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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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Results of a For loop stored in a list and putting NA when no result [on hold]

I've created a For loop to apply different models on a lot of variables : ...
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why would do (F)GLS and multilevel modeling simultaneously?

To my knowledge, we could develop a multilevel model if we have a data that has a clustered structure in order to adjust for the auto correlation happening within each cluster. Then, we also learn ...
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Missing data and unbalanced data set in 2-factors design

I'm new to statistics and I'm trying to understand what to do with my data! I have two factors : tree genotype (10 levels) and soil type (3 levels). For one genotype I have only 2 replicates in soil1 ...
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Can I take a random sample of my very large data set to overcome non-independence?

I am trying to run a regression model on a very large time series data set (comparing flow noise to vehicle speed, pitch and dive state). Because my samples are taken about every minute (with some ...
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Multivariate Generalized Least Squares

I'd like to use the generalized least squares (GLS) in the multivariate version. I have a response variable $\boldsymbol{Y}$ with dimension $n \times m$, where $n$ indicates the number of observations ...
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Significant lags at ACF and PACF plots in GLM: what should I do?

A glm.nb model I built shows significant lags at lag 1 in both ACF and PACF plots. Please see the images below. There is no way to define random effects (or ...
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Examples of how to report results of a GLS

I am looking for some good examples in the primary literature where a GLS was used. I am pretty new to mixed modelling, and while I got it working, I am struggling at the write up stage. Google ...
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Is there a way to address overdispersion in a gls model

I have autocorrelated data that show a positive linear increase. When I model them using gls, I think the summary shows overdispersion. When using GLMM etc I'd change error structure, but I don't ...
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Interrupted time series analysis of data with deterministic trend and seasonality

I am trying to evaluate the impact of an intervention on a selected outcome variable using interrupted time series data. I have aggregated a five-year data into monthly values to create a data-set 0f ...
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Is there any benefit of using GLS when the regressors are identical

I am reading Greene, Econometric Analysis, 7th Addition, I am seeking a point of clarrification. "The case of identical regressors is quite common [think a VAR mode].... In this special case, ...
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1answer
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Estimating a VAR using OLS vs GLS

I have read in several places that I can estimate a VAR model equation by equation using OLS instead of using GLS, if I have the same explanatory variables. Do I need to make any assumptions about ...
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Regression with GLS estimation, RMSE and IC on beta

as I said I need to know the formulas to calculate RMSE and confidence interval on beta in MATLAB, starting from the following estimated model. The model is AR type. Here the MATLAB code: <...
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Proving efficiency of OLS over GLS

I'm trying to prove the efficiency of OLS over GLS when the covariance matrix of the error $\varepsilon$ is mistakenly assumed to be $\sigma^2\Sigma$ instead of $\sigma^2 I$. After deriving the ...
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How to fit a gls model with a known slope

i want to fit a gls model (from nlme package) with a specified slope, so i can get the computed intercept for the best fit. I tried to set the slope with an offset. Althogh it works fine with lm, it ...
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How much of a problem is inference after model selection when few models are manually compared?

tl;dr: I found a better model than the one I first thought of while inspecting the data and performed a few steps of variable selection/model fine-tuning. I assume that this is a (mild) case of ...
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108 views

Using pairwise comparison on gls object with heterogeneity of variances?

I'm comparing total yield from fields under 5 different treatments. As you can see, the variance differed between the treatments (diagnostics from lm() fit): So I ...
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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
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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
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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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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
373 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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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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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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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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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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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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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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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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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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412 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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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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1answer
59 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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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
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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
209 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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266 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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186 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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1answer
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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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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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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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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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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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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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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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258 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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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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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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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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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 ...