Data representations

• Categorical data is neat:
  • small number of values
  • a set of $N$ variables can be represented as an $N$-dimensional table without loss of information.

• There are three main ways of representing categorical data and we can move between them:
  1. Conventional data set: one row per case;
  2. Table: one dimension per variable; and
  3. Machine-readable: one row per combination of variable categories.

• Conventional rectangular data set: one row per case, one column per variable:

  Figure: A data matrix, in the SPSS data editor...

  

• Micro-data of this form is the most general because it allows each case to have different values on any variable: for instance, it is the only way to store continuous-variable data, where it is possible that every case has a different value.

• Micro-data consisting exclusively of categorical variables can be represented as a table; the table can be re-expressed in machine-readable form, where each cell is given a row, containing the values of each of the classifying variables and the cell count:

  
  

  
  
  
  
  A `natural' format

  Table: Two table formats

  	Variable 2
  Variable 1	1	2
  1	11	12
  2	21	22
  3	31	32

  A `machine-readable' format

  1	1	11
  1	2	12
  2	1	21
  2	2	22
  3	1	31
  3	2	32

  
  

• The machine-readable format is used as input to stats programs (necessary format for programs like GLIM and Stata, acceptable for programs like SPSS and SAS).

  This format can be easily produced by stats programs (for exporting data to other programs). For instance, in SPSS:

  procedure output out='temp.dat'.  
  crosstabs /var=a(1,5) b(1,3)
            /tables=a by b
            /write=all.
  

• And finally, data in this form can be expanded back to micro-data by using weights:

  data list free /dose outcome count.
  begin data.
  1 3 15
  1 2 1
  1 1 281
  2 3 17
  2 2 0
  2 1 225
  3 3 22
  3 2 7
  3 1 283
  4 3 38
  4 2 59
  4 1 202
  5 3 144
  5 2 132
  5 1 9
  end data.
  
  weight by count.
  

• Weights make the stats procedures act as if, for instance, there were 15 different cases with dose=1 and outcome=3.

• In short, three equivalent, interchangeable formats.

Loglinear Analysis Unit 2