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Dimensional sentiment analysis has received considerable attention because it can represent affective states as continuous numerical values on multiple dimensions such as valence (positive–negative) and arousal (excited–calm). Compared to the categorical approach, which represents affective states as several discrete classes (e.g., positive and negative), the dimensional approach can provide more fine-grained (real-valued) sentiment analysis. Traditional approaches to predicting dimensional sentiment scores typically treat each dimension independently without consideration of relations between dimensions. In fact, different dimensions may correlate with each other. For example, expressions with a higher valence score usually have a higher arousal score, And higher irony expressions usually have a lower valence score. Such relations between dimensions are useful for dimension score prediction. To this end, this study proposes a multi-dimensional relation model to incorporate relations between dimensions into deep neural networks for dimension score prediction. The proposed method has two modes: internal and external. The internal mode incorporates the relations between dimensions into sentence representations before prediction, whereas the external mode builds a linear regression model that can capture the relations between dimensions to refine the predicted scores after prediction. To evaluate the proposed method, we created a Chinese three-dimensional corpus with valence-arousal-irony (VAI) ratings. Experiments using various neural network architectures demonstrate that the proposed multi-dimensional relation model outperformed those that treat each dimension independently. In addition, the internal mode outperformed the external mode, and a combination of the two modes achieved the best performance. [ABSTRACT FROM AUTHOR]