Traditional determinant analyses of the socio-economic and spatial interaction data are vulnerable to biases in parameters if estimated without important relation factors. In order to avoid this bias problem, the Odds Ratio Decomposition method (ORDEC) has been proposed and applied by the author. However, its statistical properties of decomposed factors have only been derived with Monte-Carlo simulations. This study, firstly, demonstrates an unbiased decomposition of a linearized Gravity Model. The interaction data can be unbiasedly decomposed into latent push factor, pull factor and relational factor by the Generalized Least Square method. Secondly, it is shown that determinant analyses of these decomposed latent factors can be separately conducted so that biases are contained only within the same class of the latent factors, and that unbiased and consistent estimates of determinants' parameters can be obtained. The results of this paper would greatly help us to understand both determinants of socioeconomic and spatial interaction data, and characteristics of the ORDEC. In this paper, due to limitations of space, only the unbiased decomposition of push factor and its determinant analysis are described on the premises that diagonal elements of a socio-economic or spatial interaction data matrix can be used and may be treated equivalently to non-diagonal ones. Decomposition of pull factor and relational factor can be similarly conducted, and cases without diagonal elements can be also similarly treated but with more complicated matrices.