Studying the fit between employees and their organisations and the individual and organisational outcomes of this congruence has been an interesting topic for researchers over the past decades. However, the literature does not adequately address how this fit affects other organisational attitudes - in particular organisational commitment. In this study, a theory on the mechanism by which employees' perception of person-organisation values fit impacts their affective organisational commitment and how this is impacted by their perceptions of the psychological climate is offered. Moreover, the study contributes to the literature through applying the Latent Congruence Model (LCM) developed by Cheung (2009a). Accordingly, all the hypotheses that pertain to values congruence, psychological climate and affective organisational commitment are simultaneously tested, controlling for the measurement errors. This SEM approach could be a useful analysis tool, especially as we know that, according to the simulation study of Cheung and Lau (2008), the bias in regression coefficients due to measurement error using path analysis may exceed 16% on average. Therefore, studying congruence under the frame of SEM in turn increases the accuracy and the significance of the congruence-related studies. The study was conducted in an Egyptian medium-sized textile organisation (N = 223). The results of the study supported the hypotheses that there would be positive relationships between affective organisational commitment and both perceived person-organisation values fit and psychological climate. Moreover, perceived person-organisation values fit demonstrated a positive impact on psychological climate. Importantly, psychological climate mediated the relationship between perceived person-organisation values fit and affective organisational commitment. The implications of these findings and directions for future research are discussed.