Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [blup]

Best linear unbiased prediction (BLUP) aka "conditional mode" is the most likely value of a random effect in a linear mixed model.

BLUP stands for Best Linear Unbiased Prediction. In mixed effects modeling, the random effects are not estimated. Instead, the mean and variance (and possibly covariances) of the random effects are estimated from the data. However, an analyst may reasonably wonder what the effect would be for a given study unit. These can be predicted using the model and the data.

BLUP may be contrasted with .

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Why do the estimated values from a Best Linear Unbiased Predictor (BLUP) differ from a Best Linear Unbiased Estimator (BLUE)?

I understand that the difference between them is related to whether the grouping variable in the model is estimated as a fixed or random effect, but it's not clear to me why they are not the same (if they are not the same). I am specifically…
Jeremy Miles
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Intuition about parameter estimation in mixed models (variance parameters vs. conditional modes)

I have read many times that random effects (BLUPs/conditional modes for, say, subjects) are not parameters of a linear mixed effects model but instead can be derived from the estimated variance/covariance parameters. E.g. Reinhold Kliegl et al.…
statmerkur
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Why is the estimated variance of a random effect not equal to the variance of its BLUP estimates?

I am learning mixed effect model from here. I built a simplified model and trying to extract the $\gamma$ vector from linear mixed effect model $$y=X\beta+Z\gamma+\epsilon$$ then calculate variance of $\gamma$. (It is a toy model and we only have…
Haitao Du
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Parameter estimation in the linear mixed effects model

In Parameter estimation and inference in the linear mixed effects model, page 1923, the variance \begin{equation} \begin{aligned} \text{var}(\tilde{u} - u) & = \sigma^2G - \text{var}(\tilde{u}) \\ & = \text{var}(u) - \text{var}(\tilde{u}),…
JLee
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Repeated Measures Linear mixed model notation

Not sure the right place to ask this question but struggling with specifying the correct notation and wording for my linear mixed model. Problem set up: I have a set number of biological replicates (any number doesn't matter), each biological…
Adam
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Interpreting BLUPs or VarCorr estimates in mixed models?

I am referring to the question. When estimating random effect (RE) variance or correlation, the estimations are different in VarCorr(mod) function and when calculating the variance or correlation among REs with cor(ranef(mod)). The question above…
User33268
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BLUP formula for random coefficient models, in form that allows for convenient derivatives WRT loss function

In Semiparametric Regression, Ruppert et al assert that the BLUP for $U_i$ in the model $$ \begin{equation} y_{it} = \beta_0 + U_i + \beta_1x_{it} + \epsilon_{it} \end{equation} $$ reduces to $$ \tilde{U}_i =…
generic_user
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Mixed model by gradient descent?

I can't be the first person to think about estimating variance components of mixed models by gradient descent, and then computing BLUP's at each update. Googling, I find little on the topic. But the gradients seem tractable (if messy). I suppose…
generic_user
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Calculated breeding values using markers using animal model in R

Animal model (frequently used in animal science and sometime in human or plants) is mixed model with: $y$ = $X$$b$ + $Z$$u$ + $e$ y is observed values for any quantitative variable, $Xb$ is fixed effects terms while $Zu$ is random effects, and $e$…
John
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Negative BLUP in Linear Poisson Mixed Model

For school, I'm tasked with investigating the effect of beta carotene on the prevention of skin cancer. For this, I have data on several patients that are examined over the course of 5 years in medical centers. In essence, each year the patient goes…
Gilles
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Should GBlup method and Bayesian Ridge Regression give the same results?

I am working on genomic selection and I am comparing the performance of two models, one of them is a likelihood method (GBlup) and the other is a Bayesian meyhod (Bayesian Ridge Regression). I am looking at the variance component and they are not…
marb_021
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