Questions tagged [regression-to-the-mean]
The phenomenon that on repeated testing a high value tends to be lower, and a low value higher.
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Behaviour of regression toward the mean
I have a dataset for length of right and left foot in 801 people, males and females. This is a teaching dataset without any specific question or peculiarity behind it, as far as I can tell.
Here are ...
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Why can't the slope be greater than 1 in regression to the mean for married couples' intelligence?
Consider the following example I read in Daniel Kahneman's book:
Highly intelligent women tend to marry men who are less intelligent than they are.
Kahneman argues that (slightly reworded for ...
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What is the best approach to look at association between change in X and change in Y?
What is the correct approach to analyze the association between changes in two variables with two synchronous repeated measurements?
I have calculated delta change scores for variables
X and Y both ...
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In repeated measures, how to distinguish regression to the mean from a negative lagged effect?
I have repeated measures for a quantitative variable "cry" for N = 52 participants (how much you cry at a given time), there are 30 repeated measures. The values range from 0 (not at all) to ...
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Controlling for regression to the mean in nonparametric survey response data - pre-post design - difference between groups
I have 920 pre-post responses to 5-point Likert-scale questions evaluating the impact of an educational intervention. I wish to test whether outcomes (change = post - pre) differed across different ...
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Can regression to the mean also impact heterogeneity?
I understand Regression to the Mean (RM) as a naturally (and likely randomly) occurring shift in the scores of a sample of extreme subjects (super high or low scorers) from each measurement time to ...
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Interpretation of interaction (time x intervention) in an intervention study when baseline values are unequal
I came across an intervention study that measured a significant decrease in a specific treatment group. However the starting conditions where not the same and are like*:
So there is a difference ...
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How control for a pre-treatment outcome $Y_0$ if is a strong confounder while avoiding regression to the mean bias for treatment effect on $Y_1$?
I'm facing a dilemma in a pre/post cohort matching analysis for a healthcare intervention:
Matching on the pre-treatment outcome $Y_0$ (a continuous variable) will likely lead to regression to the ...
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How does the law of large numbers relate to regression to the mean?
Intuitively, these two important statistical principles appear to describe two facets of the same phenomenon, namely that in the long run, any extreme occurrences get counter-balanced, and things tend ...
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What's complicated about regression to the mean?
Note: I am a bit of a novice when it comes to statistics and data analysis.
Reading the chapter on regression to the mean in Kahneman's Thinking Fast and Slow, I came across the following passage:
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Matching on pre-treatment outcome $z$-score in diff-in-diff analysis to avoid regression toward the mean bias in $ATT$ estimates?
There have been many articles (e.g., Chabé-Ferret (2017), Daw & Hatfield (2018), Zeldow & Hatfield (2021)) discussing the perils of matching on pre-treatment outcomes (such as patient's ...
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Why does regression to the mean work?
According to Wikipedia, regression towards the mean is "the phenomenon that arises if a sample point of a random variable is extreme (nearly an outlier), in which case a future point is likely to ...
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Applications of "Regression Towards the Mean" in Real Life
I was reading about "regression towards the mean". Over here, an explanation of this concept is provided:
"Consider a simple example: a class of students takes a 100-item true/false ...
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What does it mean for regression to the mean to "work backward in time"?
Please see the emboldened phrase below.
Then the hammer drops. The triumph of mediocrity observed by Secrist,
Hotelling points out, is more or less automatic whenever we study a variable
that’s ...
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Can Lord's paradox be caused by regression to the mean?
I am trying to understand Lord's paradox, where controlling for baseline status can affect inference. I tried to set up some data following the quotation in Wikipedia
“A large university is ...
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How to adjust estimates to account for regression to the mean?
Let us consider an example where we have a number of runners and an estimate of speed in mph for each runner. The estimate for each runner may be based on an equal or unequal number of independent and ...
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Is regression towards the mean happening when we use a control group?
I have a subset of 40000 participants in my study. From those I would like to study those with higher weight longitudinally, and compare them with those with healthy weight.
I observe, that those with ...
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Can regression to the mean be corrected by linear mixed effects?
I am wondering if regression to the mean can be corrected by using linear mixed effects models in the following case.
...
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Regression to the mean and its formula in R
In this book, the estimate of the regression to the mean phenomenon is said to be: $Prm=100(1-r)$.
Where $Prm$ is the percent of regression to the mean, and $r$ is the correlation between the two ...
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How can I test "Pollution causes people move to less polluted cities"?
I want to find an answer for the following question: "Air pollution causes people to move to less polluted cities from 1990 to 1991"?
Assume there are four cities: San Diego, Los Angeles, San ...
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Can I use the early response to a treatment to predict the full effect? - Dealing with regression towards the mean
Suppose I have a 6 week weight-loss program, that I know is only effective in a fraction of the population. I weight the participants at baseline, after 1 week and after the full 6 weeks.
$$
T_0 = ...
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Regression to the mean
I recently asked this question
In regression model with random regressors
$$(1) \ \ y = a + bx + e$$
can I change the equation to
$$(2) \ \ x = (-a/b) + (1/b)y + (-1/b)e$$
and ...
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“Regression to the mean” versus serial correlation
“Regression to the mean” says that higher pre-test values will have lower post-test values (and vice versa). This phenomenon will decrease the correlation between the pre- and post-values. However, ...
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Is there any prediction model that takes into account the regression towards the mean?
I am studying performance of football and basketball teams. The regression towards the mean is quite common in sports. One really great performance is usually followed by a less perfect one. So are ...
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Why is linear regression overestimating small values and underestimating big values?
I am trying to predict age from a couple of variables using linear regression, but when I plot predicted age against real age, I can see that small values are significantly overestimated and big ...
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Can linear mixed modeling account for regression to the mean in pre-post study?
I have a pre-post study measuring change in quality of life scores with a treatment cohort and control cohort. However, the treatment cohort is at "high risk" so regression to the mean is a real ...
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Do we have the problem of regression to the mean with non-Gaussian distribution?
I know that when we have an experiment that involves a normal distribution, regression to the mean kind of just falls out as a necessary result. But even though this is touted as a law of statistics, ...
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What are ways to prevent regression to the mean in random forest regression?
I am using Random Forest Regression (with Python sklearn, but could easily switch to R if that would work better) to predict a variable. I think my model is starting to do fairly well, however I see a ...
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Regression to the mean explained [duplicate]
Regression to the mean is a statistical phenomenon where in the long run, the results of an experiment average out. Taking the example of one's results on a test, if we've had a string of good ...
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Backwards stepwise regression, collinearity and regression to the mean
My research paper was recently rejected and some of the feedback I received was in relation to the statistical tests done/not done. I would like help in clarifying what I could do differently as the ...
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Should I fit regression line to scatter or to the mean values?
I have two random variables and I am trying to see if and how much they are correlated. One of them (say X) is discrete and the other (say Y) is continuous. I used Seaborn to do the linear regression ...
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Below chance classification after regressing out class-specific signal
I have a signal X that depends on parameters Y (condition) and S (participant). I'm interested in classifying Y based on X, but a) the YxS contingency table of numbers of observations per Y and S ...
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Repeated measures alternative regression?
Say I measure an outcome variable at two given times (always the same) for 100 people.
For example their weights today and tomorrow, or before and after a treatment.
In order to find if the outcome ...
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"Regression" versus "regression to the mean" [duplicate]
Are The two concepts really two sides of the same coin ? The latter is often referred to simply as a regression, but surely this is just an unfortunate coincidence?
The former is about predicting ...
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Reconciling regression to the mean with the independence of with-replacement sampling
Say we monitor a ski jumper's consecutive jumps (distance jumped), and we assume it is a combination (sum) of the skier's skills, + luck (modelled by a random variable). We also assume that the ...
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Distinguishing responders and non-responders in studies of classical conditioning
I am concerned about the way "response" to certain experimental manipulations in psychology is defined and then used to claim that a specific subject did or did not "respond" to justify exclusion of "...
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Why does "Regression to the Mean" have nothing to do with Regression?
Regression to the Mean is a concept in sampling not regression. Why is it not called Sampling to the Mean?
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Mean reversion of performance [closed]
I have a data set split into two time periods with the same subjects in each group. In the first 5 years they show above average performance. In the follow 5 years they perform averagely.
How do I ...
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Regression to the mean: multiple predictors
Let's say I want to predict the value of Y using the value on my predictor X. X is correlated with Y with some strength $r$ (let's say 0.5). In order to correct for regression towards the mean I ...
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Regression to the mean vs gambler's fallacy
On the one hand, I have the regression to the mean and on the other hand I have the gambler´s fallacy.
Gambler’s fallacy is defined by Miller and Sanjurjo (2019) as “the mistaken belief that random ...
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Is the concept of "Regression toward the mean" closely related to Power Analysis?
Regression toward the mean says that if a measurement is extreme at first, it will gradually tend towards the average value in subsequent measurements.
Isn't this what Power analysis all about? Why ...
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Regression to the mean with correlated and cumulative past
My colleagues and I are posing this question to our intro statistics students, but are in disagreement about the answer:
Suppose a student always got scores far above the class average throughout ...
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Regression to the mean in "Thinking, Fast and Slow"
In Thinking, Fast and Slow, Daniel Kahneman poses the following hypothetical question:
(P. 186) Julie is currently a senior in a state university. She read fluently when she was four years old. ...
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Control for regression to the mean effects when comparing propensity score matched observations?
I'm working on a project where I'm comparing the % change in total annual health care expenditures among patients who did or did not participate in a cost reduction intervention program.
We're ...
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Given the same before-after differences within groups, is it relevant whether time trajectories converge or diverge?
Both drugs are associated with the same decreases in mean blood pressure in both scenarios. Given that we attach the same meaning to any blood pressure decrease of the same amount, does scenario B ...
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Does ridge regression adequately control for regression to the mean effects in my outcome variable?
I've been asked how to control for regression to the mean effects in a difference of differences analysis on health insurance data.
We're measuring a utilization outcome both pre- and post-...
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Is a normal process mean reverting
A normal process has a lot of outcomes around the mean and then fewer and fewer outcomes away from the mean.
From this, can we conclude that a normal process reverts to the mean whenever it gets a ...
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Is the Dunning–Kruger effect mostly caused by regression to the mean?
In Bland's discussion of regression to the mean, there are several sections which detail examples of regression to the mean, which I understand to be an unavoidable consequence of not taking the mean ...
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Pre-post treatment design: accounting for reduced effect of treatment in baseline high scorers
I'm planning a study in which I want to test the effect of a treatment on a dependent psychometric variable. I expect subjects who score lower at baseline to benefit more from the treatment (larger ...
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How to test whether a series data follow Ornstein-Uhlenbeck process (OU process)?
I have some measures which seems to have some mean-reverting properties and I'm wondering whether they can be modeled as Ornstein-Uhlenbeck process (OU process). And actually I quite expect it because ...
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