Bayesian Analysis of Longitudinal Data Using Growth Curve Models bases Bayesian analysis on the principle that the application of probability depends on the degree to which a person believes a hypothesis or a proposition. The article provides a summary of the overall basics of Bayesian terms and methods beginning by reviewing terms such as priors, posteriors, and the Markov chain Monte Carlo (MCMC) method. Following the introduction, the authors explain the basic concepts of the latent basis growth model. Lastly, they incorporate an empirical example fitting a latent basis growth curve model to achievement data from the National Longitudinal Survey of Youth. The example demonstrates how to analyze data using noninformative and informative priors. The findings show that Bayesian methods are an alternative to the maximum likelihood estimation (MLE) method. Further findings suggest Bayesian methods have other strengths including systematic incorporation of prior information from previous studies. The authors found that the Bayesian method was a more plausible way to analyze small sample data as compared to the MLE method.
Bayesian methods are applicable to intemresopnse models, factor analytic models, structural equation modes, genetic models, and multilevel models. Both applied and theoretical measurement can benefit from the opportunities that Bayesian methods can bring forth. The authors point out that oftentimes the strenuous programming and computational demands of Bayesian methods as well as the complexities of the models that usually need the application of Bayesian methods make the methods seem fairly remote and frustrating for empirical researchers. Thorough this study and the examples provided the authors attempt to provide an easy way to implement Bayesian analysis.
This article provides a summary of the basis for Bayesian methods. While it is not related to intelligence analysis it does provide a breakdown of the technique, especially useful to those with no experience using Bayesian analysis. Additionally, the systematic example provided using data from the National Longitudinal Survey of Youth provides a fairly easy to follow, step-by-step example of the method.
An issue that not only arose with this article but all articles on Bayesian analysis is that although they talk about its importance in terms of analysis there are very few that apply the method directly to intelligence analysis. Statements describing Bayesian analysis such as, Bayes’ theorem is useful because it provides a way to calculate the probability of a hypothesis based on the evidence or data, is very relevant to intelligence analysis. Additionally, by discussing the probability of the data also calling it the likelihood, would allow analysists to use the correct WEP when making statements of estimated probability. Lastly, the ability of Bayesian to estimate complex models in data analysis is extremely effective. All of these were findings or statements found within the article, and all are very applicable and beneficial to the intelligence community. The application of these findings and statements to a problem faced by an intelligence analyst would demonstrate the usefulness of Bayesian analysis in these scenarios.
Finally, the article mentions that an alternative to meta-analysis are Bayesian methods that use informative priors. The authors provides a short explanation of Bayesian’s ability to do this but, considering the reliability and weight placed on meta-analysis studies, more information should be given to back up this claim. A claim like this is deserving of an entire study rather than a short paragraph and leaves the reader wondering exactly how the Bayesian method can act as an alternative to a meta-analysis. A more comprehensive explanation is necessary.
Grimm, K.J., Hamagami, F., Nesselroade, J.R., Wang, L., & Zhang, Z. (2007). Bayesian analysis of longitudinal data using growth curve models. International Journal of Behavioral Development. 31 (4), 374-383.