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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17 views

R package for inverse-variance weighting? [closed]

Can you recommend an R package for doing inverse-variance weighting? Yes, I could program the pointwise estimates again. And I could think about estimating the new variance of the combination, and ...
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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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6 views

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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115 views

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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21 views

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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25 views

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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41 views

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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22 views

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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35 views

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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36 views

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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29 views

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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59 views

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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114 views

Goodness of Fit ot Least Squares with known measurement uncertainty

We want to estimate $\beta$ for $$ y = x\beta + \epsilon $$ where $y$ and $x$ are $n\times 1$ vector and $\epsilon$ is not i.i.d, but $\epsilon \sim N(0, \sigma^2\Omega)$, where $\Omega$ and $W$ are $...
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Calculate Variance Inflation Factors for WLS (using python package?)

Is there an easy extension of VIFs (variance inflation factors) to WLS regression, hopefully easily available in Python? I have an application where I am optimizing the operation a system, modeled as ...
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85 views

Interpreting regression coefficients in weighted linear regression

I have a dataset where I'm doing Multiple Linear Regression. Examining the residuals vs fitted plot, it was seen to exhibits heteroskedasticity. As an antidote, I am doing Weighed Least Squares ...
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22 views

Weighted zero inflated negative binomial regression

Before encountering the ZINB model, my choice of model was the standard NBR model with the R function glm.nb. My dependent variable is non-negative integer in ...
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78 views

Prove variance of locally weighted regression increases with degree

I am interested in proving the following fact for locally weighted polynomial regression from The Elements of Statistical Learning by Hastie et. al. It can be shown that $||l(x_0)||$ increases with ...
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How to use survey weights correctly in logistic regression with R?

I'm currently working with data from the European Social Survey (ESS). With it come several weights varaibles to use for analyses. I tried to use them the following way conducting a logistic ...
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1answer
44 views

Ratio Estimator as WLS

Apologies in advance for whatever rules this post breaks. I'm looking at a problem where we're currently using a ratio estimator for a certain survey. $$r = \dfrac{\sum_i{y_i}}{\sum_i{x_i}}$$ This ...
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114 views

What is the likelihood ratio test for the significance of a term in a Cox's Porportional Hazards model with a weighted dataset?

(Please see reproducible example below.) When fitting a Cox proportional hazards model in R, I'm trying to compute the significance of some terms in order to drop them in case they are irrelevant, ...
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How to apply different weights on independant variables in lmer?

I am trying to build a mixed-effect model to predict an outcome based on three independant variables. Below is the line of code I wrote so far. ...
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Combining estimates from multivariate multiple regression using MICE in R?

A similar question was posted last year, but it didn't get any love, so!: I'm trying to calculate a pooled estimate after fitting a multivariate regression in multiply imputed data (having used MICE ...
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Best method for rescaling weights [duplicate]

I'm investigating the effect of overhead cover (tree canopy) on the proportion of birds (in relation to mammals) scavenging on carcasses left out in nature. For this study I placed 35 carcasses in ...
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18 views

Calculating weights for weighted regression

I want to weight my regression by the square root of a which I'm doing by applying a weighting function to my x and y variables before running the regression. I'm a bit confused, however, but whether ...
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Dynamic Linear Model (DLM) vs Weighted Linear Regression

In Applied Bayesian Forecasting and Time Series Analysis (1994, page 14), they state: The passage of time erodes the value of information - sales figures from six months ago are potentially less ...
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imbalanced regression problem + lower bound prediction + custom error weighting

I'm looking for a simple approach (e.g. defining a new target label / sample weights and then using some off-the-shelf regressor with some standard objective) for the following problem: I want to ...
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118 views

appropriate use of prior weight in glm

I am modelling the effects of several variables on the number of scallops caught. The variables are: Stratum (categorical, 23 levels), Vessel (categorical, 3 levels) , Density of scallops (continuous)...
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62 views

Comparing mixed models with weighted variance

I'm performing some linear mixed models for a psychological experiment. I'm not a statistician so my knowledge is limited. The basic idea is that: I have an experiment in which I model my response ...
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40 views

Weighted OLS predictions

I am experimenting with cross validation to determine a cap for weights in weighted OLS (because the weights become large). I first estimate $\hat{\beta}_{trn}$ using the training data. Do I (A) ...
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71 views

Non-Linear regression and variance misspecification

Given a non-linear regression model for cross-section data $$y_i = f(x_i,\theta_0) + \epsilon_i,$$ where it is assumed that $\mathbb E[y_i\lvert x_i] = f(x_i,\theta_0)$, I understand that it is a ...
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76 views

Weights formula for Weighted Linear Regression [closed]

I am working with Weighted Linear Regression. I have read that I need to calculate the weights $W_i$ to perform this regression. My question is; Which formula should be used for calculating the ...
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313 views

What does “weighted logistic regression” mean?

What does "weighted logistic regression" mean? I came across this term "weighted logistic regression"in this paper. I have read the paper a lot of times throughly. But I still can't get the idea of ...
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54 views

weighted linear regression and outliers

I am fitting a regression model with weights because without weights I have heterocedasticity. Suposse $\epsilon \sim N(0,x_i \sigma^2)$ Then check the weights through aux model Model $Y=X \beta + \...
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1answer
30 views

Variance Estimation for Least Squares with Probability Weights

I'm running a simulation study and finding that the nominal SEs of the estimated coefficients when using weights in lm in R are an underestimate of the simulation SE. I have confirmed that $\hat{\beta}...
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628 views

How does R compute r.squared for weighted least squares?

I used R for fitting a linear model using weighted least squares (due to heteroskedastic errors): $\boldsymbol{y} = \boldsymbol{X}\boldsymbol{\beta} + \boldsymbol{\varepsilon}$, where $E(\boldsymbol{\...
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Measure of association adjusting for varied number of observations per person (binary outcome and predictor)

I would like to ask a question about how to alter a model to deal with varied numbers of cases per person (1 vs. 2), or, if I should deal with it some other way, some suggestion around that. I would ...
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47 views

How to generate a weighted regression from repeated experiments in R & using a weights matrix with lm? Is this possible?

I was told in another question that glm cannot do multivariate analysis, so I'm hoping the weights matrix idea isn't doomed through lm, too. I've also spoken with 4 classmates about this (grad ...
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26 views

Stochastic/batch gradient descent (type SGD/ADAM) with weighted mean square error loss

Assume I assign uneven weights to losses of different examples, i.e. I set my SGD/ADAM to train a universal approximator f (e.g. a neural net) by minimization of a weighted mean square error: $ L = \...
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33 views

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:...
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34 views

Determining weights for fitting non-uniformly spaced measured data

I have a system of generally known behavior, and some non-uniform measurements of that behavior (let's say without measurement error). Now I want to fit a simple function to a subset of the ...
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1answer
51 views

Convergence of weighted regression solution to the solution of L1 regression

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 ...
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1answer
157 views

Confidence interval for mean of m predictions

I have a gradient boosted regression tree model (catboost). $y = F(X) + \varepsilon$ I need to compute the following - specifically the 2nd equation below, the first is trivial. $\frac{1}{m}\sum \...
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1answer
421 views

Poisson regression with offset vs poisson regression with weight [duplicate]

I would like to know the linear expression of weight and offset in terms of poisson regression in glm. for instance for offset ...
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1answer
28 views

How do I use weighted least squares in a matrix formulation of a multiple regression analysis?

If the coefficients of OLS multiple regression can be determined by: β = (X'X)^−1 * X'Y, then what formula/matrices would be used for WLS?
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55 views

Formulas for multivariate meta-regression

everyone! I'm digging in meta-regression and doing hand calculations using WLS to get better understanding of the topic. I'm fine with calculations for univariative model (that is, 1 covariate is ...
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131 views

Weighting in Likert Scale results

I have referred to similar questions on this topic, but the problem presented then was not quite in line with my research, so I have created a new question. My research is the following: I have ...
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1answer
54 views

Does local linear regression include a weighting Kernel?

I am applying a Regression Discontinuity Design (RDD) to estimate the effect of a policy change. In RDD I can apply the parametric approach (polynomial regression) and the non-parametric approach (...

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