ﻻ يوجد ملخص باللغة العربية
Marginal maximum likelihood (MML) estimation is the preferred approach to fitting item response theory models in psychometrics due to the MML estimators consistency, normality, and efficiency as the sample size tends to infinity. However, state-of-the-art MML estimation procedures such as the Metropolis-Hastings Robbins-Monro (MH-RM) algorithm as well as approximate MML estimation procedures such as variational inference (VI) are computationally time-consuming when the sample size and the number of latent factors are very large. In this work, we investigate a deep learning-based VI algorithm for exploratory item factor analysis (IFA) that is computationally fast even in large data sets with many latent factors. The proposed approach applies a deep artificial neural network model called an importance-weighted autoencoder (IWAE) for exploratory IFA. The IWAE approximates the MML estimator using an importance sampling technique wherein increasing the number of importance-weighted (IW) samples drawn during fitting improves the approximation, typically at the cost of decreased computational efficiency. We provide a real data application that recovers results aligning with psychological theory across random starts. Via simulation studies, we show that the IWAE yields more accurate estimates as either the sample size or the number of IW samples increases (although factor correlation and intercepts estimates exhibit some bias) and obtains similar results to MH-RM in less time. Our simulations also suggest that the proposed approach performs similarly to and is potentially faster than constrained joint maximum likelihood estimation, a fast procedure that is consistent when the sample size and the number of items simultaneously tend to infinity.
Factor models are a class of powerful statistical models that have been widely used to deal with dependent measurements that arise frequently from various applications from genomics and neuroscience to economics and finance. As data are collected at
Feature selection is an important and challenging task in high dimensional clustering. For example, in genomics, there may only be a small number of genes that are differentially expressed, which are informative to the overall clustering structure. E
The likelihood ratio test is widely used in exploratory factor analysis to assess the model fit and determine the number of latent factors. Despite its popularity and clear statistical rationale, researchers have found that when the dimension of the
Penalized (or regularized) regression, as represented by Lasso and its variants, has become a standard technique for analyzing high-dimensional data when the number of variables substantially exceeds the sample size. The performance of penalized regr
In this article, we introduce a two-way factor model for a high-dimensional data matrix and study the properties of the maximum likelihood estimation (MLE). The proposed model assumes separable effects of row and column attributes and captures the co