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QMPE: estimating Lognormal, Wald, and Weibull RT distributions with a parameter-dependent lower bound
Andrew Heathcote1, Scott Brown, Denis Cousineau
1School of Behavioural Sciences, University of Newcastle, Callaghan, NSW, Australia. andrew.heathcote@newcastle.edu.au
Behavior Research Methods, Instruments, & Computers : a Journal of the Psychonomic Society, Inc
|September 10, 2004
Summary
We introduce the Quantile Maximum Probability Estimator (QMPE) for response time distribution estimation. QMPE offers an alternative to Continuous Maximum Likelihood (CML) for shifted distributions, showing comparable or superior performance.
Area of Science:
- Cognitive psychology
- Psychometrics
- Computational statistics
Background:
- Accurate estimation of response time distributions is crucial for understanding cognitive processes.
- Standard methods like Continuous Maximum Likelihood (CML) can fail for certain distributions, particularly those with parameter-dependent lower bounds.
- The Quantile Maximum Probability (QMP) method offers a potential solution to these estimation challenges.
Purpose of the Study:
- To introduce and evaluate the Quantile Maximum Probability Estimator (QMPE), an open-source Fortran 90 program.
- To compare the performance of QMP estimation against CML estimation for various response time distributions.
- To identify the limitations and potential issues associated with both CML and QMP estimation methods.
Main Methods:
- Description and testing of the QMPE program.
- Estimation of parameters for ex-Gaussian, Gumbel, Lognormal, Wald, and Weibull distributions.
- Comparison of Continuous Maximum Likelihood (CML) and Quantile Maximum Probability (QMP) estimation methods.
- Monte Carlo simulations to investigate estimation performance under varying conditions.
Main Results:
- QMP estimation does not fail for shifted distributions where CML fails.
- QMP estimates are generally as good as, and sometimes better than, CML estimates.
- Both CML and QMP methods can encounter problems with small sample sizes and low skew.
Conclusions:
- QMPE provides a robust tool for response time distribution estimation, particularly for shifted distributions.
- QMP offers a reliable alternative to CML, especially when dealing with complex distribution shapes.
- Careful consideration of sample size and skew is necessary for accurate distribution estimation.