Exploratory Factor Analysis of different variable stars in the M37 field

Abstract

Variable stars in open clusters provide valuable information regarding stellar structure and evolution. We have studied photometry of different types of variable stars of the intermediateage open cluster M37. Since we don’t have sufficient prior knowledge on number and characteristics of the underline factors behind photometric variability of variable stars, the usual confirmatory factor analysis is not possible. We therefore carried out Exploratory Factor Analysis to understand the factors. We first check the factorability of the data using Bartlett’s test of sphericity and Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy and estimate the number of factors on the basis of Horns Parallel analysis. In the operable Factor Analysis framework, latent factors and errors are assumed to follow normal distribution for achieving computational and mathematical tractability. But such assumptions ignore the characteristics such as skewness and heavy tails; which may lead to inappropriate statistical inference. In this situation, we study the distributional aspects of factors and errors. We have tested normality of the data using multivariate Shapiro-Wilks test which has led to the rejection of normality hypothesis. Then we have estimated the factors and corresponding errors of the non-normal dataset using an iterative least-squares method like weighted leastsquares or generalized least squares. Next, we try to fit probability distributions (univariate for single factor and multivariate for the multi-factors model) on factors and errors. The best-fitted distributions are selected on the basis of the minimum value of information criteria like AIC, BIC, and EDC. We have considered five most general distributions viz, Normal, t, Skew Normal, Skew t, and Skew Slash. For a non-normal distribution, we study its tail and skewness. Attempt has been made to identify and interpret the factors responsible for photometric variability of different variable stars and their corresponding errors.