"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]
Questions tagged [generalized-least-squares]
257 questions
26
votes
1 answer
Bootstrapping Generalized Least Squares
Scenario:
Consider the use of bootstrapping to estimate the distribution of model parameters fitted per a linear or nonlinear generalized least squares model. In particular, assume there is a covariance matrix $C$ of the errors, which may not even…
Mark L. Stone
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11
votes
1 answer
Generalised least squares: from regression coefficients to correlation coefficients?
For least squares with one predictor:
$y = \beta x + \epsilon$
If $x$ and $y$ are standardised prior to fitting (i.e. $\sim N(0,1)$), then:
$\beta$ is the same as the Pearson correlation coefficient, $r$.
$\beta$ is the same in the reflected…
sqrt
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11
votes
1 answer
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 seems somewhat similar to GLS. One paper I stumbled…
JD Long
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10
votes
2 answers
How to interpret these custom contrasts?
I am doing a one way ANOVA (per species) with custom contrasts.
[,1] [,2] [,3] [,4]
0.5 -1 0 0 0
5 1 -1 0 0
12.5 0 1 -1 0
25 0 0 1 -1
50 0 0 0 1
where I compare intensity 0.5…
Roman Luštrik
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10
votes
2 answers
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, continuous and in the range of 50-150 (with only a few…
rnso
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9
votes
3 answers
How to do regression with known correlations among the errors?
I was wondering if there is anything you can do when you have a regression problem:
$$\begin{cases}
Y_t = \beta_1x_t + \beta_0 + \varepsilon_t \\
\left(\varepsilon_1,\ldots,\varepsilon_n\right)\sim\mathcal{N}_n\left(\mathbf{0},D \right) \\
…
Manuel
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9
votes
1 answer
Inference in linear model with conditional heteroskedasticity
Suppose I observe independent variable vectors $\vec{x}$ and $\vec{z}$ and dependent variable $y$. I would like to fit a model of the form:
$$y = \vec{x}^{\top}\vec{\beta_1} + \sigma g\left(\vec{z}^{\top} \vec{\beta_2}\right) \epsilon,$$
where $g$…
shabbychef
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8
votes
1 answer
In general, would you always prefer feasible GLS to OLS?
I know that GLS estimators only have exact distributions asymptotically, so the efficiency gains in finite samples are not all that clear. But otherwise, I'm struggling on how to attack this discussion.
Brian
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8
votes
2 answers
Why do I get same results for OLS and GLS in R?
When I run this code:
require(nlme)
a <- matrix(c(1,3,5,7,4,5,6,4,7,8,9))
b <- matrix(c(3,5,6,2,4,6,7,8,7,8,9))
res <- lm(a ~ b)
print(summary(res))
res_gls <- gls(a ~ b)
print(summary(res_gls))
I get the same coefficients and the same…
Akavall
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8
votes
1 answer
LARS - LASSO with weights
I am interested in solving the following problem
$$ \min_{\boldsymbol{\beta}} \left( \mathbf{y}-\mathbf{X}\boldsymbol{\beta} \right)^T W \left( \mathbf{y}-\mathbf{X}\boldsymbol{\beta} \right) + \lambda \left|\boldsymbol{\beta}\right|_1…
Meenakshi
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8
votes
2 answers
Non-Correlated errors from Generalized Least Square model (GLS)
As a financial institution, we often run into analysis of time series data. A lot of times we end up doing regression using time series variables. As this happens, we often encounter residuals with time series structure that violates basic…
Anand
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8
votes
1 answer
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 model). I'm trying to determine if one estimation…
mss
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8
votes
2 answers
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 equal variance) can be expressed as follows:
$$Y_i =…
Richard Border
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7
votes
2 answers
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 this. Is this an okay thing to do? I know that for…
T.J. Gaffney
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7
votes
1 answer
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 models fitted with REML that have different fixed…
Gavin Simpson
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