Generalized Cumulative Model
The test of parallel lines can help you assess whether the assumption that the parameters are the same for all response categories is reasonable. This test compares the estimated model with one set of coefficients for all categories to a generalized model with a separate set of coefficients for each category.
The Wald F test is an omnibus test of the contrast matrix for the parallel lines assumption that provides asymptotically correct p values; for small to mid-sized samples, the adjusted Wald F statistic performs well. The significance value is near 0.05, suggesting that the generalized model may give an improvement in the model fit; however, the Sequential Sidak adjusted test reports a significance value high enough (0.392) that, overall, there is no clear evidence for rejecting the parallel lines assumption. The Sequential Sidak test starts with individual contrast Wald tests to provide an overall p value, and these results should be comparable to the omnibus Wald test result. The fact that they are so different in this example is somewhat surprising but could be due to the existence of many contrasts in the test and a relatively small design degrees of freedom.
Moreover, the estimated values of the generalized model coefficients don't appear to differ much from the estimates under the parallel lines assumption.