Description Usage Arguments Details Value Author(s) Examples

This function computes regularized least squares estimates for latent factor mixed models using a ridge penalty.

1 2 | ```
lfmm_ridge(Y, X, K, lambda = 1e-05, algorithm = "analytical",
it.max = 100, relative.err.min = 1e-06)
``` |

`Y` |
a response variable matrix with n rows and p columns. Each column corresponds to a distinct response variable (e.g., SNP genotype, gene expression level, beta-normalized methylation profile, etc). Response variables must be encoded as numeric. |

`X` |
an explanatory variable matrix with n rows and d columns. Each column corresponds to a distinct explanatory variable (eg. phenotype). Explanatory variables must be encoded as numeric variables. |

`K` |
an integer for the number of latent factors in the regression model. |

`lambda` |
a numeric value for the regularization parameter. |

`algorithm` |
exact (analytical) algorithm or numerical algorithm. The exact algorithm is based on the global minimum of the loss function and computation is very fast. The numerical algorithm converges toward a local minimum of the loss function. The exact method should preferred. The numerical method is for very large n. |

`it.max` |
an integer value for the number of iterations for the numerical algorithm. |

`relative.err.epsilon` |
a numeric value for a relative convergence error. Test whether the numerical algorithm converges or not (numerical algorithm only). |

The algorithm minimizes the following penalized least-squares criterion

* L(U, V, B) = \frac{1}{2} ||Y - U V^{T} - X B^T||_{F}^2
+ \frac{λ}{2} ||B||^{2}_{2} ,*

where Y is a response data matrix, X contains all explanatory variables, U denotes the score matrix, V is the loading matrix, B is the (direct) effect size matrix, and lambda is a regularization parameter.

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

an object of class `lfmm`

with the following attributes:

U the latent variable score matrix with dimensions n x K,

V the latent variable axis matrix with dimensions p x K,

B the effect size matrix with dimensions p x d.

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 45 46 47 48 49 50 51 52 53 54 55 | ```
library(lfmm)
## a GWAS example with Y = SNPs and X = phenotype
data(example.data)
Y <- example.data$genotype
X <- example.data$phenotype
## Fit an LFMM with K = 6 factors
mod.lfmm <- lfmm_ridge(Y = Y,
X = X,
K = 6)
## Perform association testing using the fitted model:
pv <- lfmm_test(Y = Y,
X = X,
lfmm = mod.lfmm,
calibrate = "gif")
## Manhattan plot with causal loci shown
pvalues <- pv$calibrated.pvalue
plot(-log10(pvalues), pch = 19,
cex = .2, col = "grey", xlab = "SNP")
points(example.data$causal.set,
-log10(pvalues)[example.data$causal.set],
type = "h", col = "blue")
## An EWAS example with Y = methylation data and X = exposure
Y <- scale(skin.exposure$beta.value)
X <- scale(as.numeric(skin.exposure$exposure))
## Fit an LFMM with 2 latent factors
mod.lfmm <- lfmm_ridge(Y = Y,
X = X,
K = 2)
## Perform association testing using the fitted model:
pv <- lfmm_test(Y = Y,
X = X,
lfmm = mod.lfmm,
calibrate = "gif")
## Manhattan plot with true associations shown
pvalues <- pv$calibrated.pvalue
plot(-log10(pvalues),
pch = 19,
cex = .3,
xlab = "Probe",
col = "grey")
causal.set <- seq(11, 1496, by = 80)
points(causal.set,
-log10(pvalues)[causal.set],
col = "blue")
``` |

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