The extract_rcov()
function is a practical tool for extracting the residual
variance-covariance matrix from a repeated measurement ASReml model.
This function is particularly useful when dealing with various
covariance structures, including but not limited to the uniform
correlation (corv), power or exponential (expv), antedependence (ante)
and unstructured (US).
Currently, the structures available are:
corv); homogeneous variance
form.corh); heterogeneous variance
form.corgh); heterogeneous
variance form.expv); homogeneous
variance form.exph); heterogeneous
variance form.ar1v); homogeneous
variance form.ar1h); heterogeneous
variance form.ante).us).Watch the
tutorial: A good guide on fitting repeated measurement models in
ASReml by VSNi. However, it might leave you wondering how to actually
extract the fitted residual variance-covariance matrix. That’s where
extract_rcov() comes into play.
This vignette utilizes the same dataset featured in the video and
incorporates a segment of the code to showcase the functionality of
extract_rcov(). Additionally, we provide insightful figures
that aid in exploring the results.
To run this vignette, ensure you have an ASReml license.
library(ggpubr)
library(agriutilities)
library(tidyr)
library(dplyr)
library(tibble)
library(asreml)
head(grassUV) |> print()
grassUV |>
ggplot(
aes(x = Time, y = y, group = Plant, color = Plant)
) +
geom_point() +
geom_line() +
facet_wrap(~Tmt) +
theme_minimal(base_size = 15)tmp <- grassUV |>
group_by(Time, Plant) |>
summarise(mean = mean(y, na.rm = TRUE)) |>
spread(Time, mean) |>
column_to_rownames("Plant")
a <- covcor_heat(matrix = cor(tmp), legend = "none", size = 4.5) +
ggtitle(label = "Pearson Correlation")
b <- tmp |>
cor(use = "pairwise.complete.obs") |>
as.data.frame() |>
rownames_to_column(var = "Time") |>
gather("Time2", "corr", -1) |>
type.convert(as.is = FALSE) |>
mutate(corr = ifelse(Time < Time2, NA, corr)) |>
mutate(Time2 = as.factor(Time2)) |>
ggplot(
aes(x = Time, y = corr, group = Time2, color = Time2)
) +
geom_point() +
geom_line() +
theme_minimal(base_size = 15) +
color_palette(palette = "jco") +
labs(color = "Time", y = "Pearson Correlation") +
theme(legend.position = "top")
ggarrange(a, b)Let’s fit several models with different variance-covariance structures:
# Identity variance model.
model_0 <- asreml(
fixed = y ~ Time + Tmt + Tmt:Time,
residual = ~ id(Plant):idv(Time),
data = grassUV
)
# Simple correlation model; homogeneous variance form.
model_1 <- asreml(
fixed = y ~ Time + Tmt + Tmt:Time,
residual = ~ id(Plant):corv(Time),
data = grassUV
)
# Exponential (or power) model; homogeneous variance form.
model_2 <- asreml(
fixed = y ~ Time + Tmt + Tmt:Time,
residual = ~ id(Plant):expv(Time),
data = grassUV
)
# Exponential (or power) model; heterogeneous variance form.
model_3 <- asreml(
fixed = y ~ Time + Tmt + Tmt:Time,
residual = ~ id(Plant):exph(Time),
data = grassUV
)
# Antedependence variance model of order 1
model_4 <- asreml(
fixed = y ~ Time + Tmt + Tmt:Time,
residual = ~ id(Plant):ante(Time),
data = grassUV
)
# Autoregressive model of order 1; homogeneous variance form.
model_5 <- asreml(
fixed = y ~ Time + Tmt + Tmt:Time,
residual = ~ id(Plant):ar1v(Time),
data = grassUV
)
# Autoregressive model of order 1; heterogeneous variance form.
model_6 <- asreml(
fixed = y ~ Time + Tmt + Tmt:Time,
residual = ~ id(Plant):ar1h(Time),
data = grassUV
)
# Unstructured variance model.
model_7 <- asreml(
fixed = y ~ Time + Tmt + Tmt:Time,
residual = ~ id(Plant):us(Time),
data = grassUV
)We can use the Akaike Information Criterion (AIC)(Akaike, 1974) or the Bayesian Information Criterion (BIC)(Stone, 1979) for comparing the fitted models. A lower AIC or BIC value indicates a better fit.
models <- list(
"idv" = model_0,
"corv" = model_1,
"expv" = model_2,
"exph" = model_3,
"ante" = model_4,
"ar1v" = model_5,
"ar1h" = model_6,
"us" = model_7
)
summary_models <- data.frame(
model = names(models),
aic = unlist(lapply(models, \(x) summary(x)$aic)),
bic = unlist(lapply(models, \(x) summary(x)$bic)),
loglik = unlist(lapply(models, \(x) summary(x)$loglik)),
nedf = unlist(lapply(models, \(x) summary(x)$nedf)),
param = unlist(lapply(models, \(x) attr(summary(x)$aic, "param"))),
row.names = NULL
)
summary_models |> print()
summary_models |>
ggplot(
aes(x = reorder(model, -bic), y = bic, group = 1)
) +
geom_point(size = 2) +
geom_text(aes(x = model, y = bic + 5, label = param), size = 5) +
geom_line() +
theme_minimal(base_size = 15) +
labs(x = NULL, y = "BIC")In this specific scenario, the antedependence model emerges as the optimal choice, as indicated by the Bayesian Information Criteria (BIC). The 1-factor antedependence structure elegantly models the variance-covariance matrix Σω × ω with the following decomposition:
Σ−1 = UDU′ where Uω × ω is a unit upper triangular matrix and D = diag(d1, ..., dω) is a diagonal matrix.
and the order in our case is 1.
The extract_rcov() retrieves these matrices for a closer
inspection of the results.
The table below shows the summary of Wald statistics for fixed effects for the models fitted.
At first glance, the table below looks challenging to interpret; however, the function translates the summary output into tangible forms—both the actual variance-covariance matrix and the correlation matrix.
Finally, to extract the variance-covariance matrix, let’s take the best model according to the BIC and run the code:
# Plot Correlation Matrix
p1 <- covcor_heat(matrix = mat$corr, legend = "none", size = 4.5) +
ggtitle(label = "Correlation Matrix (ante)")
p1
# Plot Variance-Covariance Matrix
p2 <- covcor_heat(
matrix = mat$vcov,
corr = FALSE,
legend = "none",
size = 4.5,
digits = 1
) +
ggtitle(label = "Covariance Matrix (ante)")
p2
ggarrange(p1, p2)The plot below compares the raw correlation matrix with the one derived post-application of the antedependence model.