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One application of multilevel modeling (MLM) is the analysis of repeated measures data. Multilevel modeling for repeated measures data is most often discussed in the context of modeling change over time (i.e. growth curve modeling for longitudinal designs); however, it may also be used for repeated measures data in which time is not a factor.
Multilevel models are a subclass of hierarchical Bayesian models, which are general models with multiple levels of random variables and arbitrary relationships among the different variables. Multilevel analysis has been extended to include multilevel structural equation modeling , multilevel latent class modeling , and other more general models.
The multilevel regression is the use of a multilevel model to smooth noisy estimates in the cells with too little data by using overall or nearby averages. One application is estimating preferences in sub-regions (e.g., states, individual constituencies) based on individual-level survey data gathered at other levels of aggregation (e.g ...
Time series models (15 P) ... Multilevel model; Multilevel modeling for repeated measures; Multilevel regression with poststratification; Multinomial logistic regression;
The goal of a multilevel Monte Carlo method is to approximate the expected value [] of the random variable that is the output of a stochastic simulation.Suppose this random variable cannot be simulated exactly, but there is a sequence of approximations ,, …, with increasing accuracy, but also increasing cost, that converges to as .
The sub-models combine to form the hierarchical model, and Bayes' theorem is used to integrate them with the observed data and account for all the uncertainty that is present. The result of this integration is the posterior distribution, also known as the updated probability estimate, as additional evidence on the prior distribution is acquired.
Multilevel model; Multilinear principal component analysis; Multinomial distribution; ... STAR model – a time series model; Star plot – redirects to Radar chart;
The so-called SITAR model [7] can fit such models using warping functions that are affine transformations of time (i.e. additive shifts in biological age and differences in rate of maturation), while the so-called pavpop model [6] can fit models with smoothly-varying warping functions. An example of the latter is shown in the box.