             NONPARAMETRIC TWO-LEVEL CUMULATIVE SCALING



WHAT IS THIS PROGRAM ABOUT
==========================

The program TWOMOK is a DOS program for the non-parametric
scale analysis of two-level dichotomous data.
The nesting structure is defined by "subjects" (level-one units)
being nested in "objects" (level-two units).
Each subject provides responses on a set of m dichotomous items
with regard to the object. The objects are to be scaled,
the subjects may be considered to provide 'parallel tests'
for the objects.
This type of scaling problem was coined 'ecometrics' by
Raudenbush and Sampson (Sociological Methodology, 1999).
Examples are: pupils (subjects) who reply to questionnaires
about their teachers (objects), and employees (subjects) who
fill in questionnaires about their departments (objects).

The technique implemented in this program is described in
Snijders, T.A.B.,
Two-level non-parametric scaling for dichotomous data.
Pp. 319-338 in A. Boomsma, M.A.J. van Duijn, and T.A.B. Snijders (eds.),
"Essays on Item Response Theory".
Lecture Notes in Statistics, 157. New York: Springer, 2001.

The program was written in Turbo Pascal by Tom A.B. Snijders.
The name "TWOMOK" was chosen because the single level version
of this scaling model is often called the Mokken model
(after Robert J. Mokken who started it off in the early 1970's).


COMPARISON WITH MULTILEVEL ANALYSIS FOR BINARY DATA
===================================================

This paper is about the non-parametric scaling method used in TWOMOK.
An alternative, more well-known to people doing multilevel analysis,
is to apply the generalized hierarchical linear model
(multilevel analysis for binary outcome data) and use
the posterior means to provide scale values for the objects.
The main advantage of the non-parametric method is that
assumptions are minimal and calculations are easy
(just based on counting, no iterative calculations).
Its main disadvantage is that you cannot control for covariates.
I plan to develop in this method and additional feature of item selection,
i.e., formation of a good scale out of a larger set of items.
But that will take a while.

Please refer to this paper in your publications about this method.
The program and possible future developments
can be downloaded from the web site
http://stat.gamma.rug.nl/snijders/multilevel.htm/


INPUT DATA FORMAT
=================

The required input file has the following format.
* one line per object-subject combination.
* every line starts with an identification number for the object,
  and is followed by m integer numbers (the item scores);
  these numbers are separated by blanks;
  numbers <= bound are interpreted as "0" or "wrong",
  numbers > bound as "1" or "correct".
  (e.g. if the numbers are 0 and 1, the bound is 0)
* the bounds are asked from the user,
  and can be the same for all items, or item-dependent.
* no missing data within lines are allowed.
* the user is asked which of the items are used for the scale,
  the other items are read but ignored.
* for every object, the (one or more) lines corresponding to
  subjects for this object should be consecutive lines in the data file,
  all starting (of course) with the same object identification numbers.
* the object identification numbers of subsequent objects should be
  different; for the rest, they are arbitrary. In particular, they need
  not be increasing.

TWOMOK.IN is an example of a very small input file.

The program has limits for the number of items (denoted kmax in the
program source), for the maximal number of subjects per object
(denoted jmax), and for the number of objects (denoted imax).
If a data set is used that exceeds these limits,
then the program will stop after issueing the relevant error message.
These limits occur as constants in the program source. If necessary
they can be increased and the program can be recompiled.
In case this leads to memory problems, contact Tom Snijders at the
address below.

The program notices itself the number of items (when reading
the first data line) as well as the number of subjects for each object.
The program operates interactively; it just asks you questions about
the names of the data and output files,
whether you want to use all items,
the bounds separating "wrong" from "correct" scores,
the scale order of the items,
and about whether you wish to have object scores for output.
If you give an existing file name for output,
the contents of the file will be overwritten!

You are invited to send any comments, and the papers in which
this program is used, to

Tom Snijders
ICS / Department of Statistics and Measurement Theory
Grote Kruisstraat 2/1
9712 TS Groningen
The Netherlands
tel. +31 - (0)50 - 3636188
email T.A.B.SNIJDERS@PPSW.RUG.NL
http://stat.gamma.rug.nl/snijders/


January 10, 2001

