University:
University of Michigan
Course:
STATS 605 | Advanced Topics in Modeling and Data Analysis
Academic year:

2019
Views:

361

Pages:

19
Author:

Elsie W

Centering in MLM Raw Data (Confounding) Grand-Mean Centering (Confounding) Cf. Enders & Tofighi, 2007 Centering in MLM Between Person Effect Within Person Effect Cf. Enders & Tofighi, 2007 Centering your Data How to unconfound within-cluster and between-cluster effects in a Level 1 predictor: 1. Cluster-mean center the predictor at Level 1 1. Subtract cluster mean from raw scores in each cluster 2. Create aggregate variable of the Level 1 predictor and enter that as a predictor as well • Cluster-Centered variable: within-cluster • Aggregate variable: between-cluster • This will separate the within- and between-cluster effects and based on significance tests, you will know the locus of the effect (within-cluster, between-cluster, or both) Centering Choices 1. I’ve centered my data so that the intercept is equal to the value of my outcome variable when my predictor is zero in raw units (scale: 0 to 9). Which type of centering have I used? 1. I’ve centered my data so that the intercept is equal to the average of the corresponding cluster (e.g., my gratitude after nights when I sleep my average amount). Which type of centering have I used? 2. I’ve centered my data so that the slope of my level 1 predictor reflects the amount the outcome changes for each unit increase in the predictor scale (e.g., the increase in gratitude participants experience when sleeping for 6 hours instead of 5 hours). Which type of centering have I used? 3. I’ve centered my data so that the slope of my level 1 predictor reflects the amount the outcome changes for each unit increase in the predictor relative to the cluster mean (e.g., the increase in gratitude participants experience when sleep one hour more than their average). Which type of centering have I used? Centering your Data • Resources: • http://web.pdx.edu/~newsomj/mlrclass/ho_centering.pdf Algina, J., & Swaminathan, H. (2011). Centering in two-level nested designs. In. J. Hox, & K. Roberts (Eds.), The Handbook of Advanced Multilevel Data Analysis (pp 285-312).New York: Routledge. Enders, C.K., & Tofighi, D. (2007). Centering predictor variables in crosssectional multilevel models: A new look at an old issue. Psychological Methods, 12, 121-138. Wang, L. P., & Maxwell, S. E. (2015). On disaggregating between-person and within-person effects with longitudinal data using multilevel models. Psychological methods, 20(1), 63. Mediation and Moderation • Random effects and centering are both important issues to consider when doing mediation or moderation in MLM • Random effects – make interpreting interactions and computing indirect effects more difficult • Centering – critical in mediation to unconfound within and betweencluster effects • If people are less grateful after sleeping poorly only at the aggregate (people who are generally poor sleepers tend to be less grateful, but one night of poor sleep isn’t enough to do anything), then cannot be mediated by daily fluctuations in negative affect Random Effects and Centering Matter a lot in Moderation & Mediation – See Resources Below • General resources (both of these sites are great sources of info!): • http://davidakenny.net/cm/mediate.htm • http://www.quantpsy.org/medn.htm • Moderation in MLM • Bauer & Curran article on probing multilevel moderations: http://www.unc.edu/~curran/pdfs/Bauer%26Curran(2005).pdf • Barr article on random effects: click here • Calculators: http://www.quantpsy.org/interact/hlm2.htm • Mediation in MLM • Readable slides from Chris Preacher on multilevel mediation: http://afhayes.com/public/aps2013.pdf (this has many additional references at the end) • Zhang, Z., Zypher, M. J., & Preacher, K. J. (2009). Testing multilevel mediation using hierarchical linear models: Problems and solutions. Organizational Research Methods, 12, 695-719. On other slides: • http://quantpsy.org/pubs/bauer_preacher_gil_2006.pdf (1 model approach to MLM mediation) • https://njrockwood.com/mlmed/ (multilevel mediation macro for SPSS) • http://www.quantpsy.org/pubs/preacher_zhang_zyphur_2011.pdf (multilevel mediation in SEM) Calculators from prior slides: Calculator if 1 or 0 random effects: http://www.quantpsy.org/medmc/medmc.htm Calculator for 1-1-1 with random effects: http://www.quantpsy.org/medmc/medmc111.htm Creating a Multilevel Model 1. What is the structure of my nested data? 2. Are my effects fixed or random? 3. What type of centering should I use? 4. Which covariance matrices should I use? Covariance Matrices Two primary covariance matrices you have to deal with in MLM: • G –covariance matrix for random effects (What are the variances of the random effects? Are random effects allowed to covary?) • R – underlying error structure (residuals) • Note, these matrices are referred to by different letters in different software programs The Random Variance-Covariance Matrix Models with random slopes can estimate covariance between random effects as well as random effect variance. Gratitude Random Effect Covariance Matrix Sleep Quality The Random Variance-Covariance Matrix Models with random slopes can estimate covariance between random effects as well as random effect variance. Intercept Slope1 Slope2 Intercept Var1,1 Cov1,2 Cov1,3 Slope1 Cov1,2 Var2,2 Cov2,3 Slope2 Cov1,3 Cov2,3 Var3,3 How to Structure the Random Covariance Matrix • Can specify different matrices, here are two common ones: • Unstructured: estimates all variances and covariances • Sometimes has trouble converging if there are lots of random effects or if some variances/covariances are essentially 0 • Can start here and trim effects that are clearly non-significant • Variance Components: estimates variances but assumes covariances are 0 • Default for SPSS & SAS • Possible to have multiple RANDOM lines to specify covariances between particular random effects, e.g.,: • RANDOM X1 X2 | UN • RANDOM X3 X4 | UN Note: can only have a variable appear on ONE random line The RESIDUAL Variance-Covariance Matrix Don’t have to specify this matrix when doing MLM, and sometimes doing so will cause error because it will duplicate what is being done with random factors, but occasionally there is additional structure to the error that can be accounted for with this matrix (e.g. repeated measures data). -Some programs, such as R’s “Lme4” package won’t let you specify this matrix. SPSS and SAS will, R’s nlme package lets you specify a few specific matrices. Autoregressive Covariance Matrix This is the type of residual error matrix used with repeated measures. It specifies that time points closer to each other have stronger correlations than time points farther apart. This helps reduce the error or noise since it provides a structure to explain some of the error. Typically the expectation is that the time points are equally spaced (1-2 is the same distance as 3-4). Day 1 Day 2 Day 3 Day 4 Day 1 Day 2 Day 3 Day 4 The RESIDUAL Variance-Covariance Matrix With clustered data you have the option of using JUST the residual error matrix to adjust for non-independence of errors. This approach is called the marginal model, population-averaged model, or generalized estimating equation (GEE) model • These are models that use ONLY the R matrix (residual covariances) to account for clustering • • Adjusts for covariances in residuals without directly estimating variability between clusters (i.e., no random effects) Can be useful for repeated measures ANOVAs with missing data or timevarying covariates Covariances Matrices: Multiple Choice • All variances and covariances are freely estimated • • • • Unstructured Variance Components/Diagonal Autoregressive Other • Variances are freely estimated, covariances are constrained to 0 • • • • Unstructured Variance Components/Diagonal Autoregressive Other • Variances are assumed to be equal, covariances have weakening correlations for further apart data points • • • • Unstructured Variance Components/Diagonal Autoregressive Other • All variances and covariances are constrained to 0 • • • • Unstructured Variance Components/Diagonal Autoregressive Other Other Model Decisions: REML versus ML • You can choose to use Maximum Likelihood (ML) or Restricted Maximum Likelihood (REML) estimate • REML is typically default, it is better for smaller samples as it tends to be less biased • However, REML requires the exact same fixed effects in each model when doing model comparison, so... • If you are comparing models with different fixed effects you have to use ML Other Model Decisions: Calculating DFs • Satterthwaite: DFs are somewhere between sample size of lowest and highest levels, depending on source of variance • Default for SPSS, SAS, R – lmertest • Can be used for both REML and ML • Kenward-Roger • Can be used in R, SAS • Only applies to REML

Multilevel Modeling -4

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