SCS 2017: Longitudinal and Nested Data/References and links

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General references on multilevel and longitudinal data analysis

SEMs and Mixed Models

  • Papers on the relationship between the multilevel/mixed modeling and structural equation modeling (SEM) with latent variables:
    • Bauer, D.J. (2003). Estimating multilevel linear models as structural equation models. Journal of Educational and Behavioral Statistics, 28, 135-167. [1]
    • Curran, P.J. (2003). Have multilevel models been structural equation models all along? Multivariate Behavioral Research, 38, 529-569. [2]

Software for Multilevel Models

Issues in mixed models

Multilevel/Hierarchical/Mixed Model RSquared

Random slopes

Missing data in longitudinal studies

Multiple imputation for longitudinal studies

HMC and Stan

Important pointers

  • Don't use a prior with a smaller range than the range specified by the limits on the prior.

Blog entries

Near-zero variances

Likelihood goes to \infty but probability is nearly 0.

  • Bates (2014) Random effect variance = zero would simplify the model by dropping the variance.
    In a sense, he would lasso them to zero.
  • Gelman (2011) Avoiding boundary estimates using a prior distribution as regularization
    This 2011 blog post by Gelman discusses the use of a prior for regularization when using a 'glmer' or 'lmer' to avoid boundary correlations and boundary variances in the G matrix. He suggests a gamma(2, 1/A) where A is large for for the scale parameter, i.e. the between cluster standard deviation. The expected value of the distribution is then 2A and the density f(\phi) = \frac{1}{A^2}\phi e^{-\phi/A} approaches 0 at 0.
    Using Stan, one can use a gamma(2, 1/A) prior for the scale parameters and a LKJ_corr_cholesky(a) prior with a > 1, for the correlation matrix.
  • LKJ priors
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