All Questions
Tagged with conditioning regression
12 questions
7
votes
2
answers
334
views
When to use fixed effects or multi level models in regression?
Suppose you run an experiment where the treatment is Gatorade and the outcome is one-mile runtime. You’ve stratified on variables such as sex, height and weight so they’re well randomized and have no ...
- 3,520
2
votes
1
answer
97
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A regressor performs better under a certain regime -- how to condition that regressor to make regression better?
I ran a regression $Y \sim X_1 + X_2 + .. X_n$. I find out what one regressor , $X_1$'s performance (or correlation with $Y$) depends on another variable $t$ (not in the regression). So basically if I ...
- 220
3
votes
1
answer
105
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If $e_0$ are the OLS residuals, what is random in $\hat{\beta}_{OLS}|f(e_0) < \hat{\beta} < f^*(e_0)$?
This is a follow up question to the question I've posted here.
Suppose $Y \sim N(X\beta, \sigma^2I)$, where $y \in \mathbb{R}^n$. Let $X \in \mathbb{R}^{n \times p}$ denote a full rank design matrix. ...
- 2,683
1
vote
1
answer
1k
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Gaussian Processes as weighted averages?
I've been wondering if a "weighted average" is a valid means to consider the Gaussian Process, specifically in the context of GP Regression. The kernel (I'll be referring to the common ...
- 3,520
1
vote
0
answers
120
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How conditioning happens?
F. Elwert and C. Winship in the paper "Endogenous Selection Bias: The Problem of Conditioning on a Collider Variable" (content available here) discuss conditioning on different types of ...
5
votes
1
answer
91
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Meaning of "for each value $X = x$, the random variable Y can be represented in the form $Y = \beta_0 + \beta_1 x + \epsilon$" in linear regression
In what follows assume $Y: \ \Omega \to \mathbb R$ and $X: \ \Omega \to E$
The following quoute is from page 700 in DeGroot and Schervish - Probability and statistics, introducing a simple linear ...
- 225
2
votes
0
answers
2k
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Do fixed design prediction/estimation error guarantees translate to random design for linear regression? When and How? [closed]
Suppose I have an independent vector $X$ and a dependent scalar random variable $Y$ and I wish to construct a regression model to predict $Y$ using $X$ given data $\{(x_i,y_i)\}_{i=1}^{n}$. For ...
- 78
3
votes
2
answers
1k
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What is the physical significance of cumulative correlation coefficient?
Say, I have 2 parameters, and based on my dataset, I have iteratively calculated the correlation coefficients between them by taking the correlation of the first i terms, where i ranges from 1 to the ...
- 261
2
votes
1
answer
668
views
Investigate correlation conditional on a threshold
I have 3 variables in my data set.
(i) My gut feel says variable1 and variable2 are correlated, only when variable3 >= threshold3. What is the technique I can use to see if this holds true, to ...
- 193
6
votes
1
answer
523
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Maximum Likelihood Formulation for Linear Regression
I have seen the following for maximum likelihood estimation (MLE) for linear regression in multiple sources, e.g. here:
$$
\mathcal{D} \equiv \{(x_1, y_1), ..., (x_n, y_n)\}
$$
I do not understand ...
- 317
22
votes
2
answers
7k
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What is the difference between conditioning on regressors vs. treating them as fixed?
Sometimes we assume that regressors are fixed, i.e. they are non-stochastic. I think that means all our predictors, parameter estimates etc. are unconditional then, right? Might I even go so far that ...
- 1,007
2
votes
1
answer
3k
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How can I create a scatterplot in R using the plot function to control for covariates?
I would like to know if it is possible to create a scatterplot while controlling for covariates, such as in partial correlation. I am using R software and my code is below for the basic scatterplot.
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