Joint Correspondence Analysis (JCA) by Maximum Likelihood

Abstract

Parameter estimation in joint correspondence analysis (JCA) is typically performed by weighted least squares using the Burt matrix as the data matrix.In this paper, we show how to estimate the JCA model by means of maximum likelihood. For that purpose, JCA is defined as a model for the full K-way distribution by generalizing the correspondence analysis model for three-way tables proposed by Choulakian (1988aChoulakian ( , 1988b. The advantage of placing JCA in a more formal statistical framework is that standard chisquared tests can be applied to assess the goodness-of-fit of unrestricted and restricted models.

Alternative Methods to Multiple Correspondence Analysis in Reconstructing the Relevant Information in a Burt's Table

“…As for the interpretation of the factors, JCA is not very different from MCA, whereas the method's differences of EMC impose a different interpretation that may be further studied. Thus, JCA seems the most promising development of MCA and its properties deserve some further deepening, including the three available programs [21,41,43]: indeed, a direct comparison of these results with those obtained through Greenacre's [22] inertia evaluation through regression, may provide further insights on both methods, albeit our critics on the use of chi-square metrics for the whole Burt's table remain.…”

Item Response Modeling of Presence-Severity Items

“…Turning this into a one-way layout directly is impractical because the number of categories and hence the number of parameters are very large. Parameter restrictions such as used in log-multiplicative models (Vermunt & Anderson, 2005) or the generalized stereotype model (Johnson, 2007) may be useful.…”

“…The authors used joint correspondence analysis (JCA) to perform a basic screening and descriptive analysis of the physical and psychological symptoms. This is in accordance with Stout’s (2002) recommendation to use a less model-dependent technique prior to running IRT analysis to assess the plausibility of what he calls “essential unidimensionality.” JCA is a multivariate nominal data analysis technique based on an iterative weighted least squares analysis of the two-way margins (Greenacre, 2007; Vermunt & Anderson, 2005). JCA focuses on the two-way associations as measured by Pearson chi-square (called inertia in this literature).…”

Modeling Polytomous Item Responses Using Simultaneously Estimated Multinomial Logistic Regression Models

“…For two observed variables, LMA models, correspondence analysis, and latent class models yield very similar results; however, for more variables, the results diverge. If there are primarily only two-way interactions in data, then for a given number of parameters, the LMA (multiplicative) models tend to be superior to the additive ones (e.g., Kroonenberg & Anderson, 2006; Vermunt & Anderson, 2005).…”