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5.2.2 Subsidiary dimensions in LEM: details
To specify subsidiary dimension structures to a LEM RC model, it is necessary to adjust the LEM model command file accordingly, and also to adjust the contents of the design matrix used in the model estimation.
The LEM command file specification for using a model with subsidiary dimension structures is very simple (see also the LEM manual, p16ff). As can hopefully be seen from the 'mod' command section of the example LEM command file referred to eariler, we use the 'ass2' (association model RC-II) command once for every distinct dimension we wish to estimate scores in. If the scores are to be unconstrained within the dimension (ie separate scores possible for each base unit), we specify only three arguments, the name of the row and column variables, and the type of association model to be used. If however we wish to impose some form of constraints on the dimension structures, we specify within the 'ass2' command two additional arguments, which indicate the total number of categories within the constrained dimension for first the row variable, then the column variable. In turn, LEM will search the design matrix specified elsewhere on the command file, for instructions on how to define those constraints for each individual row or column value.
As described above, the first design matrixes contain tables which indicate which row by column combinations are treated as pseudo-diagonals. To add the identification of subsidiary dimensions to them, it is necessary simply to add, to the end of the design matrix file, two rows (vectors), n units long where n is the number of base units in the model, where successive numbers indicate which values are constrained to be equal to each other. The first vector gives the constraints for the models' row scores (male occupational units in most CAMSIS versions), and the second vector gives the constraints for the column scores (females units). Thus the dimension restrictions can be entered separately for the row and column entries (male and female occupational units), though in our example the dimensions, as substructures of the base unit, are always equivalent for men and women.
To give a simple example: if there were only 10 base units in the model, and a subsidiary dimension was used to constrain then into four different groups, a possible row to add to the design matrix might be : 1 2 2 2 2 2 3 3 4 4; for another example see the last rows of this example design matrix.
The accompanying file has an example of SPSS syntax that can be used to create indicators of the relevant dimensional structures. The section produces SPSS plain text output files where the relevant numbers are stacked into a single column; these files can be opened in a text editor such as pfe, and the 'replace' function used to replace vertical line ends ("\n") with space characters, then the subsequent horizontal line (vector) pasted to the base of the relevant design matrix (in fact it should be pasted twice, once for the male occupational units then once for the female units).
As an extension, although not dealt with here, this facility of specifying constraints in the scores across multiple dimensions in the LEM RC estimation can also be used to compare nested representations of occupational stratification schema, for instance to compare the strength of competing class categorisation schema in explaining patterns of social interaction.
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Last modified 14 February
This document is maintained by Paul Lambert (firstname.lastname@example.org)