Input Formats in Correspondence Analysis - Frequencies without Grouping Variables

If the Frequencies w/out grouping vars option button is selected [from the Input group box on either the Correspondence Analysis (CA): Table Specifications Startup Panel - Correspondence Analysis (CA) tab or the Multiple Correspondence Analysis (MCA): Table Specifications Startup Panel - Multiple Correspondence Analysis (MCA) tab], Satistica expects that the selected variables (and cases) contain frequency values only (or some other measure of correspondence).

Selection of variables for simple correspondence analysis

If a simple correspondence analysis is specified, Statistica treats each selected variable as a category or level of a categorical (column) variable, and each case as a category or level of a second categorical (row) variable. For example, the data in the example file Smoking.sta are organized in this manner:

Selection of variables and codes for multiple correspondence analysis

If a multiple correspondence analysis is selected, then the data in the selected variables (and cases) are expected to define a valid Burt table. For example, the following data specify a valid Burt table:

	Survival			Age				Location
	NO	YES		<50	50-69	69+		TOKYO	BOSTON	GLAMORGN
SURVIVAL:NO	210	0		68	93	49		60	82	68
SURVIVAL:YES	0	554		212	258	84		230	171	153
AGE:UNDER_50	68	212		280	0	0		151	58	71
AGE:A_50TO69	93	258		0	351	0		120	122	109
AGE:OVER_69	49	84		0	0	133		19	73	41
LOCATION:TOKYO	60	230		151	120	19		290	0	0
LOCATION:BOSTON	82	171		58	122	73		0	253	0
LOCATION:GLAMORGN	68	153		71	109	41		0	0	221

The Burt table has a clearly defined structure. Overall, the data matrix is symmetrical. In the case of 3 categorical variables, the data matrix consists of 3 x 3 = 9 partitions, created by each variable being tabulated against itself, and against the categories of all other variables. Note that the sum of the diagonal elements in each diagonal partition (that is, where the respective variables are tabulated against themselves) is constant (equal to 764 in this case). Technically, the Burt table is the result of the inner product of an indicator or design matrix; if the cases in that indicator matrix are assigned to categories via fuzzy coding (that is, if probabilities are used to indicate likelihood of membership in a category, rather than 0/1 coding to indicate actual membership), then the off-diagonal elements of the diagonal partitions are not necessarily equal to 0. Note that complex coding schemes can easily be implemented, and the respective Burt table computed, using Statistica Visual Basic.

In addition to selecting the variables for the analysis, you also need to specify the structure of the Burt table. Click the Specify structure of table button (on the Multiple Correspondence Analysis (MCA): Table Specifications Startup Panel - Multiple Correspondence Analysis (MCA) tab) to display the Specify the dimensions of the table dialog box, in which you specify the factor names (example, survival, age, location) and the number of levels for each factor (example, 2, 3, and 3). When processing the data, Statistica automatically checks whether the respective data specify a valid Burt table. Note that the Specify structure of table button is only available after Variables have been selected.

In addition to the variables defining the table for the analysis, you can designate some variables as Supplementary columns (variables). Note that unlike in simple correspondence analysis, where supplementary columns and rows can be added from the Correspondence Analysis Results - Supplementary points tab, in multiple correspondence analysis it is required that the supplementary columns also define a valid Burt table. Therefore, in this case, click the Variables with frequencies button [on the Multiple Correspondence Analysis (MCA): Table Specifications Startup Panel - Multiple Correspondence Analysis (MCA) tab] to specify all variables for the analysis, and then click the Supplementary columns (variables) button to display the Select the Variables that are Supplementary Column dialog box, in which you select a subset of those variables as supplementary columns. When processing the data, Statistica automatically checks whether the selected subset of variables define a valid subset (Burt table) of the overall Burt table. The variables selected as supplementary columns are not used for the computation of eigenvalues and eigenvectors, but coordinate values are computed for those columns and reported in the spreadsheet and plots of coordinates.