BAYESIAN SOLUTIONS TO MULTICOLLINEARITY CHALLENGES IN SPONTANEOUS ABORTION STUDIES

Abstract

Spontaneous abortion, a natural process in response to fetal abnormalities or disease, accounts for a significant percentage of pregnancies, especially during the first trimester. Various biological, social, and economic factors influence the occurrence of spontaneous abortion. This study employs the Tobit model to analyze data related to this phenomenon, consisting of both censored cases (zero abortions) and uncensored cases (one or more abortions). The Tobit model combines elements of the cumulative distribution function (c.d.f) and probability density function (p.d.f) for a normal distribution.
The model investigates how independent variables affect the response variable. Multicollinearity issues are detected through the Farrar-Glauber test, prompting the use of the principal components method. This method transforms the linked original variables into unlinked new variables, representing principal components, each comprising elements from the original variables. Parameter estimation for the Tobit principal components regression model employs Bayesian techniques, resolving multicollinearity problems. Finally, an algorithm is constructed in the R programming language to estimate the original coefficients for the Tobit model.