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### What is the difference between Restricted Maximum Likelihood (REML) and Maximum Likelihood (ML)? [duplicate]

I am a first year graduate student in biostatistics, and I have somewhat of an idea of the difference between REML and ML. However, I want a more in-depth understanding of each estimation method, ...
68k views

### “Model failed to converge” warning in lmer()

With the following dataset, I wanted to see if the response (effect) changes with regard to sites, season, duration, and their interactions. Some online forums on statistics suggested me to go on with ...
3k views

### Why I should use Bayesian inference with uninformative prior? [duplicate]

I am a Ph.D. student and currently I am studying Bayesian inference concerning vector autoregressive models. A lot of researchers when talking about uninformative prior, conclude that the results of ...
4k views

### Why does one have to use REML (instead of ML) for choosing among nested var-covar models?

Various descriptions on model selection on random effects of Linear Mixed Models instruct to use REML. I know difference between REML and ML at some level, but I don't understand why REML should be ...
9k views

### R mixed models: lme, lmer or both? which one is relevant for my data and why?

I have a data obtained through forest inventory conducted yearly (1994-2015) in a West African country. 10 plots of equal sizes (1 ha each) were selected from unmanaged natural forest and then ...
2k views

### Bias in the MLE of variance component in a multivariate Gaussian?

Given an $n$-vector $y$ (responses) and a design matrix $X$, I wish to fit them with a simple linear regression model $$y=X\beta+e,$$ where $e\sim\mathcal{N}(0, \sigma^2I)$. Then, we have y\sim\...
2k views

### finding best fit model using AIC in Panel Data using R

I am currently trying to find a best model using R for Panel Data. I have a project on Corporate Governance in which I collected data of various companies from 2009-2014. I found the best fit using ...
502 views

### How are calculations done for REML?

I've read a few questions on this site (e.g., https://stats.stackexchange.com/a/48676/46427), but they rarely go beyond intuitive explanations. I am particularly interested with how to calculate an ...
723 views

### Is there a way to run a multivariate mixed effects model (e.g. RDA) with an unbalanced number of observations per level of the random factor?

I have a community matrix (fish gut microbiome) from a laboratory experiment consisting of 2 treatments, each with 3 independent aquaria, which were sampled 3 times. At each sampling event 6 fish were ...
435 views

### Restricted Maximum Likelihood

Why don't we use restricted maximum likelihood to estimate parameters in non-mixed models?
594 views

### Maximum likelihood estimate for a univariate gaussian

Say we have a univariate Gaussian distribution $p(x)=\mathcal N(x|\mu, \sigma^{2})$. Then suppose we have a data set of observations $X = \{x_1, x_2, \cdots ,x_N\}^{T}$ that are drawn independently ...
384 views

### Why does the log-likelihood change when a variable is linearly transformed in a hierarchical model?

I ran into (what I think is) an inconsistency when running a random-intercept model (using the lmer function in the lme4 package in R). Here is what I do: I first run a model with a set of covariates;...
282 views

### Mixed model repeated measures with missing covariate data

Quick question on GLMM with repeated measures (crossover) design and how to deal with missing covariate data. In this context, 28 participants complete 2 conditions (crossover design with 1 week ...