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Questions tagged [generalized-least-squares]

"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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Model selection with different fixed effects and different corARMA structures

I analyzed the effect of temperature (4 different areas) on laying date: LDT ~ Aa3+Bb+Cc+Dd. Because of autocorrelation in residuals I used ...
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1answer
23 views

ANOVA selects a model with autocorrelated residuals

I want to know which temperature dataset (Aa1, Bb, Cc, Dd) is/are the best predictor for laying date (medini). First, I used simple linear regression: median...
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1answer
22 views

How to obtain the inverse of the variance covariance matrix of GLS (Random Effects Model)

In the standard GLS set up how do you find the inverse of the variance covariance matrix? $$y _ { i t } = \beta _ { 0 } + x _ { i t } ^ { \prime } \beta + \alpha _ { i } + u _ { i t } \hspace{35pt} u ...
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48 views

The feasible generalised least squares residuals

Consider the FGLS estimator. Let $\Psi'\Psi = \Omega^{-1}$ be the weighting matrix using the Cholesky decomposition. Suppose that $\Psi$ is known or already estimated. Consider the transformed ...
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1answer
56 views

Why does gls model without random effects yield a similar fit to mixed effects model?

I am trying to answer a question from Pinhiero and Bates Mixed Effects Models in S and S-Plus, explaining how random effects fail to confer any benefit over a gls model that has mixed effects. This ...
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2answers
285 views

Why use OLS when it is assumed there is heteroscedasticity?

So I'm slowly going through the Stock and Watson book and I'm a bit confused on how to deal with the issue of homoscedacity/heteroscedacity. Specifically, it is mentioned that economic theory tells ...
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11 views

What are level-2 covariance parameters within Iterative Generalised Least Squares Models to estimate multilevel models?

I am referring to Goldstein & Rasbash (1992): Efficient computational procedures for the estimation of parameters in multilevel models based on iterative generalised least squares. Computational ...
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46 views

Generalized Least Squares

A simple linear regression model satisfies all Gauss-Markov conditions except for white noise, is known I am wondering how to find the matrix Ω = Euu′ for this model. Any suggestions are welcome. ...
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1answer
35 views

Estimating the variance of the GLS estimator

Consider the linear regression model where $y = XB + u$. Assume that $\mathrm{E}[u \mid X] = 0$. Assume that $\mathrm{V}[u \mid X] = \sigma^2I$. This is the simple linear model. Now relax the ...
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32 views

Marginal model in R and SPSS

I have 2 datasets which i analyze both with R and SPSS (for professional reasons). Specifically, i use a marginal model with an AR(1) covariance structure. I have 2 covariates, namely the main effect ...
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1answer
46 views

Can the maximum-likelihood method be derived from something else?

I am an author of a paper, in which we show that the maximum-likelihood (ML) method can be derived a limiting case of an iterated weighted least-squares fit. https://arxiv.org/abs/1807.07911 We, the ...
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78 views

GEE and GLS. Are they similar?

First of all there is another question about it here, but it has no answers unfortunately...And also here, but it is more general about mixed models and GEE, while my question is more specific... So, ...
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47 views

Correlation between dependent predictor variable and dependent response variable in repeated measures experiment

I would like to determine if there is a significant relationship between a measured continuous variable (predictor variable) and a response variable, which are both measured over time and therefore ...
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0answers
23 views

What is the difference between random effect and multilevel (or mixed effect) models? [duplicate]

Multilevel models with with random intercept seem to perfectly correspond to a random effect model (in the econometric terminology). I suspect that the two concepts are essentially overlapping, ...
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224 views

Is it possible to fit mixed-models via gls?

Is it possible to fit multivariate Gaussian models implied by mixed-models through generalised least squares in R, by using, for instance, the gls function? For ...
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268 views

auto.arima vs corARMA: AR coefficient greater than 1

Using R and the nlme package, I tried to fit a gls model with a corARMA correlation ...
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0answers
88 views

FGLS estimation with possible endogenous regressors

I try to estimate the following panel model by FGLS for 32 states for 5 years: $$ y_{it} = a_i + x_{it}B + e_{it}. $$ There are 2 possible endogenous regressors in $x_{it}$ along with other ...
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1answer
40 views

Can I use chi-square to test goodness-of-fit in a generalized least-squares regression?

I am performing a generalized least squares regression based on a design matrix $X$, a response vector $Y$ and a (non-diagonal) covariance matrix $C$, assuming Gaussian errors. I'm not sure what ...
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92 views

Question concerning the weighted least squares

If the weighted least squares estimators are equal to the ordinary (unweighted) least squares estimators when when the errors have common variance $σ^2$ would it mean that the model given by the ...
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1answer
675 views

Least squares regression with variance-covariance matrix of observations

I'm trying to fit a model of the form $Y=aX+b$ based on a number of $(X,Y)$ observations with non-independent errors in $Y$. I know the variance-covariance matrix of the errors on $Y$. How can I ...
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1answer
115 views

How to calculate sandwich standard errors for generalized least squares models?

Dependent data can be modeled using covariance structures like compound symmetry, spherical, AR-1, and other. Using generalized least squares, inference can be made on the regression coefficients ...
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193 views

Prediction intervals for generalized least squares model with heteroscedastic errors

I wanted to model some data with heteroscedastic errors using a gls model of the form ...
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143 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 ...
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138 views

Is GLS a special case of GEE?

Is a Generalize Least Squares model a special case of a Generalized Estimating Equation. In other words, would a GEE with an identity link produce the same coefficients and standard errors as a GLS ...
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460 views

Time-Series GLM model with autocorrelated data

I am using GLM (quasipoission) model for analyzing daily hospital admission and air pollution data. It is a time-series study for 2 years data. I used 10 df/year for controlling seasonality. When I ...
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0answers
150 views

How to choose correlation structure in marginal models

I have a longitudinal dataset: we observed 12 subjects 3 times (with different lag for different subjects). Each time the subjects received a treatment and we concurrently measured the volume of 4 ...
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1answer
973 views

Generalized least squares results interpretation

I checked my linear regression model (WMAN = Species, WDNE = sea surface temp) and found auto-correlation so instead, I am trying generalized least squares with the following script; ...
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302 views

Calculation of standard errors in weighted least squares (WLS)?

I'm searching for the correct calculation for a confidence interval using weighted least squares regression. Let me introduce you to my problem. Guess we have thirteen ordinal classes 1 to 13. For ...
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0answers
51 views

Analyzing standardized / fractional count data

In my experiment I want to figure out how the size of different planting containers, i.e. their volume, affects the number of regenerated plant shoots from root fragments (terminology here is root ...
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0answers
322 views

OLS standard errors vs GLS standard errors

I currently have a dataset with y and x that seems to experience heteroskedasticity. Are the results consistent/within expectations? (The standard error for x from my GLS is even higher than that of ...
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2answers
112 views

Where does this instrumental variables transformation come from?

I am reading on instrumental variables estimation in linear regression, and specifically, two stage least squares estimation. Assume we have a model $$y=X\beta+\epsilon$$ Where $X$ is correlated ...
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0answers
106 views

Why do we have to estimate the autocorrelation coefficient when using GLS?

Suppose we have a linear regression model with autocorrelated error terms and we know it is AR(1) by for example investigating both the ACF and the PACF plot (I know there are probably more ...
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0answers
108 views

Why gls() is giving the same estimates for the same dataset independently of the input arguments?

I'm currently struggling with linear autocorrelated models. I have correctly simulated some datasets to understand how homoscedasticity and heteroscedasticity work and now I'm focused on correlated ...
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What is a good way to begin a search for parameter estimates in a GLM?

Following up on my answer here, I am wondering What is the reasoning for initialize expression of the family objects in ...
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196 views

Does GLS require an assumed distribution?

I am wondering if it makes sense to talk about Generalized Least Squares (GLS) without assuming a distribution on the residuals, or if it comes with implicit assumptions of normality on the residuals ...
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428 views

Iterative reweighted least squares versus MLE for heteroscedastic errors

Iterative reweighted least squares (IRLS) is used when errors are heteroscedastic. Let us assume that error comes from a distribution where its mean is zero and the variance is a function of the ...
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30 views

Solving weights in least squares to reduce distance to another vector

I'm using a procedure of WLS to find some values in a reduced space that actually generate a vector that is close to my target vector. That is, I have WLS: $\beta=(X^T W X)^{-1} X^T W Y$, and I am ...
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1answer
169 views

R- Using PGLS with discrete and continuous data

The model output coefficients list only two out of the three discrete values. What am I doing wrong? I'm relatively new to R so I hope this is not a stupid question. ...
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196 views

ANCOVA with nlme::gls: Are the slopes different from eachother and from 0?

I am trying to do an ANCOVA in R. I am using the gls function of the nlme package, because the spread of the residuals ...
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2answers
318 views

How to compare GLS models?

I have spatial data set for 35 studies. In each study, there are variables y, x1, x2, latitude, and longitude. I want to know whether adding x2 to model y~x1 will improve the simple regression model y~...
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1answer
342 views

Difference between HCCME and WLS estimator

I have a question concerning heteroscedasticity. Is there any difference between correcting for heteroscedasticity with the heteroscedastic consistent covariance matrix estimator (e.g. $HC_0$ of White ...
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91 views

Generalized Least Squares Algorithm

I hope to replicate the R package result in gls and my code looks like this ...
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0answers
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How to interpret the precision matrix in Generalised Least Square regression

Suppose we have to estimate the parameters of the regression Y(s) = b X(s) + w(s) + e with s a set of spatial coordinates, e uncorrelated error terms and w(s) = N(0,C) where C is the covariance ...
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72 views

Derivation of GLS coefficients in simple regression

Let $y_t = a + bX_t + u_t $, where $t = 1...n, X$ is not random and $x_t \neq x_s$ for $s \neq t$). $E(u_t) = 0, E(u_tu_s) = 0 $ and $ E(u_t^2) = w_t^2$ with $w_t>0$. How do we derive GLS ...
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1answer
316 views

Nonlinear least squares vs linear least squares

I would like to fit a model to data that has the form, $$f(x)=e^{a+bx+cx^2...}$$ The data is Gaussian distributed, and I was going to use a nonlinear least squares method (probably something in ...
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251 views

GLS (generalized least squares) on times series with R correlation problem

I have a lot of variables like Money supply, GDP and CPI. I have used a multiple linear model but the data are too correlated, so I tested with the glm. But I do ...
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2answers
629 views

Suitability of given AR1 model (using gls() in R) for nested time-series data?

I have nested time series data where the outcome (number of visits per month) is available for 24 months (repeated measures) across two time periods (pre- and post-intervention), for three health ...
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0answers
248 views

SEM: Why is GLS is scale invariant but ULS isn't?

Kline (2015) writes: Two methods for continuous endogenous variables with multivariate normal distributions include generalized least squares (GLS) and unweighted least squares (ULS). The ULS ...
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1answer
34 views

Transformation of model

I have the following model $y_i=\beta_1+\beta_2x_i+\epsilon_i$ with $E(\epsilon^2)=\sigma^2\exp(x_i)$ And I have to use the proper transformation to obtain a model where the variance of the error ...
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1answer
50 views

Parameter estimation in a heteroscedastic model

Consider the following model: $$Y = \mu + (1+\beta X)\epsilon,$$ where $Y$ is the dependent variable; $X$ is the independent variable; $\epsilon$ is such that $\mathbb{E}(\epsilon) = 0$ and $\mathbb{V}...