Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [wls]

14 questions
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Standard Errors with Weighted Least Squares Regression

For OLS, $\hat{\beta} = (X'X)^{-1}X'y$, and $\text{var}(\hat{\beta}) = (X'X)^{-1} X' \sigma^2 I X (X'X)^{-1}$. I can reproduce these "by hand". For WLS, with heteroskedastic errors and weights in diagonal $W$, $\hat{\beta} = (X'WX)^{-1}X'Wy$,…
bsbk
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WLS vs Dummy variable coding for heteroscedasticity

I am a beginner level stat learner (with graduate training in Applied Math) I have just read a sage book which states the following: "Dummy variables help address the issue of heteroscedasticity in residual variances given a well specified linear…
schuler
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Dealing with Heteroskedasticity: when to use WLS vs Box-Cox/Box Tidwel Transformation

Suppose you are fitting a linear model which has heteroskedastic (non-constant) residuals. I have read that there are a number of ways of dealing with this situation, including Weighted Least Squares (WLS) estimation and applying Box-Cox and/or Box…
PsychometStats
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Comparing non-nested models estimated by Weighted Least Squares

It's very common for social scientists to have binary or ordinal indicators (e.g., yes/no interview items or likert-rated questionnaire items). It's also very common for them to model their ordered/non-ordered categorical data with structural…
PyjamaNinja
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Weighted least square regression - different ways of estimating weights

Newbie here. I have a question regarding WLS regression. Specifically, I've come across different ways of estimating weights in WLS regression, the most frequent ones being: weights <- 1 / abs(fitted.values(model.lm)) weights <- 1 /…
Marina
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Weighted Least Squares, why $Var(ε_i/ \sqrt(x_i)|x_i)=1/x_i \times Var(ε_i|x_i)$?

In Weighted Least Squares we assume that $Var(ε_i|x_i)=σ^2\times x_i$. Then we divide our regression model $yi=a+b_1x_i+ε_i$ by $\sqrt{(x_i)}$, such that the "normalized" model variance is $Var(ε_i/\sqrt{(x_i)}|x_i)=1/x_i\times Var(ε_i|x_i)=1/x_i…
freelantzer
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Dealing with Heteroskedasticity in Estimated Dependent Variable model

I work on my research in finance concerning pricing of green bonds and I am running a two stage model. Stage 1 regression is an unbalanced panel fixed effects estimation. For each of my 100 green bonds in the sample, I compare its daily ask yield…
Anna Kortusova
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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 considered) but faced problems when several…
dub daze
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Confidence Interval of the mean response for Weighted Least Squares (WLS)

I know that the confidence interval of the mean response for OLS is: $$ \hat{y}(x_0) - t_{\alpha /2, df(error)}\sqrt{\hat{\sigma}^2\cdot x_0'(X'X)^{-1}x_0} $$ $$ \leq \mu_{y|x_0} \leq \hat{y}(x_0) + t_{\alpha /2, df(error)}\sqrt{\hat{\sigma}^2\cdot…
John Tokka Tacos
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FA estimation (GLS/WLS/DWLS/ULS) and robustness of these estimators

I have cross-sectional survey data, with over 4000 observations on 41 variables, and there are no missing values. Variables are not normally distributed and assumptions of multinormal distribution are violated. Within R I am using FA with varimax…
e u
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Quality of weighted least square fit

I fitted a linear regression with heteroscedescity using weighted least square method. How do I evaluate the quality of my fitting? I’m thinking by the p-value of slope/intercept. Or maybe because I minimized the cost function and that process…
HanaKaze
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Do residuals need to be normally distributed to carry out Weighted Least Square (WLS) Regression?

First of all, I have to admit I am here because I am struggling with my dissertation. With this disclaimer out of the way, here is my problem: I am trying to carry out multiple regression analysis but I cannot meet the assumptions for normal…
mv94
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Weights to use for a Weighted Least Squares model regarding tests/deaths

I'm currently doing an imaginary project where I'm investigating a possible correlation between the number of tests done for a specific disease and the number of deaths caused by said disease. I'm looking at several different areas of different…
Carlsson
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Calculate the weight of a WLS solver and evaluate an Image-To-Image Training

I have a depth map reconstruction problem that I have formulated in this form : With w(u,v) is the weighting term. To produce the two maps R and W I used a convolutional neural network. Now, I performed tests (grid search) to find the optimal ()…
SiamouR9
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