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About this BF and cmP Calculator

This calculator estimates the Bayes Factor (BF) and Approximate Correct Model Probability (cmP) values by using the Bayesian Information Criteria (BIC) [1,2] values (which can be obtained by common statistical software, such as Mplus). These values can be useful in determining the appropriate number of latent classes in finite mixture models, such as latent class analysis and latent profile analysis. For an overview and description of these statistics see [2].

This calculator can be used as a quick means to estimate the BF and cmP values, which are not readily available in all structural equation modelling (SEM) software.


Bayes Factor

The BF can be used to make a pairwise comparison of relative fit between two adjacent models (Model K and Model K + 1, where K is the number of latent classes).

  • A BF less than 3 is generally considered as weak evidence in support of Model K over Model K + 1.
  • A BF greater than or equal to 3 and less than 10 is generally considered as moderate evidence in support of Model K over Model K + 1.
  • A BF greater than or equal to 10 is generally considered as strong evidence in support of Model K over Model K + 1.

Approximate Correct Model Probability

The cmP estimates the probability of each model being the "correct" model, relative to all models tested, assuming that the "true" model is among those examined [2]. Based on the cmP, the model with the highest value is selected.


References

  1. Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6(2), 461-464. https://doi.org/10.1214/aos/1176344136
  2. Masyn, K. E. (2013). Latent class analysis and finite mixture modeling. In T. D. Little (Ed.), The Oxford handbook of quantitative methods (Vol. 2, pp. 551-611). Oxford University Press.

Citation

If you found this app useful, please use the following citation:

Fox, R. (2021). BF & cmP Calculator: A Web App for Calculating Bayes Factors and Approximate Correct Model Probability Values [Computer software]. https://doi.org/10.17605/OSF.IO/Q4Z2F


Author

Dr Robert Fox is a Lecturer in Psychology at the National College of Ireland, Dublin, Ireland.

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