Description Usage Arguments Details Value Author(s) Examples

This function returns 'direct' effect sizes for the regression of X (of dimension 1) on the matrix Y, as usually computed in genome-wide association studies.

1 | ```
effect_size(Y, X, lfmm.object)
``` |

`Y` |
a response variable matrix with n rows and p columns. Each column is a response variable (numeric). |

`X` |
an explanatory variable with n rows and d = 1 column (numeric). |

`lfmm.object` |
an object of class |

The response variable matrix Y and the explanatory variable are centered.

a vector of length p containing all effect sizes for the regression of X on the matrix Y

cayek, francoio

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 | ```
library(lfmm)
## Simulation of 1000 genotypes for 100 individuals (y)
u <- matrix(rnorm(300, sd = 1), nrow = 100, ncol = 2)
v <- matrix(rnorm(3000, sd = 2), nrow = 2, ncol = 1000)
y <- matrix(rbinom(100000, size = 2,
prob = 1/(1 + exp(-0.3*(u%*%v
+ rnorm(100000, sd = 2))))),
nrow = 100,
ncol = 1000)
#PCA of genotypes, 3 main axes of variation (K = 2)
plot(prcomp(y))
## 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)
## Compute effect sizes using lfmm_ridge
## Note that centering is important (scale = F).
mod.lfmm <- lfmm_ridge(Y = y,
X = x,
K = 2)
## Compute direct effect sizes using lfmm_ridge estimates
b.estimates <- effect_size(y, x, mod.lfmm)
## plot the last 30 effect sizes (true values are 0 and 6000)
plot(b.estimates[971:1000])
abline(0, 0)
abline(6000, 0, col = 2)
## Prediction of phenotypes
candidates <- 991:1000 #set of causal loci
x.pred <- scale(y[,candidates], scale = F) %*% matrix(b.estimates[candidates])
## Check predictions
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)
``` |

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