"Generalized least squares (GLS) is a technique for estimating the unknown parameters in a linear regression model. The GLS is applied when the variances of the observations are unequal (heteroscedasticity), or when there is a certain degree of correlation between the observations." [Wikipedia]

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GLS estimator of a VAR process

I'm studiying how to derive the GLS estimator of a VAR process. I have studied the basics well, but I don't get the last passage here: Why the product can be rewritten as a quadratic form? Intuitively ...
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3answers
102 views

Comparing OLS versus WLS residual standard error, is the smaller the better?

For a linear regression model I tried on a dataset, when I fitted OLS, the output is as follows: ...
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25 views

GLS Prais-Winsten correction with endogeneity

I have to estimate a number of regressions where a lot of autcorrelation is present. Now, for historical reasons, this autocorrelation is resolved using an iterative Prais-Winsten estimation (a ...
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1answer
117 views

How to estimate a nonlinear equation system in R?

I have trouble finding the right packages and methods to estimate a system of three nonlinear equations with cross-equation restrictions using R. I want to estimate the parameters of a CES production ...
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39 views

Difference-in-Differences Approach to Measure Treatment Effect on Relation between Two Variables

I'm familiar with standard Diff-in-Diff models, such as $$Y_{it} = b_0 + b_1 \text{post}_t + b_2 \text{treat}_i + b_3(\text{post}_t\times \text{treat}_i) + u_{it}$$ where $\text{post}_t$ is a dummy ...
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22 views

Autocorrelation consequences

If our model has autocorrelation, and we continue to use OLS, will the confidence interval be greater or lesser, as compared to the case when we use GLS in this model?
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2answers
65 views

Residual Sum of Squares from Generalized Least Squares (GLS) always 0?

Standard set-up: $$ Y=X\beta+e $$ where $e\sim N(0,\Sigma)$ We know that the GLS estimate of $\beta$ is $\hat{\beta}=(X'\Sigma^{-1}X)^{-1}X'\Sigma^{-1}Y$ The (generalized) residual sum of square is ...
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24 views

Forecasting error from GLS estimator

As well known, $\text{Var}(\beta_{gls})\leqslant \text{Var}(\beta_{ols})$. From this, we can conjecture that the following inequality also holds: $$\text{E}(y_{T+1}-X_{T}\beta_{gls}|\iota(T))^2 ...
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1answer
69 views

GLS versus Robust SE

I have been reading Mixed Effects Models and Extensions in Ecology with R by Zuur et al. where departures from iid errors (heteroscedacity and/or correlation) in linear regression (and glm) are dealt ...
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42 views

Iterative generalized least squares procedure in SPSS?

I want to test the 'poolability' of my data set for a logit regressions. Gatingnon and Reibstein (1986), proposed an iterative generalized least squares procedure to do so. Anybody has an idea how I ...
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14 views

Is my data psuedo-panel, repeated cross-section, multi-dimensional panel data, or something else?

My thoughts are that it is panel data but since the time is not a factor, I wasn't sure if it is standard panel data or something like psuedo-panel or multi-dimensional panel data. Data: I'm looking ...
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30 views

Interpretation of simultaneous and independent ordinary least squares regression

I'm using ordinary least squares to regress a noisy overdetermined system. $$y = \beta_0 x_0 + \beta_1 x_1$$ For comparison, I'm also solving the independent equations \begin{align} y &= ...
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35 views

Cannot reproduce R's nlme::gls regression coefficients

I have this simple example, where I try to get to the same factor loading as nlme::gls Prepare data ...
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1answer
55 views

Generalised Least Square and Square Root of a Positive Definite Matrix

Consider a generalised least square problem as follows. $$ \mathbf y = \sigma \mathbf x + \mathbf e, $$ where $\mathbf x, \mathbf y\in \mathbb R^n, \sigma\in(0, \infty),\mathbf e \sim \mathscr N(0, ...
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2answers
134 views

ARIMA (with xreg) vs GLS

I am fitting both an arima model (with xreg variables) and a gls model to my data in R software. They both have the same ARMA structure and variables. The ARIMA model fits to the data better. Does ...
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2answers
494 views

Lognormal Regression?

I'm trying to model a lognormal response variable. I want to take the log of the response variable and do a least-squares regression line over my predictive variable. However, I'm worried about ...
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22 views

Using Variance Function Classes for fitting a linear, multiple gls model

I have to test the effect of two predictors over a Response Variable. Such predictors show different heteroscedastic relationships with the RV. While for one predictor variance increases with ...
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1answer
549 views

How to determine if GLS improves on OLS?

I have a multiple regression model, which I can estimate either with OLS or GLS. The weights for the GLS are estimated exogenously (the dataset for the weights is different from the dataset for the ...
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1answer
37 views

Given a regression model with heteroscedasticity, find generalized least squares estimator?

I have $Y_i=\beta_0+U_i, E(U_i)=0, var(U_i)=2log|Z_i|, cov(U_i;U_j)=0$ when $i\neq j$. Suppose there are $n$ observations on $Y_i$ and $Z_i$. How do I use this information to find the GLS estimator ...
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101 views

Should I include weights in LME?

I have two case studies where I am looking at the influence of a trait (trait A) on mortality (m) of trees and seedlings. Following your comments on ...
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2answers
168 views

An example of autocorrelation in residuals causing misinterpretation

I'm looking for an example of time series data where a regression of y~x has autocorrelation in the residuals that leads to misinterpreting the model. This is for a class demonstration where I would ...
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18 views

Do I get the HRSEs from my OLS or WLS regression?

I have a multiple regression linear model which I ran a simple OLS test on. I then performed the White test and found that it was heteroskedastic. Then I performed a Weighted Least Squares ...
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22 views

xtreg, re in STATA, which R2 to report? [duplicate]

After estimating the data using xtreg, re, I notice there're 3 different measures of R-squared, within, between, and overall R-2, so my question is, can I just report the overall R2 in this case since ...
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1answer
92 views

Equivalent to Welch's t-test in GLS framework

How can Welch's t-test be expressed as a generalized least squares model? A standard independent samples t-test (where it is assumed that the samples being compared are drawn from populations with ...
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1answer
60 views

Vector Autoregression

I have a general question on VAR-methodology. In the case of asymmetric modelling I employ FGLS to exploit off diagonal covariance between residuals due to non-unique regressors between equations. Ok, ...
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2answers
205 views

Forecasting with a VAR estimated by GLS versus OLS

Suppose I have a VAR model with different regressors in different equations (this could be due to restricting some coefficients of a full VAR($p$) model to zero or having some different exogenous ...
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1answer
203 views

Estimating VAR by GLS versus OLS: efficiency

Suppose I have a VAR model with different regressors in different equations (this could be due to restricting some coefficients of a full VAR($p$) model to zero or having some different exogenous ...
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1answer
89 views

Possibility of solution in overdetermined system of moment conditions

Hayashi, in page 207-208 of his book Econometrics, ex.3 (see hint), discusses the possibility that when referring to the moment conditions that will determine the estimator formula, having an ...
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300 views

Best method to create growth charts

I have to create charts (similar to growth charts) for children of ages 5 to 15 years (only 5,6,7 etc; there are no fractional values like 2.6 years) for a health variable which is non-negative, ...
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83 views

LS vs MLE for Gaussian Conditional Random Field estimation

Is there such a thing as Least Squares estimation for the conditional mean and covariance of a conditional gaussian random field? I'm looking at this paper by Wytock and Kolter 2013, in which they ...
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1answer
195 views

GLS versus FGLS

Can anyone simplify how GLS estimation is different from FGLS estimation? I understand that the covariance matrix is estimated in FGLS using OLS. What are some other differences?
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1answer
167 views

Determine weights in weighted least squares regression

Assume we have a cross-section of $N$ stocks. $Y_i$ is an sample variance estimate of stock returns for stock $i$. This sample variance is estimated using $T_i$ number of observations. All $T_i$ are ...
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221 views

Groupwise heteroskedasticity

I know how to derive the GLS estimator of beta (theoretical GLS), but there a slight change to the question and i am not quite sure how to go about it. A researcher has reason to believe that the ...
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1answer
97 views

Prove that System FGLS is Consistent

In the Systems of Equations framework, such as Seemingly Unrelated Regression (SUR), suppose we have $g=1,\ldots,G$ equations. Let $\mathbf{X}_i$ be a $G \times K$ matrix, $\mathbf{y}_i$ be $G \times ...
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39 views

strange coeficient estimates in GLS with ranked variables

Somebody could explain me why the estimated coefficients of a multiple regression through GLS seem not to pass through the majority of observations? Here is a example: ...
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118 views

GLS, heteroskedasticity and Ridge Regression/Lasso

I am hoping to use a regularised regression technique, using cross validation, to fit a linear model to a set of predictors which have some highly correlated variables. However, I also know (highly ...
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2k views

Generalized Least Squares vs Ordinary Least Squares under a special case

This question regards the problem of Generalized Least Squares. Vectors and matrices will be denoted in bold. Premises. Let $N,K$ be given integers, with $K \gg N > 1$. The transpose of matrix ...
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221 views

In CFA, when is ML estimation preferable and when is GLS preferable?

To a lesser extent I am also interested in when one should use Unweighted Least Squares, and other less common methods. I have been taught ML as a default but have just done a CFA and model fit was ...
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81 views

Is there any difference between normal distribution theory and least square theory?

Different approaches are available for determining the effect of an IV(Independent variable) on another variable. How the two assumptions cited in the question affect the estimates.
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40 views

How to convert 3 factor variables to fewer variables for gls() in R

I've got a dataset with 3 factor variables with only one interaction. Y is the response and A,...
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136 views

Goodness-of-fit value from orthogonal distance regression

I have two sets of data, $x$ and $y$, with poissonian distributions. I want to check if the relation between $x$ and $y$ is a proportionality $y = ax + b$, so I used some algorithms to do Bivariate ...
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1answer
553 views

In general, would you always prefer feasible GLS to OLS?

I know that GLS estimators only have exact distributions asymptotically, so the efficiency gains in finite samples are not all that clear. But otherwise, I'm struggling on how to attack this ...
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113 views

Non-significant variables in the best model

I am trying to to run model selection on a large dataset (>500 samples and > 50 vars). I ran GLS (using a self written script for selecting models based on AICc), but the problem is that the best GLS ...
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1answer
117 views

Variance structure with multiple covariates in GLS

I am building a GLS model following protocol in "Zuur, 2009. Mixed effects models..." on p.90. I have 5 continuous predictors. VarConstPower variance structure works best for me. At first the fixed ...
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1answer
99 views

Is there a “generalized least norm” equivalent to generalized least squares?

In a standard regression problem \begin{equation} \mathbf{y} = \mathbf{X} \beta + \mathbf{e} \ , \end{equation} the solution to $\beta$ when the system is overdetermined is $\hat{\beta}= ...
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850 views

Effects Coding in R

I am in interested in how do effect coding in R. I know that someone else has asked this question (i.e How to do regression with effect coding instead of dummy coding in R?). Here is the lm() model on ...
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1answer
554 views

Comparing multiple gls' objects using anova.gls

I got a warning message when I was trying to do anova for two nlme::gls objects. Here is an example: ...
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1answer
360 views

Variance estimation in Random Effects model

I'm studying panel data models in my introductory econometrics class, especially random effects models. Consider the model: $$y_{it}=x_{it}'\beta +c_i+u_{it}$$ with the assumptions ...
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306 views

Omitted dummy variable in panel gls?

In Stata, I have panel data for the years 2008-2012, across 7 firms. I assign a value corresponding to id for all firms. (id ...
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214 views

GLS regression versus linear mixed models in R

I am looking for papers in the management area that discuss more on the use of linear mixed models in R. Yet all I am getting the results where most, if not all, use GLS regression technique. Would ...