The second edition of the textbook, Multilevel Analysis: An introduction to basic and advanced multilevel modeling, written by Tom A.B. Snijders and Roel J. Bosker, appeared November 2011 at Sage Publishers. The official publication year, however, is 2012. The Sage announcement of this book is here, and here is the table of contents. The book was totally updated compared to the first edition, with new chapters on missing data, survey weights in multilevel analysis, and miscellaneous methods (Bayesian estimation, sandwich standard errors, latent class models). Each chapter (from 2 to 17) ends with a glommary, which is a combination of a glossary and a summary, giving the main terms and an overview of the chapter. Here is a set of slides which can be used for teaching. This webpage contains:

> mlbook_red < read.table("mlbook2_r.dat", header=TRUE)For reading this file into other software, delete the top line but note that it contains the variable names.
obey mlbook2_r.obe
> mlbook_mm < read.table("mlbook2_mm.dat", header=TRUE)For reading this file into other software, delete the top line but note that it contains the variable names.
obey mlbook2_bb.obeIf you wish to use this data file in other software, just delete the top and bottom text lines that contain the information for MLwiN.
obey mlbook2_b.obeIf you wish to use this data file in other software, just delete the top and bottom text lines that contain the information for MLwiN.
> mlbook_b < read.table("mlbook2_b.dat", header=TRUE)
> level2 < read.table("rel_level2.txt", header=TRUE)For reading this file into other software, delete the top line but note that it contains the variable names.
Note that you can download the files below in many browsers by rightclicking on the file, and choosing something like "save as".
HLM 
MLwiN 
R 
Mplus 
SAS 
Stata 
Chapter Title  
Chapter 3  CH3ex7.obe  Chap03_np.do  Statistical Treatment of Clustered Data  
Chapter 4  mlbook_hlm_chapter4.zip  CH4568.obe  ch45.r  chap4.do  The Random Intercept Model  
Chapter 5  mlbook_hlm_chapter5.zip  CH4568.obe  ch45.r  chap5.do  The Hierarchical Linear Model  
Chapter 6  mlbook_hlm_chapter6.zip  CH4568.obe  ch6.r  chap6.do  Testing and Model Specification  
Chapter 7  How much does the model explain?  
Chapter 8  mlbook_hlm_chapter8.zip  CH4568.obe  ch8.r  chap8.do  Heteroscedasticity  
Chapter 9  ch9.r  chap9.do  Missing Data  
Chapter 10 
ch10.obe ch10_infl.obe 
ch10.r  chap10.do  Assumptions of the Hierarchical Linear Model  
Chapter 11  Designing Multilevel Studies  
Chapter 12  chap12.do  Other Models and Methods  
Chapter 13  chap13.do  Imperfect Hierarchies  
Chapter 14  PISA.obe  pisa_b.R  chap14.do  Survey Weights  
Chapter 15 
soep5560_21.obe Example15_12.obe 
ch_15.r  Longitudinal Data  
Chapter 16  CH16.obe  ch16.r  Multivariate Multilevel Models  
Chapter 17 
ch17.r ch17_ex6.r 
chap17.do Chap17A_np.do 
Discrete Dependent Variables 
Alastair H. Leyland, Peter P. Groenewegen, Multilevel Modelling for Public Health and Health Services Research, Cham: Springer, 2020.
Although framed in the context of healthrelated research, it is also useful as a general introduction. The book has three extensive MLwiN tutorial chapters.
For these tests, there are the R packages ClusterRankTest and clusrank, both available from CRAN.
A paper contrasting the use of multilevel (hierarchical linear) models with methods that control in a simpler way for clustering of data, e.g., the sandwich estimator:
A different approach to latent class modeling:
Other R packages
A function to calculate the explained variance and residual intraclasscorrelation (as treated in Section 17.4) for estimates obtained from ordinal is contained at the end of script ch17.r.
The text should be:
When comparing Tables 4.4 and 5.1, it can be concluded
that m1  m0 = 2 parameters are added and the deviance diminishes
by D0  D1 = 24888.02  24864.87 = 23.15.
Testing the value of 23.15 in Table 6.2 for p=1
yields p < 0.001.
Thus, the significance probability of the random slope for IQ in the model
of Table 5.1 is p < 0.001.
Materials Oxford Spring School, April 2012