Estimation of logistic regression models in small samples. A simulation study using a weakly informative default prior distribution

En este trabajo se utilizaron simulaciones para comparar el rendimiento de las estimaciones clásica y bayesiana en modelos de regresión logística utilizando muestras pequeñas. En las simulaciones realizadas, las condiciones fueron variadas, incluyendo el tipo de relación entre los valores de las variables dependientes e independientes (es decir, los valores vinculados y no vinculados), el tipo de variable (binario y continuo), y diferentes valores de la distribución binomial y la simetría (distribuciones simétricas y con asimetría positiva). La aplicación Iterativa de la estimación de mínimos cuadrados ponderados se utilizó como método de estimación para ajustarse a los modelos, tanto en la estimación clásica como en la bayesiana. Una distribución de tipo escasamente informativa fue elegida como la distribución a priori para la estimación bayesiana. Los resultados de la simulación muestran que las estimaciones bayesianas proporcionan una distribución más estable, pero que no son capaces de resolver los problemas generados por distribuciones asimétricas basadas en muestras pequeñas. Será preciso plantear nuevos trabajos en el ámbito del estudio del efecto de las distribuciones asimétricas utilizando diferentes tipos de distribuciones a priori(AU)

In this paper, we used simulations to compare the performance of classical and Bayesian estimations in logistic regression models using small samples. In the performed simulations, conditions were varied, including the type of relationship between independent and dependent variable values (i.e., unrelated and related values), the type of variable (i.e., binary and continuous), and different Binomial distribution values and symmetry (i.e., symmetry and positive asymmetry). Iteratively re-weighted least squares was used as the estimate method to fit the models in both the classical and Bayesian estimations. A weakly informative default distribution was chosen as the prior distribution for Bayesian estimation. The simulation results demonstrate that Bayesian estimations provide more stable distributions but are not able to solve problems generated by asymmetric distributions based on small samples. Additional research using different kinds of priors that is addressed at solving problems caused by asymmetry is needed(AU)

Classical and Bayesian estimation in the logistic regression model applied to diagnosis of child attention deficit hyperactivity disorder.

The limitations inherent to classical estimation of the logistic regression models are known. The Bayesian approach in statistical analysis is an alternative to be considered, given that it makes it possible to introduce prior information about the phenomenon under study. The aim of the present work is to analyze binary and multinomial logistic regression simple models estimated by means of a Bayesian approach in comparison to classical estimation. To that effect, Child Attention Deficit Hyperactivity Disorder (ADHD) clinical data were analyzed. The sample included 286 participants of 6-12 years (78% boys, 22% girls) with ADHD positive diagnosis in 86.7% of the cases. The results show a reduction of standard errors associated to the coefficients obtained from the Bayesian analysis, thus bringing a greater stability to the coefficients. Complex models where parameter estimation may be easily compromised could benefit from this advantage.