Abstract
This piece is meant to help you understand and master two-level linear modeling in an accessible, swift, and fun way (while being based on rigorous and up-to-date research). It is divided into four parts: PART 1 presents the three key principles of two-level linear modeling. PART 2 presents a three-step procedure for conducting two-level linear modeling using SPSS, Stata, R, or Mplus (from centering variables to interpreting the cross-level interactions). PART 3 presents the results from a series of simulations comparing the performances of SPSS, Stata, R, and Mplus. PART 4 gives a Q&A addressing multilevel modeling issues pertaining to statistical power, effect sizes, complex design, and nonlinear two-level regression. The empirical example used in this tutorial is based on genuine data pertaining to ʼ90s and post-ʼ00s boy band member hotness and Instagram popularity. In reading this paper, you will have the opportunity to win a signed picture of Justin Timberlake.
Highlights
You need to compare the deviance of the two models using a two-degree-of-freedom likelihood-ratio test, noted as LR χ2
‘As a second step, we built an intermediate model using hotness and period of success as predictors, and we performed a likelihood-ratio test to see whether estimating the slope residuals improved the fit
There is only one simulation study that compared the performance of various statistical software programs (McCoach et al, 2018), but this study focused on differences in the variance term estimation and left aside the issue of coefficient estimation
Summary
The empirical example used in this tutorial is based on genuine data pertaining to90s and post-ʼ00s boy band member hotness and Instagram popularity. The interpretation of the level-2 coefficient estimate B01 × Xj is the same as in any traditional linear regression: An increase of one unit in Xj is associated with a change of B01 in the value of the outcome Yij (in our example, compared to members from ’90s boy bands, the popularity score of members from post-’00s boy bands is higher by B01 points on average). A cluster-mean centered level-1 predictor will lead you to estimate the pooled within-cluster effect: A deviation of one unit in hotness from the boy band-specific mean will be associated with a change of B10 in the popularity score. Cluster-mean centering will change the value of the fixed intercept B00, which will become the overall value of predictor x cmc ij is set at zero, that is, the predicted popularity score of a boy band member with the average level of hotness within his boy band.. That you have made a decision regarding the need to include slope residuals, you can include your cross-level interaction(s) (if you have one) and build your final model:
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