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Goodness-of-fit processes for logistic regression: simulation results
David W Hosmer1, Nils Lid Hjort
1Department of Biostatistics and Epidemiology, University of Massachusetts, 715 North Pleasant St, Amherst, MA 01003-9304 USA. hosmer@sschoolph.umass.edu
Statistics in Medicine
|September 14, 2002
Summary
New weighted goodness-of-fit tests were compared to existing methods. One new weighted test showed comparable power across simulations and excelled in detecting omitted interaction terms, offering practical recommendations.
Area of Science:
- Statistical modeling
- Goodness-of-fit testing
- Regression analysis
Background:
- Assessing model fit is crucial in statistical analysis.
- Existing goodness-of-fit tests have limitations in detecting specific model misspecifications.
- New weighted statistical process tests are proposed.
Purpose of the Study:
- To compare the performance of new weighted goodness-of-fit tests against established methods.
- To evaluate the power of these tests in detecting various forms of model lack-of-fit.
- To provide practical recommendations for choosing appropriate goodness-of-fit tests.
Main Methods:
- Monte Carlo simulations were employed to assess test performance.
- New weighted tests were compared to Hosmer-Lemeshow, Pearson chi-square, and unweighted sum-of-squares tests.
- Simulations varied sample sizes (100 and 500) and types of model misspecification.
Main Results:
- All tested goodness-of-fit statistics demonstrated correct size across simulations.
- Power varied significantly based on the type of misspecification and sample size.
- New weighted tests showed comparable or superior power, particularly for detecting omitted interaction terms.
Conclusions:
- No single goodness-of-fit test is universally superior for all misspecification scenarios.
- One novel weighted test demonstrates robust performance across diverse simulation settings.
- The study offers practical guidance for selecting goodness-of-fit tests in regression modeling.