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We propose generalized mixed reduced rank regression for the analysis of mixed response variables and mixed predictor variables. The response variables can be a mixture of numeric, ordinal, and binary variables for which we combine, in a single model, ideas from linear regression, logistic regression, and cumulative logistic regression. The predictor variables can be a mix of binary, nominal, ordinal, and numeric data. For categorical predictor variables, we propose to use optimal scaling, that provides optimal quantifications of the predictor variables. All these elements are combined into a single multivariate regression model, where we place a rank restriction on the matrix with regression coefficients to reduce the dimensionality. A majorization-minimization algorithm is proposed for maximum likelihood estimation of the model parameters. The methodology will be illustrated using data from the Eurobarometer survey.

MM algorithm, nominal, ordinal, numeric, dichotomous