Questions tagged [multilevel-analysis]

Statistical analysis of datasets comprising several levels of hierarchy (e.g., students nested in classes nested in schools or hierarchical forecasting). For questions about mixed models use [mixed-model] tag. For nested random effects, use [nested-data].

Overview

Multilevel analysis is a general term referring to statistical methods appropriate for the analysis of data sets comprising several types of unit of analysis. The levels in the multilevel analysis are another name for the different types of unit of analysis. Each level of analysis will correspond to a population, so that multilevel studies will refer to several populations...

-T.A.B. Snijders, Multilevel Analysis, p. 673-677 in M. Lewis-Beck, A.E. Bryman, and T.F. Liao (eds.), The SAGE Encyclopedia of Social Science Research Methods (Volume II). Sage, 2003.

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Crossed vs nested random effects: how do they differ and how are they specified correctly in lme4?

Here is how I have understood nested vs. crossed random effects: Nested random effects occur when a lower level factor appears only within a particular level of an upper level factor. For example, pupils within classes at a fixed point in time.…
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Under what conditions should one use multilevel/hierarchical analysis?

Under which conditions should someone consider using multilevel/hierarchical analysis as opposed to more basic/traditional analyses (e.g., ANOVA, OLS regression, etc.)? Are there any situations in which this could be considered mandatory? Are there…
Patrick
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How to deal with hierarchical / nested data in machine learning

I'll explain my problem with an example. Suppose you want to predict the income of an individual given some attributes: {Age, Gender, Country, Region, City}. You have a training dataset like so train <- data.frame(CountryID=c(1,1,1,1, 2,2,2,2,…
Ben
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What's the relation between hierarchical models, neural networks, graphical models, bayesian networks?

They all seem to represent random variables by the nodes and (in)dependence via the (possibly directed) edges. I'm esp interested in a bayesian's point-of-view.
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What's the difference between "deep learning" and multilevel/hierarchical modeling?

Is "deep learning" just another term for multilevel/hierarchical modeling? I'm much more familiar with the latter than the former, but from what I can tell, the primary difference is not in their definition, but how they are used and evaluated…
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When to use fixed effects vs using cluster SEs?

Suppose you have a single cross-section of data where individuals are located within groups (e.g. students within schools) and you wish to estimate a model of the form Y_i = a + B*X_i where X is a vector of individual level characteristics and a a…
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What does "independent observations" mean?

I'm trying to understand what the assumption of independent observations means. Some definitions are: "Two events are independent if and only if $P(a \cap b) = P(a) * P(b)$." (Statistical Terms Dictionary) "the occurrence of one event doesn't…
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Equations in the news: Translating a multi-level model to a general audience

The New York Times has a long comment on the 'value-added' teacher evaluation system being used to give feedback to New York City educators. The lede is the equation used to calculate the scores - presented without context. The rhetorical strategy…
Andrew
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Why is a $p(\sigma^2)\sim\text{IG(0.001, 0.001)}$ prior on variance considered weak?

Background One of the most commonly used weak prior on variance is the inverse-gamma with parameters $\alpha =0.001, \beta=0.001$ (Gelman 2006). However, this distribution has a 90%CI of approximately…
David LeBauer
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Fisher information in a hierarchical model

Given the following hierarchical model, $$ X \sim {\mathcal N}(\mu,1), $$ and, $$ \mu \sim {\rm Laplace}(0, c) $$ where $\mathcal{N}(\cdot,\cdot)$ is a normal distribution. Is there a way to get an exact expression for the Fisher information of the…
emakalic
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How to calculate the confidence interval of the mean of means?

Imagine that you repeat an experiment three times. In each experiment, you collect triplicate measurements. The triplicates tend to be fairly close together, compared to the differences among the three experimental means. Computing the grand mean is…
Harvey Motulsky
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R package for multilevel structural equation modeling?

I want to test a multi-stage path model (e.g., A predicts B, B predicts C, C predicts D) where all of my variables are individual observations nested within groups. So far I've been doing this through multiple unique multilevel analysis in R. I…
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Clustered standard errors vs. multilevel modeling?

I've skimmed through several books (Raudenbush & Bryk, Snijders & Bosker, Gelman & Hill, etc.) and several articles (Gelman, Jusko, Primo & Jacobsmeier, etc.), and I still haven't really wrapped my head around the major differences between using…
RickyB
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Random forest on multi-level/hierarchical-structured data

I am quite new to machine learning, CART-techniques and the like, and I hope my naivete isn't too obvious. How does Random Forest handle multi-level/hierarchical data structures (for example when cross-level interaction is of interest)? That is,…
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Writing out the mathematical equation for a multilevel mixed effects model

The CV Question I'm trying to give (a) detailed and concise mathematical representation(s) of a mixed effects model. I am using the lme4 package in R. What is the correct mathematical representation for my model? The Data, Science Question, and R…
rbatt
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