Simple Pictures are Guttman's Ideal

"Simple routines have been established which require no knowledge of statistics, which take less time than the various manipulations now used by various investigators (such as critical ratios, biserial correlations, factor analysis, etc.), and which give a complete picture of the data not afforded by other techniques. The word `picture' might be interpreted here literally, for the results of the analysis are presented and easily assimilated in the form of a `scalogram', which at a glance gives the configuration of the qualitative data."

Guttman, Louis (1944) A basis for scaling qualitative data. American Sociological Review, 9:2, p.139

"These types [of person] could be shown in a chart (`a scalogram') where there is one row for each type of person and one column for each category of attribute [item] .... the scale analysis would establish an order among the rows and the columns." (ibid. p. 144)

False3 True2 False1 True3 False2 True1
x x x      
  x x x    
    x x x  
      x x x

In Guttman's original method, there is a separate column for each possible category of each attribute or item. Each column (attribute category) is checked for the presence or absence of that category for each person. Thus the column "False3" is checked if the person (row) responded false to attribute 3. Guttman uses cluster analysis by eye to reorder the rows and columns into a parallelogram:
"The `parallelogram' pattern in the chart, (such a chart, where one column is used for each category of an attribute, we call a scalogram), is necessary and sufficient for a set of dichotomous attributes to be expressible as simple functions of a single quantitative variable." (ibid. p. 144)

In later usage, each item is assigned only one column in the scalogram. Response category values are entered directly, so that the desired Scalogram pattern becomes a triangle. The conventional Scalogram orders the persons (rows) by raw score descending, and the items (columns) by raw score ascending.

Simple Pictures are Guttman's Ideal Guttman L. … Rasch Measurement Transactions, 1998, 12:3 p. 642.


Please help with Standard Dataset 4: Andrich Rating Scale Model



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