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].
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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 ...
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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
<...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 - ...
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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 ...
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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 ...
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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 ...
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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 ...
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Difference between multilevel modelling and mixed effects models?
What is the difference between Multilevel/Hierarchical Modelling and Mixed Effects Models?
Wikipedia considers them to be the same, i.e. two different names for the same thing. But I think they are ...
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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 ...
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How to respond to reviewers asking for p-values in bayesian multilevel model?
We were asked by a reviewer to provide p-values as to better understand the model estimates in our bayesian multilevel model. The model is a typical model of multiple observations per participant in ...
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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 ...
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How is ARMA/ARIMA related to mixed effects modeling?
In panel data analysis, I have used multi-level models with random/mixed effects to deal with auto-correlation issues (i.e., observations are clustered within individuals over time) with other ...
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Product Demand Forecasting for Thousands of Products Across Multiple Stores
I'm currently working on a demand forecasting task, with data on tens of thousands of products across a couple thousand stores. More specifically,I have a few years' worth of daily sales data per ...
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Compute partial $\eta^2$ for all fixed effects anovas from a lme4 model
Disclamer: I wasn't sure where to post this question: CV or SO, but eventually decided to try here first
I've been asked by one of the reviewers to add effects sizes (preferably $\eta^2_p$ which is ...
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OLS with clustered standard errors vs. multilevel modeling when the main interest is at the individual level [duplicate]
Possible Duplicate:
Under what conditions should one use multilevel/hierarchical analysis?
I have been reading various papers dealing with multilevel analysis, and to be honest, I am still ...
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What precisely does it mean to borrow information?
I often people them talk about information borrowing or information sharing in Bayesian hierarchical models. I can't seem to get a straight answer about what this actually means and if it is unique to ...
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Is multilevel modelling simpler, more practical, or more convenient using Bayesian methods or frequentist methods?
In this community wiki page a twice-upvoted comment asserted by @probabilityislogic asserted that "Multi-level modelling is definitely easier for bayesian, especially conceptually." Is that true, and ...
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Illustrative datasets and analysis for multilevel modelling
I recently took an introductory course on multilevel modelling. Most of the datasets and examples we used were from the social sciences. I've just got a 2 week internship in a biostatistics department,...
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Why use a beta distribution on the Bernoulli parameter for hierarchical logistic regression?
I'm currently reading Kruschke's excellent "Doing Bayesian Data Analysis" book. However, the chapter on hierarchical logistic regression (Chapter 20) is somewhat confusing.
Figure 20.2 describes a ...
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Hierarchical Bayesian Model (?)
Please apologize my butchering of statistical lingo :) I have found a couple of questions on here that are related to advertising and click through rates. But none of them helped me very much with my ...
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Is there a method for constructing decision trees that takes account of structured/hierarchical/multilevel predictors?
Is there a method for constructing decision trees that takes account of structured/hierarchical/multilevel predictors, that would allow me to impose domain knowledge or constraints on interactions for ...
user6666
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Comparison of the jacknife vs the bootstrap
I am interested in understanding the relative pros and cons of bootstrap versus jacknife resampling. Both are used in iterative algorithmic approaches to estimating the precision of a prediction or ...
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Standardized beta weights for a multilevel regression
How can one obtain standardized (fixed effect) regression weights from a multilevel regression?
And, as an "add-on": What is the easiest way to obtain these standardized weights from a ...
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Multilevel model vs. separate models for each level
What are the advantages and disadvantages of running separate models vs. multilevel modeling?
More particularly, suppose a study examined patients nested within doctors' practices nested within ...
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Managing high autocorrelation in MCMC
I'm building a rather complex hierarchical Bayesian model for a meta-analysis using R and JAGS. Simplifying a bit, the two key levels of the model have
$$ y_{ij} = \alpha_j + \epsilon_i$$
$$\alpha_j =...
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MCMC converging to a single value?
I'm trying to fit a hierarchical model using jags, and the rjags package. My outcome variable is y, which is a sequence of bernoulli trials. I have 38 human subjects which are performing under two ...
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Why is it OK to model demographics as random effects in bayesian multilevel models?
In Bayesian multilevel models (with, say, people nested within congressional districts) I sometimes see individual level demographic variables like race modeled as random effects.
So here’s a slightly ...
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Multiple Membership vs Crossed Random Effects
I see that there is a multiple-membership tag, but I can't find a good explanation of what a multiple membership model is, or how to go about fitting one.
In my limited understanding, it seem very ...
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Highly irregular time series
I have data for the population of a number of different fish, sampled over a period of about 5 years, but in a very irregular pattern. Sometimes there are months between samples, sometimes there are ...
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Notation for multilevel modeling
The formula one needs to specify for training a multilevel model (using lmer from lme4 R ...
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Multilevel multivariate meta-regression
Background:
I'd like to conduct a meta-regression using studies which have (1) several outcomes/constructs (= multivariate) and (2) multiple effect sizes for every of these outcomes because of ...
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Should I bootstrap at the cluster level or the individual level?
I have a survival model with patients nested in hospitals that includes a random-effect for the hospitals. The random effect is gamma-distributed, and I am trying to report the 'relevance' of this ...
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What is the "variance component parameter" in mixed effect model?
On page 12 of Bates' book on mixed effect model, he describes the model as follows:
Near the end of the screenshot, he mentions the
relative covariance factor $\Lambda_{\theta}$, depending on the ...
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Stratified classification with random forests (or another classifier)
So, I've got a matrix of about 60 x 1000. I'm looking at it as 60 objects with 1000 features; the 60 objects are grouped into 3 classes (a,b,c). 20 objects in each class, and we know the true ...
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What is hierarchical prior in Bayesian statistics?
What are hierarchical priors?
How do they differ from the general concept of priors?
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Regression: Interaction Effects vs Random Effects
I'm struggling to understand the difference between creating an interaction effect in linear regression vs a random effect. Both allow the algorithm to identify a different slope for a coefficient ...
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Hierarchical models for multiple comparisons - multiple outcomes context
I've just been (re-)reading Gelman's Why we (usually) don't have to worry about multiple comparisons. In particular the section "Multiple outcomes and other challenges" mentions using a hierarchical ...
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Torn between PET-PEESE and multilevel approaches to meta-analysis: is there a happy medium?
I am currently working on a meta-analysis, for which I need to analyze multiple effect sizes nested within samples. I am partial to Cheung's (2014) three-level meta-analysis approach to meta-analyzing ...
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How to test random effects in a multilevel model in R
I have been reading a good book called Applied Longitudinal Data Analysis: Modeling Change and Event Occurrence by Judith Singer and John Willet. The book shows that by modeling in 2 levels, we can ...
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Use of ICC in multilevel modelling
Ive just recently started learning about the ICC and multilevel models and I've been told that one way to determine whether a MLM is warranted is by checking the size of the ICC. I'm struggling to ...
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Why the exchangeability of random variables is essential in hierarchical bayesian models?
Why the exchangeability of random variables is essential for the hierarchical Bayesian modeling?
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Clustered standard errors and multi-level models
Stata allows estimating clustered standard errors in models with fixed effects but not in models random effects? Why is this?
By clustered standard errors, I mean clustering as done by stata's ...
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How to conduct a multilevel model/regression for panel data in Python?
I have yearly data over time (longitudinal data) with repeated measures for many of the subjects. I think I need multilevel modeling/regressions to deal with sure-to-be correlated clusters of ...
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Borrowing strength
What are the principles of Borrowing Strength?
What does it mean in terms of estimating parameters for hierarchical models?
Where can this information can be read from?
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