A Multivariate Logistic Distance Model for the Analysis of Multiple Binary Responses
- 208 Downloads
We propose a Multivariate Logistic Distance (MLD) model for the analysis of multiple binary responses in the presence of predictors. The MLD model can be used to simultaneously assess the dimensional/factorial structure of the data and to study the effect of the predictor variables on each of the response variables. To enhance interpretation, the results of the proposed model can be graphically represented in a biplot, showing predictor variable axes, the categories of the response variables and the subjects’ positions. The interpretation of the biplot uses a distance rule. The MLD model belongs to the family of marginal models for multivariate responses, as opposed to latent variable models and conditionally specified models. By setting the distance between the two categories of every response variable to be equal, the MLD model becomes equivalent to a marginal model for multivariate binary data estimated using a GEE method. In that case the MLD model can be fitted using existing statistical packages with a GEE procedure, e.g., the genmod procedure from SAS or the geepack package from R. Without the equality constraint, the MLD model is a general model which can be fitted by its own right. We applied the proposed model to empirical data to illustrate its advantages.
KeywordsMultivariate binary data Biplots Multidimensional scaling Multidimensional unfolding Marginal model Clustered bootstrap Generalized estimating equations
- AKAIKE, H. (1973), “Information Theory and an Extension of the Maximum Likelihood Principle”, in Proceedings of the Second International Symposium on Information Theory, eds. B.N. Petrov and F. Csaki, Budapest: Akademiai Kiado, pp. 267–281.Google Scholar
- BEESDO-BAUM, K. et al. (2009), “The Structure of Common Mental Disorders: A Replication Study in a Community Sample of Adolescents and Young Adults”, International Journal of Methods in Psychiatric Research, 18, 204–220.Google Scholar
- BOOMSMA, A., and HOOGLAND, J.J. (2001), “The Robustness of LISREL Modeling Revisted”, in Structural Equation Modeling: Present and Future, eds. R. Cudeck, S. de Toit, and D.Sörbom, Chicago: Scientific Software International, pp. 139–168.Google Scholar
- COSTA, P.T., and MCCRAE, R.R. (1992), Revised NEO Personality Inventory (NEO-PRI) and NEO Five-Factor Inventory (NEO- FFI) Professional Manual, Odessa, FL: Psychological Assessment Resources.Google Scholar
- KRUSKAL, J.B., and WISH, M. (1978), Multidimensional Scaling, Sage Publications.Google Scholar
- R DEVELOPMENT CORE TEAM (2013), “R: A Language and Environment for Statistical Computing”, Computer Software Manual Version 3.0.2, Vienna, Austria, http://www.r-project.org/.
- SAS INSTITUTE INC. (2011), “SAS/STAT Software”, Computer Software Manual Version 9.3, Cary, NC, http://www.sas.com.
- TER BRAAK, C.J.F., and VERDONSCHOT, P.F.M. (1995), “Canonical Correspondence Analysis and Related Multivariate Methods in Aquatic Ecology”, Aquatic Sciences, 57(3), 1015–1621.Google Scholar
- VAN DER HEIJDEN, P.G.M., MOOIJAART, A., and TAKANE, Y. (1994), “Correspondence Analysis and Contingency Models”, in Correspondence Analysis in the Social Sciences, eds. M.J. Greenacre and J. Blasius, New York: Academic Press, pp. 79–111.Google Scholar
- WEI, X. (2012), “%PROC_R: A SAS Macro That Enables Native R Programming in the Base SAS Environment”, Journal of Statistical Software, 46.Google Scholar
- WORKU, H.M., and DE ROOIJ, M. (2016), “Properties of Ideal Point Classification Models for Bivariate Binary Data”, Psychometrika (accepted for publication).Google Scholar
- ZIEGLER, A., and ARMINGER, G. (1995), “Analyzing the Employment Status with Panel Data from GSOEP - A Comparison of the MECOSA and the GEE1 Approach for Marginal Models”, Vierteljahreshefte zur Wirtschaftsforschung, 64, 72–80.Google Scholar
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.