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Medical questionnaires are a valuable source of information but are often difficult to analyse due to both their size and the high possibility of them having missing values. This is a problematic issue in biomedical data science as it may complicate how individual questionnaire data is represented for statistical or machine learning analysis. In this paper, we propose a deeply-learnt residual autoencoder to simultaneously perform non-linear data imputation and dimensionality reduction. We present an extensive analysis of the dynamics of the performance of this autoencoder regarding the compression rate and the proportion of missing values. This method is evaluated on motor and non-motor clinical questionnaires of the Parkinson's Progression Markers Initiative (PPMI) database and consistently outperforms linear coupled imputation and reduction approaches. [ABSTRACT FROM AUTHOR]