Collaborative tagging systems allow users to attach tags to diverse sharable contents in social networks. These tags provide usefulness in reusing the contents for all community members as well as their creators. Three-dimensional data composed of users, items, and tags are used in the collaborative tag-based recommendation. They are generally more voluminous and sparse than two-dimensional data composed of users and items. Therefore, there are many difficulties in applying existing collaborative filtering methods directly to them. Latent factor models, which are also successful in the area of collaborative filtering recently, discover latent features(factors) for explaining observed values and solve problems based on the features. However, establishing the models require much time and efforts. In order to apply the latent factor models to three-dimensional collaborative filtering data, we have to overcome the difficulty of establishing them. This paper proposes various methods for determining preferences of users to items via establishing an intuitive model by assuming tags used for items as latent factors to users and items respectively. They are compared using real data for concluding desirable directions.