O liczbie klas w modelu analizy czynnikowej z dwoma zmiennymi ukrytymi - Kapłon, Robert (Determining the Number of Clusters in Factor Analysis with Two Latent Variables, 2007)
When the number of components in mixture models is not known, the problem arise. The most natural and obvious approach seems to be testing a hypothesis. Un fortunately with mixture models regularity conditions do not hold therefore minus twice the log likelihood ratio test statistic does not follow the usual chi-squared distribution. Some authors suggest using bootstrap for assessing the null distribution of that statistic. But this method is computationally very intensive. For the reasons synthetic measures are often used. So far, many empirical comparisons have been made of these various criteria to compare the performance of the selection of the number of components in Gaussian mixture. Because factor analysis with two latent variables has not been in these comparisons therefore the aim of this paper is to fill the gap.
Prace Naukowe Akademii Ekonomicznej we Wrocławiu. Taksonomia (14); 2007; nr 1169, s. 253-260