MULTILEVEL ANALYSIS

General information about multilevel analysis can be found at the web sites of the
Centre for Multilevel Modelling (CMM) in Bristol,
and the
Papers on Multilevel Modeling at the UCLA website.

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.

This page contains information about:

1. The textbook, Multilevel Analysis: An introduction to basic and advanced multilevel modeling , written by myself and Roel Bosker.
2. Some MLn/MLwiN macros for multilevel model diagnostics and for fitting the Social Relations Model, including the PreML.inc utility for exporting data from SPSS to MLwiN.
3. The program PINT for determining sample sizes in two-level modeling.
4. A method for two-level scale analysis , implemented in the program TWOMOK.
   This is now superseded by various functions in the mokken package at CRAN.

1. MULTILEVEL TEXTBOOK

   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:

   1. Some of the data sets used in examples, with set-ups for running the examples in MLwiN and in HLM;
   2. A short introduction to MLwiN using examples of Chapters 4, 5, and 14;
   3. Some addenda and errors.

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2. MLN/MLWIN MACROS

   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.

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   PINT

   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 11).
   Other relevant publications about sample sizes in multilevel analysis are

   • Snijders, T.A.B., Sampling, Chapter 11 (p. 159-174) in A. Leyland and H. Goldstein (eds.) (2001) Multilevel Modelling of Health Statistics, (contains an example for PinT).
   • Snijders, T.A.B., Power and Sample Size in Multilevel Linear Models; p. 1570-1573 in B.S. Everitt and D.C. Howell (eds.), Encyclopedia of Statistics in Behavioral Science. Chicester (etc.): Wiley, 2005 (Volume 3).

   Material for PinT:

   • Download Windows version Pint 2.11. [240KB]
   • Download Windows version Pint 2.12. [280KB]
     This differs from version 2.11 only in that it can handle larger numbers of variables.
   • View extensive manual in Adobe Acrobat Reader format.

   • Download Delphi 5 source code of PinT 2.11. [53KB]
   • Download Delphi 5 source code of PinT 2.12. [54KB]
   • Download old DOS version 1.61 with very brief documentation.[30KB]

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   TWOMOK

   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.

   • Download program TWOMOK with very brief documentation.[28KB] This is a zipped file containing the DOS program, a concise description of the program, and a small example data set.
   • Snijders, T.A.B. (2001). 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.
     
   • Crisan, D. R., Van de Pol, J. E., and Van der Ark, L. A. (2016). Scalability coefficients for two-level polytomous item scores: An introduction and an application. In L. A. Van der Ark, D. M. Bolt, W.-C. Wang, and M. Wiberg (Eds.), Quantitative Psychology Research. New York, NY: Springer.
     DOI: http://dx.doi.org/10.1007/978-3-319-38759-8_11
   • Letty Koopman, Bonne J.H. Zijlstra, and L. Andries van der Ark. A two-step, test-guided Mokken scale analysis, for nonclustered and clustered data. Quality of Life Research 31 (2022), 25-36.
     DOI: https://doi.org/10.1007/s11136-021-02840-2

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