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.

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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 (...
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1answer
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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 ...
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2answers
681 views

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/...
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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 $$ \...
5
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1answer
219 views

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 ...
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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 ...
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1answer
270 views

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 ...
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Can any one give me inf how I can form X, Z, R, G, and A matrices using dummy variables using the posted info below?

$Y=Xb +Zu + e$, where y represents a vector of observed (measured) phenotype values, $b$ is vector of unknown parameters for “fixed" effects, while $X$ is corresponding design matrix, $u$ is vector ...
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1answer
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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 ...
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2answers
1k views

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 ...