Yesterday I tweeted about nested data, with multi-level models (MLM) versus OL + cluster-robust variance estimation (CRVE). This made me think about another confusion that arise, between what are called fixed versus random effects.
Let’s begin with a simple relationship between a covariate X and Y in nested data, e.g. students i nested in school j. We are interested in understanding the relationship between X and Y at the student level.
Approach 1: Assume the schools are fixed, but that students are a random sample within these schools. Assume the relationship between X and Y is the same in all schools. This often amounts to including a dummy variable for each school in the model. Here I use OLS to estimate β_1.
Approach 2: Assume schools are fixed, but the relationship between X and Y can vary across schools. Now add in interactions. Here I use OLS to estimate separate relationships between X and Y for each school (η_1, …, η_J).
Approach 3: Assume the schools are a random sample from some population, but treat the relationship between X and Y as the same in all schools. Estimate β_1 using generalized least squares (GLS).
Approach 4: Assume schools are random, but now that the relationship between X and Y can vary across schools (also treated as random). Same as Approach 3 but change the last equation. Estimate both β_1 and the variation across schools.
Ok, here’s where the language gets confusing. Approach 3 is referred to as “Fixed” (as in ‘treat the relationship between X and Y as fixed’) in the MLM literature, but as a “Random Effects” model in economics!
In summary: Multi-level modelers use “fixed” or “random” for coefficients, while economists use “fixed” or “random” for models.
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I’m going to begin today with a bold claim: Being an applied statistician is a lot like being an ethnographer.
I say this both based upon years of experience working in collaborative projects and consulting and based on my experience studying ethnography. (Recall: before my PhD in statistics, I started and quit a PhD in sociology).
Very often a question asked is not the ‘real’ question at hand. Typically, the person asking has a sense of the problem, but may not know exactly how to ask the question.
I work primarily with nested data. One example is in experiments, with students nested in schools. Another is meta-analysis, with effect sizes nested in studies. In this thread, I’ll focus on students nested in schools, but this applies more generally.
Question 1: Do you need to take nesting into account in your analysis? Our world is naturally nested – students in classrooms in teachers in schools in districts and so on. Does this mean we need to take all of these levels into account? No.
Nesting only needs to be accounted for if it is part of how our sample of data is generated – either how the data is selected (sampled) or the who gets an intervention being studied (assignment).
Hello everyone – I’m so excited (and nervous!) to get to tweet with you all this week. I’ll start by telling you some general things about myself.
I’m an Associate Professor of Statistics at Northwestern University and a Faculty Fellow at the Institute for Policy Research. I also Co-Direct the Statistics for Evidence-Based Policy and Practice Center. For more info see here: bethtipton.com
I call my field “Social Statistics” and I much of what I study has to do with the role of statistics in the creation and use of evidence for decision making, particularly in the field of education research.
The #DataFeminism book also made me look inward and examine my own biases, which I am exceedingly grateful for.
Namely, it forced me to reckon with some of my fundamental operating assumptions as a statistician & data scientist.
Examples threaded below...
In chapter 3, the authors discuss the role of emotion in data visualization, specifically calling out giants in the field like Edward Tufte and Alberto Cairo (no snitch tagging, please) for what is presented as an anti-emotion stance.
On Tufte: "Any ink devoted to something other than the data themselves ... is a suspect and intruder to the graphic. Visual minimalism, according to this logic, appeals to reason first. ... Decorative elements ... are associated with messy feelings ... and emotional persuasion."
For #ThrowbackThursday I thought I'd highlight some of the amazing women who have been mentors (and friends) to me. Without support from an amazing community of women in mathematics & statistics I would not be where I am today! #WomenInSTEM