Meaning of “trait” in MCMCglmm

问题:

Like in this post I'm struggling with the notation of MCMCglmm, especially what is meant by trait. My code ist the following

library("MCMCglmm")

set.seed(123)
y <- sample(letters[1:3], size = 100, replace = TRUE)
x <- rnorm(100)
id <- rep(1:10, each = 10)
dat <- data.frame(y, x, id)

mod <- MCMCglmm(fixed = y ~ x, random = ~us(x):id,
            data = dat,
            family = "categorical")

Which gives me the error message For error structures involving catgeorical data with more than 2 categories pleasue use trait:units or variance.function(trait):units. (!sic). If I would generate dichotomous data by letters[1:2], everything would work fine. So what is meant by this error message in general and "trait" in particular?

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Edit 2016-09-29: From the linked question I copied rcov = ~ us(trait):units into my call of MCMCglmm. And from https://stat.ethz.ch/pipermail/r-sig-mixed-models/2010q3/004006.html I took (and slightly modified it) the prior list(R = list(V = diag(2), fix = 1), G = list(G1 = list(V = diag(2), nu = 1, alpha.mu = c(0, 0), alpha.V = diag(2) * 100))). Now my model actually gives results:

MCMCglmm(fixed = y ~ 1 + x, random = ~us(1 + x):id, 
         rcov = ~ us(trait):units, prior = prior, data = dat,
         family = "categorical")

But still I've got a lack of understanding what is meant by trait (and what by units and the notation of the prior, and what is us() compared to idh() and ...).

Edit 2016-11-17: I think trait is synoym to "target variable" or "response" in general or y in this case. In the formula for random there is nothing on the left side of ~ "because the response is known from the fixed effect specification." So the rational behind specifiying that rcov needs trait:units could be that it is alread defined by the fixed formula, what trait is (y in this case).

回答1:

units is the response variable value, and trait is the response variable name, which corresponds to the categories. By specifying rcov = ~us(trait):units, you are allowing the residual variance to be heterogeneous across "traits" (response categories) so that all elements of the residual variance-covariance matrix will be estimated.

In Section 5.1 of Hadfield's MCMCglmm Course Notes (vignette("CourseNotes", "MCMCglmm")) you can read an explanation for the reserved variables trait and units.