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In real life, we frequently encounter ordinal variables depending upon independent covariates. The latent linear regression model is useful for modelling such data. One can find the model's parameters' maximum likelihood estimate (MLE). Though noted for its optimum properties, a small proportion of outliers may destabilize the MLE. This paper uses the minimum density power divergence estimate (MDPDE) as a robust alternative. The roles of different link functions are analysed in this context. We discuss their asymptotic properties in this setup. Unlike the MLE, the MDPDEs are robust for– lower values of the gross error sensitivity, and very high breakdown point. Also, the slope's MDPDEs never implode. In simulation studies for pure data, MDPDEs perform almost as good as the MLE. However, the MDPDEs outperform the MLE in data contamination. Moreover, MDPDEs are very competitive with the other robust alternatives. Finally, this article is wrapped up with a real-data example. [ABSTRACT FROM AUTHOR]