# Questions tagged [weighted-regression]

Weighted least squares regression is a generalization of OLS regression used when different data points have different importance, or "weights". See also [weighted-data].

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### What happens if the weights are plot?

Binary Regression for Images I'm not very good at coding, so couldn't really test much this hypothesis. But if weights are a sort of "measure of importance" of a particular pixel, then if ...
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### Including a weighting variable in a linear regression

I'm looking at how temperature affects length. My length variable is the mean length calculated for every year, it is derived from ~10,000 data points. Not every year had the same sampling effort (e.g....
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### How to determine sample weights, when the prevalence in the population is based on percentages

The central question is: How to do I determine the weights, when prevalence in the population is expressed as percentages? I have posted this related question on Stack Overflow: According to the ...
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### Should you always weight observations by exposure in a Poisson/Rate GLM

There are many great posts here on the importance of using an offset in a rate regression. For example, if you are modeling the the propensity of murder in towns, using population of town $n_i$ and ...
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### BART for aggregated data

I have experimental data with more than a million units in treatment and control and a (numeric) outcome variable "y". I want to detect heterogenous treatment effects along 5 numeric ...
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### Using the residual standard deviation of a weighted standard regression for effect size computation

I'm facing a trivial problem but I want to be sure that the approach is appropriate. I have a situation in which n subjects perform a task with k trials for each subject. k is not a fixed number and ...
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### Bayesian regression learning (RVM) on weighted data (data with different importance/exposure)

I am working with an extension of the relevance vector machine (RVM) by Tipping (2001), and want to model some data which requires handling of an exposure column (different importance). Is someone ...
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### Seeking authoritative references on weighted ANOVA

I would be grateful for any reference, such as a textbook or peer-reviewed journal article (of any vintage), that contains explicit formulas for conducting a weighted ANOVA with arbitrary weights. ...
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### Statsmodels heteroskedasticity test: consider weight of data next to difference in variance

For a current project, I have generated a number of data points that show a clear triangular pattern: When trying to quantify this pattern through a Statsmodels Breusch-Pagan test, the data however ...
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### Improve Adaboost that using weighted logistic regression instead of decision trees

I implemented Adaboost that using weighted logistic regression instead of decision trees and I managed to get to 0.5% error, I'm trying to improve it for days with no success and I know it possible to ...
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### t-test to compare weighted means

I have an unbalanced panel of paired differences. That is, my panel consists of 100 firm time series of paired differences with varying length. I have tested wether the unweighted mean is different ...
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### Why is importance-weighted empirical risk minimization finite-sample biased?

Classical risk minimization (RM) minimizes the expected loss over the training distribution $p_{\mathrm{train}}(x)$, $$\theta^*_{RM} = \arg \min_\theta E[\ell(x, \theta)]_{p_{\text{train}}}.$$ As the ...
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### Estimation of measurement reliability

I have the following statistical setting: I have two unknowns $a$ and $b$ an I have two measurements of their values corrupted by noise distibuted uniformly in $[-e,e]$ and I have exact value of $e$ ...
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### Conditional logit (fixed effects logit) regression for propensity score estimation

Is using clogit problematic in estimating propensity scores (e.g., for weighted OLS regressions)? I have an individual-year panel data and a treatment that occurs every year for some of the ...
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### Extending external validation diagnostics to experiments with continuous treatment

Does the external validation diagnostic methods discussed in Stuart et al. (2011) (i.e., inverse propensity score weighted regressions) also apply to the experimental setting in which the treatment is ...
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### Compound Independent Probability of Random Events

I'm trying to write a solver for random data and I hit a bit of a statistics brick wall, I wonder if someone might be able to shed some light. If we consider a bag of 10 balls, each one is unique and ...
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### In a weighted least squares regression, can we use the weight as a control variable?

I have found Weighted Least Squares with Endogenous Weights but the answers primarily tackle the question of when $w_i$ correlates with $\epsilon_i$. I would like to ask if we use $w_i$ as a control ...
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### Algorithm to estimate aggregated outcome variable

I am looking for an algorithm that can estimate weights for an aggregated weighted average. The difficulty is that my outcome variable is an aggregated group variable. I have the following data that ...
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### Weighted Least Squares vs Monte Carlo comparison

This is a copy of a question originally posted on stackoverflow I have an experimental dataset of the following values (y, x1, x2, w), where y is the measured quantity, x1 and x2 are the two ...
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### Weighted least squares using poisson regression link-log example in R

I'm studying about “weighted least squares” using poisson regression example. And I could got it for poisson link “identity” as following. it would be well because of the same one to minimize (or ...
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### Determining weights for fitting non-uniformly spaced measured data (v2)

Let's pretend I have some data to which I want to fit a line. If the data are uniformly spaced along the x-axis, I get the following: If the data are not uniformly spaced, I get a different fit line:...
I have read in this paper that the weighted regression solution converges to the solution of L1 regression, for weights, $$W_i=1/|y_i-\hat y_i|$$ I worked this out but unfortunately, I lost. Could ...