In genome-wide association studies (GWAS), logistic regression is one of the most popular analytics methods for binary traits. Multinomial regression is an extension of binary logistic regression that allows for multiple categories. However, many GWAS methods have been limited application to binary traits. These methods have improperly often been used to account for ordinal traits, which causes inappropriate type I error rates and poor statistical power. Owing to the lack of analysis methods, GWAS of ordinal traits has been known to be problematic and gaining attention. In this paper, we develop a general framework for identifying ordinal traits associated with genetic variants in pedigree-structured samples by collapsing and kernel methods. We use the local odds ratios GEE technology to account for complicated correlation structures between family members and ordered categorical traits. We use the retrospective idea to treat the genetic markers as random variables for calculating genetic correlations among markers. The proposed genetic association method can accommodate ordinal traits and allow for the covariate adjustment. We conduct simulation studies to compare the proposed tests with the existing models for analyzing the ordered categorical data under various configurations. We illustrate application of the proposed tests by simultaneously analyzing a family study and a cross-sectional study from the Genetic Analysis Workshop 19 (GAW19) data.