# 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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### What does it mean that BLUP is unbiased, given a linear two-level model?

Suppose we have the following mixed effects model for observation $Y_{ij}$ of pupil $i$ in school $j$: $Y_{ij}=b_0 + u_j + e_{ij}$ Here, $b_0$ is a fixed parameter for the "grand mean", $u_j$...
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### How to compare plant response to stress?

I am looking for advice on analysis of a greenhouse experiment. I had 3 levels of stress (drought) treatments, and seeds were from 4 enviromental "Sources". I grew 5 plants per "Line&...
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### Relationship between BLUP and variance parameter

When performing a mixed-effects analysis, one gets the mean (beta coefficients) of the fixed effects and the variance parameter for each of the random effects included in the model. Additionally, ...
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### Simplistic linear estimator for a probability vector

I am working on a problem where the unknown probabilities $p_i$ are related to observed rates/frequencies $\pi_\alpha$ as $$\pi_\alpha = \sum_iW_{\alpha i}p_i,$$ where $W_{\alpha i}$ is known (...
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### Why not us conditional modes (BLUPs) for further analyses?

De Waters et al. (2017 ;2019) used conditional modes (BLUPs) from a generalized linear mixed model to further examine individual differences. In their experiment, they performed a temporal delay task (...
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1 vote
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### Making inferences on BLUPs/conditional means from multilevel model

We're currently running a conjoint experiment in 26 countries with 2000 participants per country and would like to use a multilevel model. We've done up most of the pre analysis plan and run some ...
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### Mixed model via ridge regression

A mixed model can be recast as a ridge regression for a specific regularization parameter $\lambda$ that penalizes only the random effects -- aka dummy variables for the grouping levels. Fitting a ...
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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 ...
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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{aligned} \text{var}(\tilde{u} - u) & = \sigma^2G - \text{var}(\tilde{u}) \...
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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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### 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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### 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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