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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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Why are 1/SE or 1/variance commonly used as weights in regressions?

I'm trying to do a meta-analysis for the first time, comparing measurements of a simple experiment treatment against a control in a variety of species. I started by fitting a mixed-effects model to ...
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How to compute a weighted mean as a measure of central tendency?

Imagine I have data points in triplicates, as follows $$ L=\begin{pmatrix} p_{11} & p_{12} & p_{13}\\ p_{21} & p_{22} & p_{23}\\ & \vdots &\\ p_{n1} & p_{n2} & p_{n3} \...
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Propensity Score Matching and Weighted Regression Analysis

I have a dataset of ~N=1000 and I want to estimate the average causal/treatment effect of an exposure on an outcome. I've used propensity score matching to balance baseline covariates, and my matched ...
J2019's user avatar
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1 answer
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How critical/serious is the heteroscedasticity in my data (Breusch-Pagan test significant at p=.03)?

edit below I am doing this analysis for the first time. How concerned should I be about heteroscedasticity in my data? Here's the scatterplot of predicted values vs residuals: The Breusch-Pagan test ...
mbp's user avatar
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6 votes
2 answers
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Impact of class weights on logistic regression - excessively low p-values and narrow confidence intervals

I am currently working on a logistic regression problem with an imbalanced dataset. The total number of rows in my input is 51220 (class_0=49,654, class_1=1,566). I use 3 predictors (1 continuous and ...
Panos's user avatar
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Extremely Small Output Weight Values in Echo State Network

I have an echo state network that is producing an output weight matrix with extremely small output weights (on the order of 10^-200). Ideally, these weights should be within a more reasonable interval,...
Jonathan Frutschy's user avatar
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13 views

Best way to approach sensor fusion

I'm fusing acceleration data from an accelerometer and the derived acceleration from a distance sensor to learn about sensor fusion. The derived acceleration (2nd derivative) from the distance sensor ...
pchandr3's user avatar
4 votes
1 answer
39 views

Regression weighted by variable Z vs including Z as a control variable

I want to understand the relationship between X and Y, with a control variable Z. What are the differences (in assumption, interpretation of $\beta$, etc) between (1) the regression model of $Y = \...
yliu95's user avatar
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2 votes
1 answer
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Use of weights in non-linear least square fitting

I would like to have your suggestions and help concerning my problem. I have images generated on a position sensitive detector. The signal for each pixels corresponds to the amount of 'particles' ...
toto's user avatar
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Any special technique for case control data where # control matches can vary per case (up to 3 matches per case)?

I have case control data, of cancer cases and healthy controls (1 row per participant). I am doing 3 rounds of matching where round 1 does 1 match per case, round two does another match per case and ...
Sakshi Tewari's user avatar
3 votes
1 answer
129 views

Weighted least squares for a linear model

Background I have a 2-dimensional dataset $\{y_i, x_i\}_{i=1}^N$ in the coordinates $y,x$. I'm trying to fit the dataset with the trivial model $$\tag{*}y=mx$$ where $m$ is a (scalar) parameter that ...
matteogost's user avatar
1 vote
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377 views

Using Inverse probability of CENSORING weights with already ps-matched data

EDIT according to Willems2016--------------- I have data of treated and untreated persons of which the covariate age (assume there is just one covariate) is ...
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18 views

Prediction Interval formula for WLS regression

I have been unable to find a non-matrix notation formula to calculate prediction interval for a weighted least squares regression. For OLS, I have $$y = \hat y \pm t\times \sqrt{\left(\textrm{MSE}\...
Laurie's user avatar
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1 vote
1 answer
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Weights in binary logistic regression

I am conducting a vote-counting meta-analysis where the only information I have from each study is the direction of the treatment effect (positive or negative) and the sample size. My plan is to fit a ...
Andrew Siefert's user avatar
1 vote
0 answers
34 views

Coefficient covariance matrix of inverse probability weighted regression

I am interested in computing an estimate $\hat\Sigma_\hat\beta$ of the asymptotic covariance matrix of the parameter estimates $\hat\beta$ in a regression of $Y$ on $\{X, Z\}$, weighted by weighs $\...
Noah's user avatar
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Thin plate regression splines: weighted version, risk of oversmoothing?

Is any specific caution needed when using thin plate regression splines with weights? Is there possible "interaction" between penalization of curvature and weighted likelihood, potentially ...
GAMer's user avatar
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1 answer
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What is the objective function for weighted lasso & ridge?

For weighted OLS, the objective function can be written as $$ \arg \min_{\beta} ||W^{0.5}(y - X\beta)||^2 $$ This is quite similar to the objective function for plain OLS, except without the $W$ term: ...
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Weighted least squares with measurment errors: how to get proper standard errors for coefficients?

If we have outcome variable as measurements with associated SD as form of measurement uncertainty and we want to incorporate the uncertainty information in linear regression model, what is the proper ...
NeuroPanda's user avatar
1 vote
0 answers
76 views

Power analysis for an IPTW (Inverse Probability of Treatment Weighting) model?

I have a sample of N=1,615, and 319 of those cases (19.75%) received the treatment. The prevalence of the outcome of interest is about 0.09 for the whole sample. Ultimately, I want to conduct IPTW to ...
Ray's user avatar
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The Hat matrix in the weighted least square

From the ordinary least squares (OLS) problem, given a design matrix $X_{n\times p}$ and a response $y_{n \times 1}$, we want to find $$ \hat\theta = \arg\min_\theta \|X\theta-y\|^2. $$ In this case, ...
pbb's user avatar
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2 answers
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Is it reasonable to subset a survey design object by dependent (outcome) variable and fit a weighted logistic regression model?

I would like to study which factors are associated with an outcome which has more than two categories. After considering multinomial logistic regression model (which I find is very challenging to ...
Willi Zhang's user avatar
2 votes
1 answer
88 views

Inverse probability weighting led to a decreased R-squared value

I used inverse probability weighting to correct for selection bias in my sample. After including inverse probability weights in my model, I observed that the R2 actually decreased compared to the ...
zjppdozen's user avatar
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82 views

Weighted least squares estimator variance using noisy weights

I have a linear system with uncorrelated, heteroscedastic noise, $Y \propto \mathcal{N}(Xβ,Σ)$ where $Σ$ is a diagonal matrix with elements $σ_{ii}^2$. The MLE is given by weighted least squares (WLS) ...
dperl's user avatar
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32 views

Weighted regression with no variance within cluster

Given a clustered data set with no variation within a cluster, shouldn't a regression weighted with the inverse cluster size give the same results as a regression with only one observation per cluster?...
Irazall's user avatar
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1 vote
0 answers
27 views

Seeking Feedback on Mixed-Effects Model with Weighted Observations

I've been working on a project where I'm comparing different methods using a mixed-effects model, and I'd appreciate some feedback on my approach. Background: I have a dataset with several variables: ...
Almog Angel's user avatar
1 vote
0 answers
104 views

Matching weights vs 'weighting' weights?

What is the difference between matching weights obtained from full matching (with propensity score or mahalanobis distance, using MatchIt and then match.data in R) and the "weighing" weights ...
guest4411's user avatar
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14 views

Generalized Linear Model optional weights

In Introduction to General and Generalized Linear Models by H. Madsen & P. Thyregod, the ML estimator for $\beta$ is defined in eq. 4.42 (p.106) as $$W(\beta) = \text{diag}\bigg\{\frac{w_i}{g'(\...
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43 views

Performing a Bayesian (or Bayesian-like) linear regression

I'm trying to model the relationship between two variables. Without going into details on how I get this expectation, my belief on the relationship between the variables looks like this: However, as ...
gammapoint's user avatar
2 votes
1 answer
56 views

Treatment Effect Insignificant with OLS but Significant After IPTW

I'm working with some observational data and wanted to assess the effect of variable (D) on outcome (Y) after controlling for a vector of covariates (X). As the data is observational, I wanted account ...
statslearner12's user avatar
1 vote
1 answer
29 views

Cluster uncertainty in Linear Regression

Is it possible to introduce cluster probabilities into a regression? Consider the Old Faithful Geyser data set. Most clustering algorithms find 2 clusters when analysing eruption times and waiting ...
29703461's user avatar
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0 answers
31 views

How to summarize a weighted regression in research paper

New here so apologies if I'm not doing this right. I'm writing up a research paper and my advisor/statistician provided me the following data to report in this paper. He said he completed a variance ...
juju's user avatar
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1 vote
0 answers
187 views

How to calculate F-statistic from a svyglm model in R

I am struggling to figure out the correct way to calculate the F-statistic of a regression model that uses complex survey data in R. I am using svyglm from the R survey package. Would the below code ...
TerrenceWeast's user avatar
1 vote
0 answers
89 views

Calculating R-squared (coefficient of determination) from WLS linear regression with zero intercept

I need to calculate the R^2 for a weighted least squares (WLS) regression model which is also a regression through the origin (RTO). I'd like to use it for comparing the quality of the fits for the ...
Virag's user avatar
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1 vote
0 answers
82 views

Regression Model for a Ratio Outcome with Count Variables as Numerator and Denominator

I have a dataset where each row corresponds to a country and contains independent variables such as "per capita income" and "mean education status." Additionally, there are two ...
insan's user avatar
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2 votes
0 answers
49 views

Reasoning weighted regression via causal inference

I want to follow a similar approach to what was done in the paper of Bornkamp et al. in 2021 (DOI: 10.1002/pst.2104). More specifically they added a link to a R markdown file (https://oncoestimand....
jerome's user avatar
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0 answers
79 views

Weighting linear / logistic regression data points by explanatory variable sample size

[EDIT: had fundamental misunderstanding, rephrasing question - thanks to @whuber for catching that] I have some pretty simple regressions (linear & logistic) predicting a rate (continuous response ...
TY Lim's user avatar
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1 vote
1 answer
562 views

how to understand the weights in PSM?

When using propensity score matching or weighting, a column of weights is generated that is used to estimate the effect of interest. According to a blog I read, there are three types of weights ...
Plumber's user avatar
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1 vote
1 answer
66 views

Feasible GLS estimator

I'm approaching for the first time GLS estimators. Suppose that $\operatorname{Var}(u|x)=\sigma^2 h(x)$, where $h(x)$ is some function of the explanatory variables that determines the ...
Dimitru's user avatar
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0 answers
47 views

Logistic regression for hierarchical / nested (3 level) data

Research Problem We are trying to help universities recruit as many students as possible for different projects for a good cause. To be eligible for any project offered by their university, students ...
Verena W's user avatar
1 vote
1 answer
424 views

Calculating outcomes in IPTW

I have a few questions concerning what to do next after balancing your population with IPTW. This is a code just to have an example: ...
user19745561's user avatar
1 vote
0 answers
83 views

Calculating weights for a weighted least squares regression on a differenced time series

I am looking for guidance on whether I am approaching my problem correctly. I have an annual time series { $x_{1}$, $x_{2}$, ..., $x_{t-1}$, $x_{t}$ }, where each observation is the estimated median ...
squeegee's user avatar
2 votes
0 answers
110 views

Include confidence intervals of samples in nlme model

I have a continuous response variable (leaf length), which has been repeatedly measured in 45 experimental plots over several growing seasons. My goal is to properly estimate at which day of the year (...
Patrick Möhl's user avatar
2 votes
1 answer
226 views

Design-based standard errors in svyglm but w/o weights or stratification

For inverse probability weighting (IPW) in R the use of survey::svyglm is well established. I want to compare the results of 10K+ (!) models with and without the ...
jay.sf's user avatar
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0 votes
0 answers
212 views

Geographically weighted random forest and categorical covariate

I am about to use geographically weighted random forest (GWRF) for regression prediction (I want to predict a continuous raster). I have one dependent and 4 independent variables. One of my ...
Nikos's user avatar
  • 111
0 votes
1 answer
111 views

Implementing SUR on weighted regression models

I have two equations: fit1= svyglm(Y1 ~ X1 + X2 + X3, design= design.mnps, data= data) fit2= svyglm(Y2 ~ X1 + X2 + X3, design= design.mnps, data= data) ...
User123's user avatar
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3 votes
1 answer
234 views

Heteroscedasticity robust variance-covariance matrix for weighted multivariate regression

I need heteroscedasticity robust standard errors for a multivariate linear model (MLM) with weights. In R we usually use sandwich::vcovHC with type ...
jay.sf's user avatar
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1 vote
1 answer
26 views

Times series with autocorrelated errors

I'm following the "Time Series Analysis and Its Applications With R Examples" from Shumway and Stoffer. In chapter 3.8 they talk about Regression with Autocorrelated Errors. "They use ...
Warhawk1987's user avatar
2 votes
1 answer
236 views

Interpretation of weights in a GLM

I want to know whether my interpretation of GLM weights is correct. On R documentation of GLM it says that Non-NULL weights can be used to indicate that different observations have different ...
Anja Krause's user avatar
1 vote
1 answer
96 views

Should I take logarithm of weights in WLS regressions

I am new here. I have a question regarding the anlaytical weights used in ivreghdfe or reghdfe regressions. People usually take aweights in STATA, my question is how we deal with the weight if the ...
anniejerry's user avatar
0 votes
0 answers
507 views

Timeseries - How are the window/span size and 'frac' in LOWESS related?

Many software implementations of locally weighted scatterplot smoothing (LOWESS), such as those in Python and R, require a frac parameter as an input. I am confused as to how frac is mathematically ...
Kartik's user avatar
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