This week introduces mobility tables. Moving forward from our discussion last week of the intergenerational transfers of occupation, mobility tables help to more formally relate associations between class of origin and destination class. The Basic Structure of Mobility Tables Mobility tables take some denition of classes, using evolved from Goldthorpe's neoWeberian schema and takes a measure of a sample intended to be representative of the population and places each population member in a table cell. The rows of the table indicate the class the individual came from (the origin class);
the columns of the table are the individual's current class position (the destination class). The rows and columns of the table are organized in such a way that the diagnol represents immobility. Interpreting mobility tables in terms of structure and exchange requires making certain assumptions.
Mobility Tables Origin and Destinations.

Destination

Origin

F11

F12

F13

F21

F22

F23

F23

F23

F33

Looking at frequency, Chisquare test of a particular model that says the two variables are independent.
Chisquare is the measure of difference between observed and expected if independent. Larger the Xsquare greater the deviance.
If no association between origin and destination, all you need is row effect, column effect and grand mean. F=abc
If there is an association F=a*b_{i}*c_{j}*g_{ij},
Log(F) = log(a)+log(b)+…
If you estimate all parameters for all cells, you get perfect association, but too many parameters and not helpful.
Want a model where we don’t use all parameters, want more parsimonious.
Want to make sure it reproduces the correct frequency in the marginal frequency.
Log linear implies different constraints on frequency. Chisquare measures the goodness of fit of a specific model, can estimate other models between statistically independent and perfectally saturated model (in which Chisquare =0)
Map out regions and within each region (group of cells) the association is the same. Get a pattern of expected frequencies that work with expected model and get a Chisquare that tells how much expected frequency are with observed frequency.
Constant Flux (book) known as the core model
Quasiperfect mobility. Diagonal cells in the table are immobility. Another model is to estimate separate diagonal cells (immobility) and if it doesn’t happen can equally go up or down in mobility.
Problem with topological models is that very different models can be good, but other models may also be good and mapping is arbitrary.
Another ways is to scale/order the categories and use a single parameter in the difference in origin and destination based on number of cells up or down. The uniform association models have a single parameter to describe association.
Quasiuniform association model where immobility is considered, assumes a higher concentration of cases on the diagnol and the rest of the parameters are consistent and depend on how far apart (number of classes) move.
Don’t need to use integers to scale, may use different numbers i.e. average status, SES, percentage not specialized, those with specialized training.
Can compare countries, genders, time, etc by comparing models. Look for differences in marginal distribution to tell how much structure mobility (up and down). Also can measure absolute mobility.
Unidiff is a very popular model to compare. Forces them to keep same measures of association, but the magnitude of them can vary. Proportional is preserved.
Looking at the average occupation overtime of parent and children, get strong immobility. 