Generalized least squares (GLS) is an estimation method when errors are heteroscedastic or correlated in linear regression models.

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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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Multiple comparison in the unequal variance case

I have found procedures such as Tamhanes T2, Dunnets T3 and the Games & Howell procedure that deal with unequal variances in the one-way model. However, I have a Randomized complete block design, ...
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Regression Puzzle GLS var/covar matrix of B given summary statistics

There is a problem posted back in 2009 that I found that has me puzzled. I believe the estimates are from a generalized linear regression because after some thought it seems $X'X$ is impossible to ...
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Phylogenetic GLS with categorical response variable

I want to perform phylogenetic comparative analysis on a multilevel (3 level) categorical response variable, preferentially in R. Does anyone know how to do that or if there is a way to do at least? ...
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48 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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46 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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49 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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87 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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67 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 ...
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gls R correlation setting form to default

Just looking for some instruction please. I wish to set an autoregressive correlation within a gls model. I am having trouble understanding this part of the syntax ...
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54 views

Interpretating negative GLS coefficients (seasonality removed)

I fit a multiple GLS model with time series as a response and explanatory variables. I previously removed the seasonality and trends by using ...
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Using GLS and weights to solve heterogeneity of variances?

I’m fairly new to scientific significance testing and getting into the topic more and more. I have a multifactorial dataset with Respiration rate as response variable and Temperature and CO2 partial ...
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62 views

pseudo Anova Table for a GLS regression

I fit a couple of GLS models, using the nlme pakage (gls() function), and I would like to obtain the pseudo ANOVA table as ...
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Detrending & cross-correlation function

I am looking for some help with my time-series data. What is the best method of detrending/transformation of these two variables, so I do not violate assumptions of stationarity when applying a cross ...
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142 views

Fit Linear Model Using Generalized Least Squares with Unknown Covariance Matrix

I want to fit a linear model of y on x with respect to a grouping factor and with respect to a covariance structure of dependent variable within groups. I have a dataset similar to the following. ...
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383 views

Why do I get same results for OLS and GLS in R?

When I run this code: ...
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616 views

Comparing GLS models with different fixed variables using AIC: REML or ML?

I am using gls in nlme. My response variable is spatial so I am using gls with correlation structure. I am determining which structure to use based on Zuur 2009, comparing AIC scores of models with ...
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706 views

How to calculate the regression variance for a GLS model?

I need to calculate the regression variance ($\sigma^2$) in order to estimate both the confidence intervals and the prediction intervals in a gls regression analysis. For the analysis, the covariance ...
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138 views

Variance associated with factors in GLS (nlme)

First time posting here, so thank you ahead of time for your help. I'd like to estimate the variances associated with two factors in a relatively simple, but unbalanced GLS model, and I am unsure how ...
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202 views

Generalized least squares with insignificant predictor variable

Suppose I have fitted an standard linear regression mode $Y=\beta_0+\beta_1X_1+\beta_2X_2+\beta_3X_3+\epsilon$. Based on the ACF plot or PACF plot of the residuals for this regreesion model, I found ...
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How to specify in r spatial covariance structure similar to SAS sp(pow) in a marginal model?

I'm currently translating existing code from SAS to R. I'm working on longitudinal data (CD4 count over time). I have the following SAS code : ...
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470 views

Robust standard error in generalized least squares regression

Suppose we have a correlated outcome $\mathbf{y}$ and a bunch of predictors $\mathbf{X}$. For some reason, we know the variance/covariance matrix of the error term $(\epsilon)$, say $\mathbf{V}$. In ...
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247 views

Performing a GLS cross-sectional regression using R

Is there a function in R that could perform GLS cross-sectional regression for multiple cases all at once? For example, when regressing stock returns over beta for 100 stocks over a 10-year time ...
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579 views

How to interpret these custom contrasts?

I am doing a one way ANOVA (per species) with custom contrasts. ...
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Evaluation of a GLS fit

My first post in this useful community. Ive been trying to use GLS methods in non-linear mixed effects models and have found this post, Prediction with GLS extremely informative and helpful. Some of ...
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proof FGLS asymptotically efficient

Prove that FGLS is asymptotically efficient. Does one have to use Cramer Rao to do this?
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Can I use generalised least squares with a binomial distribution and a nested structure?

I'm trying to fit linear models to my data in R. I need to use a generalised least squares method as I have heterogeneity of variance in one of my variables. I was planning to use varIdent, as the ...
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Inference in linear model with conditional heteroskedasticity

Suppose I observe independent variable vectors $\vec{x}$ and $\vec{z}$ and dependent variable $y$. I would like to fit a model of the form: $$y = \vec{x}^{\top}\vec{\beta_1} + \sigma ...
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Prediction with GLS

Let's say I build a Generalized Least Squares model. I follow the standard procedure and first estimate a LM model. Then I create an error-response covariance matrix based on the residuals of this ...
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528 views

How to get equivalent ANOVA in R for a model with and without a random effect?

My question is: Is there a way to either force Anova() to somehow analyze gls objects (which internally are almost identical ...
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2k views

Fitting a generalized least squares model with correlated data; use ML or REML?

Reading the Linear Mixed Model (LMM) literature I am aware that fitting a model using REML provides better estimates of variance parameters than fitting via ML. However, we should not compare nested ...
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Is there a GLS estimator that has lower variance than OLS for sum of parameters in linear model under Gauss-Markov conditions?

I have a model $$Y=\beta_0 + \beta_1 x_1 + \beta_2x_2 +\epsilon$$ I would like the minimum variance unbiased estimate of $\gamma=\beta_1 + \beta_2$. Assuming the Gauss Markov conditions hold, but ...
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344 views

Estimation of time series regression using GLS

I am trying to estimate time series model using gls method. The data is monthly from sep 1997 to april 2011 First I estimate the model and know that the erorr are IMA(1,1). For that I use the code ...
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379 views

Difference between GLS and SUR

I've been reading some about Generalized Least Squares (GLS) and trying to tie it back to my basic econometric background. I recall in grad school using Seemingly Unrelated Regression (SUR) which ...