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Collecting sensitive data using surveys is one of the most challenging tasks facing survey methodologists as people may choose to answer questions untruthfully to present themselves in a positive light. In 2014, Mneimneh et al. proposed mixed Rasch models to detect socially desirable answering behaviors. This approach combines item response theory models with latent class analysis to differentiate substantive and biased answering patterns. Their results identified two latent classes, one of which was consistent with socially desirable answering. Our aim is to expand their approach to detecting social desirability by using a mixture confirmatory factor analysis (CFA) in round 7 of the European Social Survey. First, we attempt to estimate social desirability in three constructs separately (RQ1): effect of immigration on the country, allowing people to come in the country and social connection, using a mixture CFA. We then extend the analysis by (RQ2) introducing constraints between the latent classes, (RQ3) combining different constructs in one model, and (RQ4) comparing results in Belgium and the United Kingdom. In contrast with the paper published by Mneimneh et al. in 2014, the models with two latent classes do not have the best model fit. In addition, validation with the presence of a third person, the respondent's reluctance to give answers and personality traits are not systematically in line with our expectations. A small simulation shows that the method would work if the data would behave as we expect, with social desirability being the main factor influencing answering patterns. We conclude that a mixture CFA might not be able to identify social desirability in different survey contexts, especially in complex data as originating in cross-national social surveys. [ABSTRACT FROM AUTHOR]