Mobility Table

Historical Development

Essentially developed in sociology from the 1950s, the statistical methodology of mobility tables was primarily based on the computation of indexes. The mobility ratio or Glass's index was proposed as the ratio of each observed frequency in the mobility table to the corresponding expected frequency under the hypothesis of statistical independence (also called “perfect mobility”). Yasuda's index and Boudon's index were based on the decomposition of total mobility as the sum of two components: structural or “forced” mobility (the dissimilarity between marginal distributions implies that all cases cannot be on the diagonal) and net mobility (conceived of as reflecting the intensity of association). However, with time, the shortcomings of mobility indexes became increasingly clear.

Since the 1980s, the new paradigm has been to analyze mobility tables from two perspectives. Total immobility rate (Σi ƒii/ƒ++), outflow percentages (ƒij /ƒi+), and inflow percentages (ƒij /ƒ + j) are simple tools to describe absolute (or observed) mobility. But absolute mobility also results from the combination of the marginals of the table with an intrinsic pattern [Page 654]of ASSOCIATION between the variables. The study of relative mobility consists of analyzing the structure and strength of that association with LOG-LINEAR MODELS and ODDS RATIOS.

Among these models, “topological” or “levels” models are an important class based on the idea that different densities underlie the cells of the mobility table. In the two-way multiplicative (log-linear) model Fij = αβiγjδij, positing δij = 1 for all i and all j leads to the independence model. It assumes that a single density applies for the entire table; that is, each of the mobility or immobility trajectories is equally plausible (net of marginal effects). Positing δij = δ if i = j and δij = 1 otherwise corresponds to a two-density model (with one degree of freedom less than the independence model) called the uniform inheritance model because δ, which is usually more than 1, captures a propensity toward immobility common to all categories. Assuming that this propensity is specific to each category (δij = δi if i = j) leads to the quasi-perfect mobility model. With the insight that the same density can apply to cells on and off the diagonal, R. M. Hauser (1978), following previous work by Leo Goodman, proposed the general levels model: Fij = αβiγjδk if the cell (i, j) belongs to the kth density level.

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