lfmm2: Fitting Latent Factor Mixed Models (Least squares algorithm)
In LEA: LEA: an R package for Landscape and Ecological Association Studies

Description Usage Arguments Value Author(s) References See Also Examples

Latent Factor Mixed Models (LFMMs) are factor regression models in which the response variable is a genotypic matrix, and the explanatory variables are environmental measures of ecological interest or trait values. The lfmm2 function estimates latent factors based on an exact least-squares approach. The resulting object can be used by the function lfmm2.test to identify genetic polymorphisms exhibiting association with ecological gradients or phenotypes, while correcting for unobserved confounders. An MCMC estimation algorithm is implemented in the function lfmm.

1	lfmm2 (input, env, K, lambda)

`input`	A genotypic matrix or a character string containing a path to the input file. The genotypic matrix must be in the `lfmm{lfmm_format}` format without missing values (9 or `NA`). See `impute` for completion based on nonnegative matrix factorization and consider R packages for reading large matrices.
`env`	A matrix of environmental covariates or a character string containing a path to the environmental file. The environment matrix must be in the `env` format without missing values. Response variables must be encoded as `numeric`.
`K`	An integer corresponding to the number of latent factors.
`lambda`	A positive numeric value for a ridge regularization parameter. The default value is set to 1e-5.

lfmm2 returns an object of class lfmm2Class that contains $K$ estimated latent factors and their loadings.

The following method can be applied to an object of class lfmm2Class:

lfmm2.test

P-values adjusted for latent factors computed by lfmm2.

Olivier Francois

Caye K, Jumentier B, Lepeule J, Francois O. (2019). LFMM 2: fast and accurate inference of gene-environment associations in genome-wide studies. Molecular biology and evolution, 36(4), 852-860.

lfmm.data impute lfmm2.test pca lfmm tutorial

### Example of analysis using lfmm2 ###


# Simulation with 10 target loci, with effect sizes ranging between -10 an 10 
# n = 100 individuals and L = 1000 loci

X <- as.matrix(rnorm(100)) # causal environmental variable
B <- rep(0, 1000) 
target <- sample(1:1000, 10) # target loci
B[target] <- runif(10, -10, +10) # effect sizes

# Creating hidden factors and loadings

U <- t(tcrossprod(as.matrix(c(-1,0.5,1.5)), X))+ matrix(rnorm(300), ncol = 3)
V <- matrix(rnorm(3000), ncol = 3)

# Simulating a binarized matrix containing haploid genotypes 
# Simulation performed with the generative LFMM

Y <- tcrossprod(as.matrix(X), B) + tcrossprod(U, V) + matrix(rnorm(100000, sd = .5), nrow = 100)
Y <- matrix(as.numeric(Y > 0), ncol = 1000)

######################################
# Fitting an LFMM with K = 3 factors #
######################################

mod2 <- lfmm2(input = Y, env = X, K = 3)

# Computing P-values and plotting their minus log10 values 
# Target loci are highlighted

pv <- lfmm2.test(object = mod2, input = Y, env = X, linear = TRUE)
plot(-log10(pv$pvalues), col = "grey", cex = .4, pch = 19)
points(target, -log10(pv$pvalues[target]), col = "red")