its p-value is provided for hypothesis testing.

Conclusions:

The developed SPSS macros extend the capabilities of regression analysis by enabling comparisons of any two fitted values.
These tools are particularly valuable for complex models involving interactions, polynomial terms, or regression splines.
The macros enhance statistical rigor by providing essential inferential statistics for previously untestable comparisons.