Alternative Definitions of Complexity for Practical Applications of Model Selection Criteria

Defining and quantifying complexity is one of the major challenges of modern science and contemporary societies. This task is particularly critical for model selection, which is aimed at properly identifying the most adequate equations to interpret the available data. The traditional solution of equating the complexity of the models to the number of their parameters is clearly unsatisfactory. Three alternative approaches are proposed in this work. The first one estimates the flexibility of the proposed models to quantify their potential to overfit. The second interprets complexity as lack of stability and is implemented by computing the variations in the predictions due to uncertainties in their parameters. The third alternative is focused on assessing the consistency of extrapolation of the candidate models. All the upgrades are easy to implement and typically outperform the traditional versions of model selection criteria and constitute a good set of alternatives to be deployed, depending on the priorities of the investigators and the characteristics of the application.

Improved Treatment of the Independent Variables for the Deployment of Model Selection Criteria in the Analysis of Complex Systems

Model selection criteria are widely used to identify the model that best represents the data among a set of potential candidates. Amidst the different model selection criteria, the Bayesian information criterion (BIC) and the Akaike information criterion (AIC) are the most popular and better understood. In the derivation of these indicators, it was assumed that the model’s dependent variables have already been properly identified and that the entries are not affected by significant uncertainties. These are issues that can become quite serious when investigating complex systems, especially when variables are highly correlated and the measurement uncertainties associated with them are not negligible. More sophisticated versions of this criteria, capable of better detecting spurious relations between variables when non-negligible noise is present, are proposed in this paper. Their derivation is obtained starting from a Bayesian statistics framework and adding an a priori Chi-squared probability distribution function of the model, dependent on a specifically defined information theoretic quantity that takes into account the redundancy between the dependent variables. The performances of the proposed versions of these criteria are assessed through a series of systematic simulations, using synthetic data for various classes of functions and noise levels. The results show that the upgraded formulation of the criteria clearly outperforms the traditional ones in most of the cases reported.

Using Model Selection Criteria to Choose the Number of Principal Components

The use of information criteria, especially AIC (Akaike’s information criterion) and BIC (Bayesian information criterion), for choosing an adequate number of principal components is illustrated.

Latent profile analysis of human values: What is the optimal number of clusters?

Latent Profile Analysis (LPA) is a method to extract homogeneous clusters characterized by a common response profile. Previous works employing LPA to human value segmentation tend to select a small number of moderately homogeneous clusters based on model selection criteria such as Akaike information criterion, Bayesian information criterion and Entropy. The question is whether a small number of clusters is all that can be gleaned from the data. While some studies have carefully compared different statistical model selection criteria, there is currently no established criteria to assess if an increased number of clusters generates meaningful theoretical insights. This article examines the content and meaningfulness of the clusters extracted using two algorithms: Variational Bayesian LPA and Maximum Likelihood LPA. For both methods, our results point towards eight as the optimal number of clusters for characterizing distinctive Schwartz value typologies that generate meaningful insights and predict several external variables.

Bayesian multilevel model on maternal mortality in Ethiopia

Maternal mortality is one of the socio-economic problems and widely considered a serious indicator of the quality of a health. Ethiopia is considered to be one of the top six sub-Saharan countries with severe maternal mortality. The objective of this study was to investigate the effects of the Demographic and Socio-economic determinant factors of maternal mortality in Ethiopia. Data from the 2016 Ethiopia Demographic and Health Survey indicated that the sample of women (15–49) was (n = 10,103). The Bayesian multilevel we were used to explore the major risk factors and regional variations in maternal mortality in Ethiopia. Markov chain Monte Carlo methods with non-informative priors have been applied. The Deviance Information Criterion model selection criteria were used to select the appropriate model. The analysis result, 145 (1.43%) mothers were died due to pregnancy. Using model selection criteria Bayesian multilevel random coefficient was found to be appropriate. With this model, Age of mother, marital status, number of living children, wealth index and Education are found to be the significant determinants of maternal mortality in Ethiopia. The study indicated that there was within and between regional variations in maternal mortality. Inference is the fully Bayesian multilevel model based on recent Markov chain Monte Carlo techniques. The socioeconomic, demographic and environmental determinants included in the study were found to be statistically significant. The result of the Bayesian multilevel model in this study has shown that educational attainment, wealth index, an age of mother, status and number of living children was a significant factor of maternal mortality.