"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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when variances are unequal between groups. (Welch ANOVA in r)

I want to know why the results are different between oneway.test() and gls() I assume the variance are different across ...
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21 views

Model selection in PGLS?

I am using Phylogenetic General Least Squares in the R package 'caper'. I have 4 predictor variables and I would like to know which are correlated with my response variable, while taking the ...
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28 views

Is AIC a valid criterion for the selection of variance structures in GLS?

In generalized least squares, I’ve specified a weights function that accounts for heterogeneity in residual variance that exist along the range of a covariate. The validation graphs (residuals ...
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2answers
127 views

Proving that the estimators of coefficients and variance in GLS model are independent

I have come across this question in a textbook: I have a linear model $Y=Xb+u$ with for instance autocorrelation, in order to introduce GLS $Y^*=X^*b+u^*$ (with $Z^* = \Omega^{-1/2}Z$). Then an ...
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Degrees of freedom of a multiple comparission using estimability and lsmeans

I have a doubt about the degrees of freedom of a multiple comparission test. My data have the following structure: One data for each day, for 14 days, in each year season (auttum, winter, spring and ...
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70 views

Example of OLS vs GLS with AR1 residuals for teaching in R

I'm looking for an example to show my class. We are covering OLS vs GLS with autocorrelated errors -- I've got the class to the point where they understand (some of them) why the the standard errors ...
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1answer
22 views

Estimating the residual variance by using a varFunc in nlme

I'm using a linear model to predict a dependent variable (the score to a test) starting by the age of a person. As shown in the figure below, the variability decreases when the age increases (data are ...
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41 views

Fitting heteroscedastic models using gls function

Consider the following heteroscedastic model: $$y_i = f(x_i, \beta) + g(x_i, \theta)\varepsilon_i, i = 1, \ldots, n, \tag{1}$$ where $f(\cdot, \beta)$ is the regression function and $g(\cdot, \theta)$ ...
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66 views

What to do if time series data remains autocorrelated?

Data: I have 92 years of monthly climate data. One of my variables is a drought index (SPEI) ranging from -2 (dry) to 2 (wet). All the data can be found here. Data Structure: ...
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38 views

Econometric. OLS vs GLS

I would like to know exactly what is the difference between OLS and GLS and how GMM enter in it. Thanks.
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1answer
62 views

Equivalence of the OLS and GLS estimates

I am looking at a handful of problems where I am trying to fit a linear model using generalized least squares (GLS) where the covariance matrix of the error term is relatively "nice". I was wondering ...
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153 views

Why I got different variance-covariance matrices for different subjects from getVarCov function from R nlme package?

I fit a linear model using generalized least squares with gls {nlme} function in R. Then I use a ...
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12 views

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
229 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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66 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
166 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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44 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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23 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
102 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
127 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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69 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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20 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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62 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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255 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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874 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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24 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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2k 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
40 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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194 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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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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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
170 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
62 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
261 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
268 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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94 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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341 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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93 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
262 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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228 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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276 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
128 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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41 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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159 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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1answer
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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306 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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86 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.