help  mltrsq                              Katja Moehring and  Alexander Schmidt

Calculating R-squared after two-level mixed models (beta version)


mltrsq [ , ] [ full ]

mltrsq is part of the mlt (multilevel tools) package.


mltrsq is an postestimation command for xtmixed (Stata Version 12 or above). It works after mixed models with two levels. mltrsq gives two different R-squared values for each level:

(1.) R-squared as proposed by Snijders and Bosker (1994: 350-354), also see Snijders and Bosker (1999, 99-105); and

(2.) R-squared proposed by Bryk and Raudenbush (1992: 68).

mltrsq will use the same Likelihood-function that has been specified for xtmixed. Note that in Stata 12 the default Likelihood-function is Maximum Likelihood (mle).

mltrsq provides different statistics as scalars. These results can be used with estimates table or estout (if installed). We provide the following statistics:

+----------+ ----+ scalars +------------------------------------------------------- e(N_l2) number of level-2 units

e(sb_rsq_l1) level-1 Snijders/Bosker R-squared

e(sb_rsq_l2) level-2 Snijders/Bosker R-squared

e(br_rsq_l1) level-1 Bryk/Raudenbush R-squared

e(br_rsq_l2) level-2 Bryk/Raudenbush R-squared


full lists additionally the Harmonic mean of the level-2 group sizes, which is used for the calculation of the R-squared according to Snijders and Bosker, and the Random-effects parameters of the specified model and the null-model. mltrsq will also report the variance components of the null model and the last model estimated by the user.


Load data set (ISSP 2006) . net get mlt . use redistribution.dta

Multilevel regression of "Support for income redistribution" . xtmixed gr_incdiff sex age incperc rgdppc gini || Country: , mle var

Calculate R-sqaured . mltrsq

Use statistics in estimation table . est store m1 . esttab m1, stats(N_l2 sb_rsq_l1 sb_rsq_l2)


ISSP (2006): International Social Survey Programme - Role of Government IV, GESIS StudyNo: ZA4700, Edition 1.0, doi:10.4232/1.4700.

Tom A.B. Snijders, and Roel J. Bosker (1994): “Modeled Variance in Two-Level Models.” Sociological Methods & Research 22 (3), 342-363.

Tom A.B. Snijders and Roel J. Bosker (1999): Multilevel Analysis. An Introduction to Basic and Advanced Multilevel Modeling. London: Sage.

A.S. Bryk and S.W. Raudenbush (1992): Hierarchical Linear Models in Social and Behavioral Research: Applications and Data Analysis Methods. Newbury Park, CA: Sage Publications.


Katja Moehring, GK SOLCIFE, University of Cologne, moehring@wiso.uni-koeln.de, www.katjamoehring.de.

Alexander Schmidt, GK SOCLIFE and Chair for Empirical Economic and Social Research, University of Cologne, alex@alexanderwschmidt.de, www.alexanderwschmidt.de.

Also see