lfmm.R
In lfmm: Latent Factor Mixed Models

## ------------------------------------------------------------------------
#devtools::install_github("bcm-uga/lfmm")

## ------------------------------------------------------------------------
library(lfmm)

## ------------------------------------------------------------------------
## Simulated phenotypes for Arabidopsis thaliana SNP data
data("example.data")
## Simulated (and real) methylation levels for sun-exposed tissue sampled
data("skin.exposure")

## ------------------------------------------------------------------------
Y <- example.data$genotype
pc <- prcomp(Y)
plot(pc$sdev[1:20]^2, xlab = 'PC', ylab = "Variance explained")
points(6,pc$sdev[6]^2, type = "h", lwd = 3, col = "blue")

## ------------------------------------------------------------------------
Y <- skin.exposure$beta.value
pc <- prcomp(Y)
plot(pc$sdev[1:20]^2, xlab = 'PC', ylab = "Variance explained")
points(2,pc$sdev[2]^2, type = "h", lwd = 3, col = "blue")

## ------------------------------------------------------------------------
Y <- example.data$genotype
X <- example.data$phenotype #scaled phenotype

## ------------------------------------------------------------------------
## Fit an LFMM, i.e, compute B, U, V estimates
mod.lfmm <- lfmm_ridge(Y = Y, 
                       X = X, 
                       K = 6)

## ------------------------------------------------------------------------
 ## performs association testing using the fitted model:
 pv <- lfmm_test(Y = Y, 
                 X = X, 
                 lfmm = mod.lfmm, 
                 calibrate = "gif")

## ------------------------------------------------------------------------
pvalues <- pv$calibrated.pvalue 
qqplot(rexp(length(pvalues), rate = log(10)),
       -log10(pvalues), xlab = "Expected quantile",
       pch = 19, cex = .4)
abline(0,1)

## ------------------------------------------------------------------------
 ## Manhattan plot
 plot(-log10(pvalues), 
      pch = 19, 
      cex = .2, 
      xlab = "SNP", ylab = "-Log P",
      col = "grey")
 points(example.data$causal.set, 
        -log10(pvalues)[example.data$causal.set], 
        type = "h", 
        col = "blue")

## ------------------------------------------------------------------------
Y <- scale(skin.exposure$beta.value)
X <- scale(as.numeric(skin.exposure$exposure))

## ------------------------------------------------------------------------
## Fit and LFMM, i.e, compute B, U, V estimates
mod.lfmm <- lfmm_ridge(Y = Y, 
                       X = X, 
                       K = 2)
 
## Perform association testing using the fitted model:
pv <- lfmm_test(Y = Y, 
                X = X, 
                lfmm = mod.lfmm, 
                calibrate = "gif")

## ------------------------------------------------------------------------
## Manhattan plot
plot(-log10(pv$calibrated.pvalue), 
     pch = 19, 
     cex = .3,
     xlab = "Probe", ylab = "-Log P",
     col = "grey")
causal.set <- seq(11, 1496, by = 80)
points(causal.set, 
       -log10(pv$calibrated.pvalue)[causal.set], 
       col = "blue")

## ------------------------------------------------------------------------
Y <- example.data$genotype
X <- example.data$phenotype #scaled phenotype

## ---- message = FALSE----------------------------------------------------
## Fit an LFMM, i.e, compute B, U, V estimates
mod.lfmm <- lfmm_lasso(Y = Y, 
                       X = X, 
                       K = 6,
                       nozero.prop = 0.01)

## ------------------------------------------------------------------------
## performs association testing using the fitted model:
pv <- lfmm_test(Y = Y, 
                X = X, 
                lfmm = mod.lfmm, 
                calibrate = "gif")

## ------------------------------------------------------------------------
pvalues <- pv$calibrated.pvalue 
qqplot(rexp(length(pvalues), rate = log(10)),
       -log10(pvalues), xlab = "Expected quantile",
       pch = 19, cex = .4)
abline(0,1)

## ------------------------------------------------------------------------
## Manhattan plot
plot(-log10(pvalues), 
     pch = 19, 
     cex = .2, 
     xlab = "SNP", ylab = "-Log P",
     col = "grey")
points(example.data$causal.set, 
       -log10(pvalues)[example.data$causal.set], 
       type = "h", 
       col = "blue")

## ------------------------------------------------------------------------
## Simulation of 1000 genotypes for 100 individuals (y)
u <- matrix(rnorm(300, sd = 1), nrow = 100, ncol = 3) 
v <- matrix(rnorm(3000, sd = 2), nrow = 3, ncol = 1000)
w <- u %*% v
y <- matrix(rbinom(100000, size = 2, 
                   prob = 1/(1 + exp(-0.3*(w 
                   + rnorm(100000, sd = 2))))),
                   nrow = 100,
                   ncol = 1000)

## Simulation of 1000 phenotypes (x)
## Only the last 10 genotypes have significant effect sizes (b)
b <- matrix(c(rep(0, 990), rep(6000, 10)))
x <- y%*%b + rnorm(100, sd = 100)

## ------------------------------------------------------------------------
mod <- lfmm_ridge(Y = y, 
                  X = x,
                  K = 2)

## ------------------------------------------------------------------------
candidates <- 991:1000 #causal loci
b.values <- effect_size(Y = y, X = x, lfmm.object = mod) 
x.pred <- scale(y[,candidates], scale = F)%*% matrix(b.values[candidates])

## ------------------------------------------------------------------------
##Compare simulated and predicted/fitted phenotypes
plot(x - mean(x), x.pred, 
     pch = 19, col = "grey", 
     xlab = "Observed phenotypes (centered)", 
     ylab = "Predicted from PRS")
abline(0,1)
abline(lm(x.pred ~ scale(x, scale = FALSE)), col = 2)

## ------------------------------------------------------------------------
pred <- predict_lfmm(Y = y, 
                     X = x,
                     fdr.level = 0.25, 
                     mod)
 
##Compare simulated and predicted/fitted phenotypes
plot(x - mean(x), pred$pred, 
     pch = 19, col = "grey", 
     xlab = "Observed phenotypes (centered)", 
     ylab = "Predicted from PRS")
abline(0,1)
abline(lm(pred$pred ~ scale(x, scale = FALSE)), col = 2)