ロジャースの地域別人口分析法とその方法のわが国における地域別人口の構造分析への適用

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The purpose of this paper is to grasp and clarify the structure of the Roger's method of analysis of regional population and to try to introduce the "adjustment matrix of generalized Leslie matrix G", A. According to the Roger's model of regional population, regional population at time n, {K^<(n)>} is expressed by [numerical formula] (A) This equation can be rewritten in the following form. [numerical formula] (B) If we give numbers, n, n-1, ……, 2, 1 to the G's from the first G to the last G in the above equation (equation (B)), the equation is expressed by [numerical formula] (C) The matrix (generalized Leslie matrix) with subscript t, G_t is regarded as the specific generalized Leslie matrix for the period from time t-1 to time t. And, if the G_t (t=1, 2, ……, n) is not equal to G_t' (t'=1, 2, ……, n ; t'〓t), then G_t can be expressed by the equation: [numerical formula] (D) where the symbol "*" shows the Hadamard product or Shur product, and the A_<t_1> is the adjustment matrix of generalized Leslie matrix G_<t_1>. When we introduce the specific generalized Leslie matrix into the calculation of the future regional population {K^<(n)>}, we will be able to find a future regional population other than that which is obtained by using the constant generalized Leslie matrix G, although we can not find the stable equivalent. Therefore, we can say the (constant) generalized Leslie matrix G proposed by Rogers is very important for analysing the structure or character of future regional population, while the specific generalized Leslie matrix G_t will be used for finding the future regional population when the future structure of the matrix G can be estimated or supposed. When the specific generalized Leslie matrix is adopted for calculating the future regional population, the adjustment matrix of generalized Leslie matrix G, A will be used as the indicator of the change of the matrix G. We have another usage of the matrix A. If we have some G's which are actually obtained by surveys of population, and they are, for example, G_1, G_2, and G_3, then we can compare the structure of these G's to each other by using the matrix A. If we regard G_1 as a standard generalized Leslie matrix, then G_2 and G_3 will be expressed by G_2=A_2*G_1 (E.1) and G_3=A_3*G_1 (E.2) where matrices A_2 and A_3 are the adjustment matrix of generalized Leslie matrix which are regrded as the indicator of the difference between matrices G_1 and G_2 and the difference between matrices G_1 and G_3.
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ロジャースの地域別人口分析法とその方法のわが国における地域別人口の構造分析への適用

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