Disjoint factor analysis with cross-loadings (original) (raw)

Second-Order Disjoint Factor Analysis

Psychometrika, 2021

Hierarchical models are often considered to measure latent concepts defining nested sets of manifest variables. Therefore, by supposing a hierarchical relationship among manifest variables, the general latent concept can be represented by a tree structure where each internal node represents a specific order of abstraction for the latent concept measured. In this paper, we propose a new latent factor model called second-order disjoint factor analysis in order to model an unknown hierarchical structure of the manifest variables with two orders. This is a second-order factor analysis, which—respect to the second-order confirmatory factor analysis—is exploratory, nested and estimated simultaneously by maximum likelihood method. Each subset of manifest variables is modeled to be internally consistent and reliable, that is, manifest variables related to a factor measure “consistently” a unique theoretical construct. This feature implies that manifest variables are positively correlated wi...

Joint Factor Analysis

1987

In this paper we discuss the problem of factor analysis from the Bayesian viewpoint. First, the classical factor analysis model is generalized in several directions. Then, prior distributions are adopted for the parameters of the generalized model and posterior dis-

A New Algorithm for Computing Disjoint Orthogonal Components in the Parallel Factor Analysis Model with Simulations and Applications to Real-World Data

Mathematics

In this paper, we extend the use of disjoint orthogonal components to three-way table analysis with the parallel factor analysis model. Traditional methods, such as scaling, orthogonality constraints, non-negativity constraints, and sparse techniques, do not guarantee that interpretable loading matrices are obtained in this model. We propose a novel heuristic algorithm that allows simple structure loading matrices to be obtained by calculating disjoint orthogonal components. This algorithm is also an alternative approach for solving the well-known degeneracy problem. We carry out computational experiments by utilizing simulated and real-world data to illustrate the benefits of the proposed algorithm.

Factor Analysis and DIF

2001

Abstract: We report on a psychometric study of the Center for Epidemiologic Studies Depression (CES-D) scale with 600 community-dwelling adults between the ages of 17 and 87 years. The mean age for males is 46 years (N=310) and 42 years for females (N=290). We propose and test a one-factor measurement model with confirmatory factor analysis, which takes into account method effects. The method effects represent the distinction between positively and negatively worded items. Also, we studied gender based differential item functioning (DIF) using a method proposed by Zumbo (1999). These DIF analyses were followed-up by nonparametric item response (IRT) DIF and differential test functioning. Our results indicate that the proposed measurement model fits and hence helps one understand the disparate literature on the factorial structure of the CES-D. This one factor model was also completely invariant (including method effects) across genders. With regard to the item level analyses investi...

Approximated Penalized Maximum Likelihood for Exploratory Factor Analysis: An Orthogonal Case

Psychometrika

The problem of penalized maximum likelihood (PML) for an exploratory factor analysis (EFA) model is studied in this paper. An EFA model is typically estimated using maximum likelihood and then the estimated loading matrix is rotated to obtain a sparse representation. Penalized maximum likelihood simultaneously fits the EFA model and produces a sparse loading matrix. To overcome some of the computational drawbacks of PML, an approximation to PML is proposed in this paper. It is further applied to an empirical dataset for illustration. A simulation study shows that the approximation naturally produces a sparse loading matrix and more accurately estimates the factor loadings and the covariance matrix, in the sense of having a lower mean squared error than factor rotations, under various conditions.

Latent Factor Decomposition Model: Applications for Questionnaire Data

2021 43rd Annual International Conference of the IEEE Engineering in Medicine & Biology Society (EMBC), 2021

The analysis of clinical questionnaire data comes with many inherent challenges. These challenges include the handling of data with missing fields, as well as the overall interpretation of a dataset with many fields of different scales and forms. While numerous methods have been developed to address these challenges, they are often not robust, statistically sound, or easily interpretable. Here, we propose a latent factor modeling framework that extends the principal component analysis for both categorical and quantitative data with missing elements. The model simultaneously provides the principal components (basis) and each patients' projections on these bases in a latent space. We show an application of our modeling framework through Irritable Bowel Syndrome (IBS) symptoms, where we find correlations between these projections and other standardized patient symptom scales. This latent factor model can be easily applied to different clinical questionnaire datasets for clustering analysis and interpretable inference.