The endpoint stiffness of the human arm has been long recognized as a key component ensuring the quasi-static stability of the arm physical interactions with the external world. Similarly, the understanding of the joint stiffness behavior can provide complementary insights, e.g., on the underlying stiffness regulation principles across different joints including the nullspace stiffness profiles. Traditionally, the experimental modeling and estimation of the human arm joint stiffness is achieved by the transformation of the identified arm endpoint stiffness to the joint coordinates. Due to the underlying kinematic redundancy, the obtained joint stiffness matrix is rank-deficient which implies that the information in the joint stiffness matrix is incomplete. While in robotics applications this issue can be addressed by designing a desired nullspace stiffness behavior through appropriate projections, the use of a similar technique in the identification of human joint stiffness profile is meaningless. Hence, the first objective of this work is to address this issue by developing a novel technique to identify the complete and physiologically meaningful joint stiffness of human arm. Second, we present a model-based online estimation technique to estimate the seven-dimensional complete joint stiffness in various arm poses and activation levels of the two dominant arm muscles that correspond to the geometric and volume modifications of the joint stiffness profile, respectively.