Mixed linear model
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Caroline,
Here are some references that you might find useful for
graphing interactions. The list was given by Cam McIntosh on the semnet
listserv. Of these, i think the Bauer and the Preacher references might be most
helpful to you.
Gene Maguin
Garcia, R., & Kandemir, D. (2006). An illustration of
modeling moderating variables in cross-national studies. International Marketing
Review, 23(4), 371-389.
Bauer, D. J., & Curran, P. J. (2005). Probing interactions in fixed and
multilevel regression: Inferential and graphical techniques. Multivariate
Behavioral Research, 40(3), 373-400.
http://www.unc.edu/~dbauer/manuscripts/bauer-curran-MBR-2005.pdf Hayes, A.F., & Matthes, J. (2009). Computational procedures for
probing interactions in OLS and logistic regression: SPSS and SAS
implementations. Behavior Research Methods, 41, 924-936.
http://www.comm.ohio-state.edu/ahayes/MODPROBE.pdf
O'Connor, B.P. (1998). SIMPLE: All-in-one programs for exploring
interactions in moderated multiple regression. Educational and Psychological
Measurement, 58(5), 836-840.
https://people.ok.ubc.ca/brioconn/simple/simple.html
Whisman, M. A., & McClelland, G. H. (2005). Designing, testing,
and interpreting interactions and moderator effects in family research. Journal
of Family Psychology, 19, 111-120.
Dawson, J.F., & Richter, A.W. (2006). Probing three-way
interactions in moderated multiple regression: development and application of a
slope difference test. Journal of Applied Psychology, 91(4),
917-926.
Preacher, K. J., Curran, P. J., &
Bauer, D. J. (2006). Computational tools for probing interaction effects in
multiple linear regression, multilevel modeling, and latent curve analysis.
Journal of Educational and Behavioral Statistics, 31(4), 437-
448.
http://www.unc.edu/~dbauer/manuscripts/preacher-curran-bauer-2006.pdf
http://www.people.ku.edu/~preacher/interact/index.html
Fletcher, T.D. (August 8, 2010).
Quantitative Psychology Tools: Package ‘QuantPsyc’.
http://cran.r-project.org/web/packages/QuantPsyc/QuantPsyc.pdf
http://cran.r-project.org/web/packages/QuantPsyc/index.html Armstrong, D. (May 19, 2010). Dave Armstrong’s Miscellaneous Functions:
Package ‘DAMisc’, Version 1.0.
http://cran.r-project.org/web/packages/DAMisc/DAMisc.pdf
http://cran.r-project.org/web/packages/DAMisc/index.html From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of CAROLINE TILLOU Sent: Friday, June 10, 2011 3:59 PM To: [hidden email] Subject: Mixed linear model
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Gene, thank you for making the references available on this list. Steve
From: SPSSX(r) Discussion [mailto:[hidden email]]
On Behalf Of Gene Maguin Caroline,
Here are some references that you might find useful for graphing interactions. The list was given by Cam McIntosh on the semnet listserv. Of these, i think the Bauer
and the Preacher references might be most helpful to you. Gene Maguin Garcia, R., & Kandemir, D. (2006). An illustration of modeling moderating variables in cross-national studies. International Marketing Review, 23(4), 371-389. Bauer, D. J., & Curran, P. J. (2005). Probing interactions in fixed and multilevel regression: Inferential and graphical techniques. Multivariate Behavioral Research, 40(3),
373-400. Hayes, A.F., & Matthes, J. (2009). Computational procedures for probing interactions in OLS and logistic regression: SPSS and SAS implementations. Behavior Research Methods,
41, 924-936. O'Connor, B.P. (1998). SIMPLE: All-in-one programs for exploring interactions in moderated multiple regression. Educational and Psychological Measurement, 58(5), 836-840. Whisman, M. A., & McClelland, G. H. (2005). Designing, testing, and interpreting interactions and moderator effects in family research. Journal of Family Psychology, 19, 111-120. Dawson, J.F., & Richter, A.W. (2006). Probing three-way interactions in moderated multiple regression: development and application of a slope difference test. Journal of Applied
Psychology, 91(4), 917-926. Preacher, K. J., Curran, P. J., & Bauer, D. J. (2006). Computational tools for probing interaction effects in multiple linear regression, multilevel modeling, and latent curve
analysis. Journal of Educational and Behavioral Statistics, 31(4), 437- 448. Fletcher, T.D. (August 8, 2010). Quantitative Psychology Tools: Package ‘QuantPsyc’. Armstrong, D. (May 19, 2010). Dave Armstrong’s Miscellaneous Functions: Package ‘DAMisc’, Version 1.0. From: SPSSX(r) Discussion [mailto:[hidden email]]
On Behalf Of CAROLINE TILLOU
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In reply to this post by Carol
Dear Caroline,
I program a different excel file to report results after running each multilevel analysis. The steps I follow are the following: - Before running the Mixed model, Grand-center all variables (substract them the mean of the whole population), so with all predictors equal to cero (the grand mean) the level 2 residual plus gamma 00 (the common intercept) will be the "mean" of your DV for a hypothetical "representative individual" belonging to each level-2 group. - Then, using the coefficients of the regression and the interaction, calculate the effect of the changes in one IV (ceteris paribus) in the dependent variable for this "representative individual". - Recall that When you have interactions you have to take into account the beta coefficient of the principal variable and the interaction. If one of the interaction IV is a dummy (which is mostly the case), then it is useful to present 2 predicted value curves in the same graph (for both groups). - Point estimates calculated this way for predicted values are pretty straightforward. Nevertheless, prediction intervals at a certain confident level are more difficult. You have to use the Var-Covar Matrix, in order to calculate the SE of the predicted value. Mail me if you need a deeper explanation of the steps to follow. |
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