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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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Appropriate weighting factor in weighted least squares regression

I'd like to construct a regression model with expenditure on a certain public service (a continuous variable in £s) as the predictor, and productivity (represented as a continuous variable on an index)...
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Restricted Weighted Linear Regression in R

I have to follwing issue. I would like to run a linear regression imposing a constraint on the weighted coefficients. Let me construct an example: Consider the following cross-sectional regression $...
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Why do stabilized IPW weights give the same estimates and SEs as unstabilized weights?

In Cole & Hernán (2008), the authors mention that using stabilized weights can decrease the variance of the effect estimate. Regular inverse probability weights use the probability of being in the ...
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Different error weighting for positive and negative residuals for OLS?

For OLS-estimators in multivariate regression analysis, it logically doesn't matter whether an error is positive or negative. I was wondering if in some situations it might make sense to weight a ...
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Problem from Introductory Wooldridge regarding WLS

I was reading the book introductory econometrics by "Wooldridge", and in Chapter 8 (Heteroscedasticity), it is stated that (see pink part) I could not understand, if $u$ and $x$ are uncorrelated, ...
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Calculate mean by decile in Svydesign object

So, I´m working with ENIGH - Database, which stands for ¨National Survey of Household Income and Expenses¨ in Spanish, this is an exercise conducted by the Mexican government and like most surveys of ...
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Weighted least square - intervals of prediction

Lets assume that we have the following data set with problems of heteroscedasticity: ...
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Are GLMs just glorified WLS regressions?

When performing weighted least squares $L = \frac{1}{2} \sum_i w_i r_i^2$, Aitken showed that one ought to weight each sample by the inverse of its variance $w_i=1/\sigma_i^2$. This leads to gradients ...
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Probability Weights and Dropping Observations

I am trying to determine how applied empirical analyses adjust probability weights after dropping observations. For example, say I have a strict subset of the population that takes a 2013 cross ...
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Posterior distribution of ATE with Bayesian propensity score model?

I am using propensity score weighting (PSW) to estimate the average treatment effect (ATE) of some treatment $D$ on an outcome $Y$ with covariates $X$. I have seen several ways in the literature (both ...
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Iteratively Reweighted Least Squares Poisson Regression with Non-Canonical Link, eventually in R

I am attempting to implement iteratively reweighted least squares (IRLS) for a poisson regression with a non-canonical link function. My understanding of IRLS is only basic at this point, so please ...
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When to use variance stabilizing method?

Let's suppose we want to estimate $p$ from $m$ independant realisations of $X\sim Bin(n,p)$: $x_1,x_2,\dots,x_m$, with respective size $n_i$ $i$ in $\{1,\dots,m\}$. Let $p_i$ be $p_i:=x_i/n_i$. To ...
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How to fit a weighted mixed effects model?

I am looking to get help into specifying the structure of the variance matrix within the gls() function in R's nlme package (or recommendations of other packages ...
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1answer
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Inverse probability weighting (IPW) with positive and negative treatments?

I am studying the effects of the government intervention which can take two directions and is usually represented as follows: $Treat = \left\{\begin{matrix} & +1 (intervene), if state A\\ &...
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Using regression weights when $Y$ might be measured with bias

Suppose we observe data $Y, X$ and would like to fit a regression model for $\mathbf{E}[Y \,|\, X]$. Unfortunately, $Y$ is sometimes measured with a systematic bias (i.e. errors whose mean is nonzero)....
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Using White's Robust Co-variance Matrix vs Weighted Least Squares to correct for heteroscedasticity

I've been trying to figure this out for a bit. How does using White's robust co-variance matrix in OLS vs weighted least squares affect mean response confidence intervals? I've experimented with ...
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What's the formula to estimate the shape parameter of Pareto distribution using weighted least squares method?

I'm trying to simulate my own method using R to estimate the shape parameter of Pareto distributed data by weighted least squares. I searched via several links of research papers, but I could not find ...
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Which is the right way to handle imbalanced data in a regression problem?

I'm working on a regression problem with imbalanced data, and I would like to know if I'm weighting the errors correctly. I'll try to illustrate the concept with a simple example. Imagine I'm ...
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How to find proper weights for summation of 3 dependent variables

I have time series for 3 variables, say energies from 3 sources (e1, e2, e3). I have checked their dependency using the calculation of the correlation of each pair and found that their dependency is ...
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1answer
107 views

weighted IV estimation by plm

I apply plm package to do fixed effects IV regression but find something which I couldn't understand. Theoretically, if we only have one endogenous variable and one IV, the IV estimator should be ...
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Risk classification with non uniform risk exposure (truncated observation period)?

I have N individuals who are exposed to a risk. The risk exposure is in year fractions (from 1/365 to 1). More or less 1/4 of the observations are exposed to the risk for an entire year. I want to ...
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Penalized regressions with forecast package and ets in R

Is there a way within the forecast package and ets to remap or penalize residuals based on some user defined function? E.g. If one wanted to impose a skew in error minimization, is this possible? ...
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Principal Component Analysis with weights

In a Principal Component setting, I want to solve the minimization problem $$\min_{\{f_t\}^T_{t=1}, \Gamma} SSR$$ where $$ SSR = \sum^T_{t=1}(y_t - \Gamma f_t)' R'_t R_t (y_t - \Gamma f_t)$$ $...
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Weighted Regression where Weights are associated with Response Variable

I am trying to carry out a simple linear regression analysis represented by the standard formulation: $$ y_i = \beta_0 + \beta_1x_i +\epsilon_i $$ However, there is an issue with my data. There is no ...
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1answer
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How to use White-test to check if the heteroscedasticity has been effectively dealt with by a WLS?

Consider an OLS model with $n$ observations and $p$ explanatory variables (including an intercept term) $$y=X\beta + \epsilon$$ We may use a White test to (approximately) check for the presence of ...
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How to use weighted data in linear modeling?

I have data from studies where each study has the means for that sub sample and the sample size is n, so the n is a frequency. There is one categorical predictor. The dependent variable is a % (the % ...
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I am looking for an explanation of inference of results from weighted regression for a ratio of two continous variables.

I am performing a weighted regression for a ratio $R = \frac{Y}{X}$ using $X$ as weights. Y and X are normal and they are not independent. Is it valid to use $X$ as weights? What is the interpretation ...
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221 views

Weighted linear regression from log-likelihood?

I have 500 time-series and for each one, I compute the best (aka max likelihood) parameter α in a model that I'm testing, along with the corresponding log-likelihood. Now I wish to uncover a linear ...
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Switching attention - is there a statistical tool to mimic perceptive response?

I was driving this morning to work. Another car made sudden lane change. I noticed an interesting thing: for a brief moment my attention focused in this car. It almost physically felt that everything ...
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How to do a regression with a percent as the dependent variable and with sample mean values?

I have 60 sample of data from various studies. All I get is a mean for x and y, and a sample size. Furthermore y is a percentage. Sometimes we get the standard error of the mean. IIRC, percentages ...
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1answer
201 views

How to fit a line to data using weighted least squares (WLS) regression?

I am newbie to WLS regression topic. I am being asked to fit a line to a data using WLS. I am working in minitab. My data is as follows: cost (independent variable) (x-axis); production (dependent ...
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Standard error implications when combining IPTW and difference-in-differences

My question is about combining Inverse Probability of Treatment Weighting (IPTW) with a difference-in-difference regression with two periods (pre and post treatment). Basically, I first computed the ...
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Fitting model with error on independent variable

This is the second part of a question started here. However, as this touches a different problem inside the same overall issue I decided do separate it into two questions. I've made a series of ...
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Goodness of fit for weighted regression

Is there a goodness of fit metric similar to R^2 that can be used to evaluate a weighted regression? In my particular case, my data points are cities and I weight a regression of this data by city ...
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2answers
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Which weighting to use for regression analyses at different levels of aggregation

I run a study with subjects in 400 groups of heterogeneous sizes ranging from 2 to 20 individuals. I have outcome data at the group level and at the individual level. Treatment was randomly assigned ...
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Formulating the Netwon Raphson

If this is the dataset under consideration and ...
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181 views

Does assigning “prior weights” in a binomial GLM have the same effect as maximizing a weighted likelihood?

I am doing logistic regression where there is some uncertainty about the labels for some of the points. For example, I might only be 90% sure that person 1 is actually a "Yes"--meaning I'm 10% sure ...
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1answer
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Weight of variables in Regression

let's say I have a model with variables Y, X1, X2, X3 and X4. How can I tell how much each variables account for? For example, the model is Y = Bx + Bx2 + Bx3..... Now if I wanted to look at it this ...
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Meta-analysis with binary variable and weighting with sample size - Is it possible?

I am trying to conduct a meta-analysis with my data on private equity performance versus the public stock market. The binary outcome is if private equity outperforms the public stock market (Yes = 1, ...
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Misspecified regression & asymptotics

Consider the weighted regression coefficient $\hat{\beta} = (X'WX)^{-1}X'WY$ where the regression is possibly misspecified and $W$ is known. Let $\beta_* = (E[X'WX])^{-1}E[X'WY]$ and the related ...
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intercept in manually weighed regression

Why does manually weighting a regression require the intercept term to be dropped? Consider a model $$y=b_0 + b_1x + \epsilon, $$ a simple linear regression. In classically weighted regression ...
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Can analytic weights be converted into sampling weights?

I am running a linear probability model, so I know I need to correct for heteroskedasticity. Since I know the variance of the error (from theory) to be $y(\pmb x)(1-y(\pmb x))$ where $y$ is the ...
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Correlation with adjustment

I have data from several animals that are tested daily for 15 days on the presence of seizures. I have the latency of the seizures(when it begins after the start of experiment) and they occur on some ...
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Normality and weighting scores by difficulty

I want to conduct a 2 x 3 x 2 mixed model ANOVA with Group (malus/bonus contract) as a between-subjects factor, time pressure (nine, 12 and 15 seconds) as a within-subjects factor and loss aversion (...
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Noisy Observation of Matrix of Certain Rank

Consider a rank k matrix, call it M, of size nxm. All the elements are non-negative. Now do a noisy observation of it and assume independent Poissonian errors (the error on element $M_{ij}$ is ...
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Closest approximation of a Poisson GLM using weighted least squares analysis to take into account mean/variance relationship

I have an application where I would like to approximate a Poisson GLM with identity link, i.e. a glm of the form ...
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1answer
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What is the most efficient way to compute the weighted least squares estimator?

If we have the estimator $(X^{T}WX)^{-1}X^{T}Wy$ where the diagonal of W contains the inverted weights, what is the fastest/most efficient way to solve it? I know with OLS, the estimator is typically ...
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FGLS vs M estimator

I have been reading a lot that in Robust Regression, there are 2 ways of handling heteroskedasticity. 1)WLS - In SAS PROC ROBUST procedure, M estimator and Iteratively Reweighted Least Square. 2) FGLS ...
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Weighted least squares: how do I find weights

I have a dataset of the cars and their corresponding speed and distance and the R output. I am asked to find weights for the first 2 cars. First I find the residual for each car: $e_i=Y_i-\hat{Y}_i$ ...