In these data, there are two training programmes being compared (variable: train) and the participants (identified by the variable: id) are tracked over several weeks (variable: week). The data are fake but inspired by real-life research. Let's create some simulated data for an imaginary research study into rehabilitation for amputees learning to use electrically-controlled prosthetic hands. The u and v values are normally distributed around zero, by convention. Then, there is also a random intercept u, which is different for every cluster in the data's multilevel structure, and a random slope v, which contributes to the effect of x on y. The betas are simple regression coefficients. X is an independent variable or predictor, y is the dependent variable or outcome of interest, but we don't observe y directly, only y*, which is the censored version at a threshold h. One neat way of thinking about the advantage of multilevel models is that they split up the unexplained variance into observation-level and cluster-level variance, and in doing so, give deeper understanding and more nuanced conclusions about the data. That might be exam results clustered by student, or trees clustered by plantation, or whatever. In these equations, i indexes the individual cases and j the clusters of cases that define the multilevel structure. Let's look at a simple mathematical representation. Tobit models have been available in Stata for a while, but version 15 now includes multilevel versions with random intercepts and random slopes. In this blog post, we'll use some simulated data so that we know what relationships we expect to see, and they will be censored with an upper limit, or as the jargon goes, right-censored. Chemical sensors may have a lower limit of detection, for example. Tobit models are made for censored dependent variables, where the value is sometimes only known within a certain range. Multilevel Tobit regression models in Stata 15 Stata Tips #19 - Multilevel Tobit regression models in Stata 15
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