A very brief overview of the main ideas of multilevel analysis is in T.A.B. Snijders, Multilevel Analysis, p. 673-677 in M. Lewis-Beck, A.E. Bryman, and T.F. Liao (eds.), The SAGE Encyclopedia of Social Science Research Methods (Volume II). Sage, 2003.
A textbook,
Multilevel Analysis: An introduction to basic and advanced
multilevel modeling ,
written by myself and Roel Bosker, appeared in 1999 at Sage Publishers,
and the second edition in November 2011.
By clicking here you go to the webpage for the second edition, with data sets and software setups.
By clicking here you go to the page for the first edition of this book, which contains:
A number of macros are available for use in the multilevel computer program MLn/MLwiN: for model checking and for fitting the Social Relations Model.
PinT is a program for Power analysis IN Two-level designs (for
determination of standard errors and optimal sample sizes in
multilevel designs with 2 levels). It was written by Tom
Snijders, Roel Bosker, and Henk Guldemond.
The newest (Windows) version is 2.12 (September 2007), a minor change
(this version can handle more variables) from version 2.11 (April 2003).
This program calculates approximate standard errors for
estimates of fixed effect parameters in hierarchical linear
models with two levels. The formulae are derived in the
following publication.
Snijders, T.A.B. & Bosker, R.J., Standard errors and sample
sizes for two-level research,
Journal of Educational Statistics, 18 (1993), 237-259.
Some references to sample size determination in multilevel studies,
not mentioned in my textbook (Snijders & Bosker, 1999),
can be found on the
web page of the book (go to Chapter 10).
Other relevant publications about sample sizes in multilevel
analysis are
Material for PinT:
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Non-parametric scale analysis for two-level data (ecometrics)
Snijders (2001) describes a method for non-parametric
scale analysis of two-level 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 in which this subject is nested.
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).
This method is implemented in functions MLcoefH and MLweight in the R package mokken.
An older stand-alone DOS implementation is the program TWOMOK.