The question of sample size here is important. As discussed in this note, the test for proportional odds is known to be liberal with small sample sizes. Your graphical assessment might be more important. Also, as discussed in this note and in the "Details: Overdispersion: Rescaling the Covariance Matrix" section of the LOGISTIC documentation, the Pearson and deviance statistics require replication within the subpopulations in order to be valid. If there is suitable replication, then the similarity of the two statistics suggests they are providing a reasonable test of fit and their significance could be due to overdispersion or an incorrectly specified model. You might want to try adding complexity to the model (interactions, quadratic terms, splines, etc.) as seems reasonable to try to achieve a correctly specified model. If these statistics are still significant, then you might have a problem with overdispersion. The second note mentioned above discusses this.
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