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5 votes
1 answer
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Very basic questions about choosing weights for WLS

Hi all – very new to stats and ML here (though with plenty of math experience – I’m not a student looking for homework help, I’m 58, know plenty of math, and am looking to expand my skills).

I ...
Steve Lane's user avatar
2 votes
1 answer
56 views

Why does `systemfit` yield different results for OLS and WLS under cross-equation restrictions?

I am following up on the question "Why does systemfit yield identical results for OLS and WLS?". It deals with estimating a system of linear equations ...
Richard Hardy's user avatar
2 votes
2 answers
79 views

Why does `systemfit` yield identical results for OLS and WLS?

I am estimating a system of seemingly unrelated regressions (SUR) using the systemfit package in R. Each of the equations has one unique regressor and one common ...
Richard Hardy's user avatar
0 votes
1 answer
102 views

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
  • 41
0 votes
0 answers
28 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
  • 1
0 votes
1 answer
35 views

change in p-value (significance) of the interaction term in moderated regression after using WLS instead of OLS

I am running a moderated regression, N = 1515. I have one outcome variables, one moderator, one predictor and 5 controls. I am using SPSS for my analysis. I first performed linear regression to check ...
Tg51's user avatar
  • 1
1 vote
1 answer
216 views

What is the matrix $(X'\Omega^{-1}X)$ in Generalized Least Square / Weighted Least Square? [closed]

What is the matrix $(X'\Omega^{-1}X)$ X) in Generalized Least Square / Weighted Least Square? More precisely, We know:
Dr. T's user avatar
  • 23
1 vote
0 answers
168 views

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: ...
Marina's user avatar
  • 61
0 votes
0 answers
202 views

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 ...
mv94's user avatar
  • 1
0 votes
1 answer
933 views

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 ...
Karamell's user avatar
1 vote
0 answers
80 views

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 $...
freelantzer's user avatar
1 vote
0 answers
65 views

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 ...
Anna Kortusova's user avatar
2 votes
0 answers
984 views

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 (...
PsychometStats's user avatar
1 vote
0 answers
72 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 ...
dub daze's user avatar
3 votes
1 answer
333 views

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 ...
schuler's user avatar
  • 31
2 votes
1 answer
3k views

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) + ...
John Tokka Tacos's user avatar
3 votes
1 answer
513 views

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/...
PyjamaNinja's user avatar
1 vote
0 answers
756 views

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 ...
e u's user avatar
  • 31
2 votes
1 answer
556 views

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 ...
HanaKaze's user avatar
  • 155
6 votes
1 answer
8k views

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 ...
bsbk's user avatar
  • 1,197