minusloglik: Minus log-likelihood of copula models.
In CJAMP: Copula-Based Joint Analysis of Multiple Phenotypes
Description
Usage
Arguments
Details
Value
Examples
Description
Function to compute the minus log-likelihood of the joint distribution
of Y1 and Y2 given the predictors predictors_Y1
of Y1 and predictors_Y2 of Y2 in a copula model
for given parameter values parameters. Implemented are the
Clayton and 2-parameter copula. The function assumes quantitative
predictors and uses an additive model, i.e. for categorical predictors
with more than 2 levels, dummy variables have to be created beforehand.
Accordingly, if single nucleotide variants (SNVs) are included as
predictors, the computation is based on an additive genetic model if
SNVs are provided as 0-1-2 genotypes and on a dominant model if SNVs
are provided as 0-1 genotypes.
Usage
1
2
Arguments
copula
String indicating whether the likelihood should be computed
under the Clayton ("Clayton") or 2-parameter copula
("2param") model.
Y1
Numeric vector containing the first phenotype.
Y2
Numeric vector containing the second phenotype.
predictors_Y1
Dataframe containing the predictors of Y1
in columns.
predictors_Y2
Dataframe containing predictors of Y2
in columns.
parameters
Named integer vector containing the parameter estimates
of the marginal and copula parameters, for which the
log-likelihood will be computed. For details and the
necessary format of the vector, see the details below.
Details
The number of predictors is not fixed and also different predictors
can be supplied for Y1 and Y2. However, for the functioning
of the log-likelihood function, the parameters vector has to be
supplied in a pre-specified form and formatting:
The vector has to include the copula parameter(s), marginal parameters
for Y1, and marginal parameters for Y2 in this order.
For example, for the 2-parameter copula with parameters φ, θ
and marginal models
Y1 = α0 + α1*X1 + α2*X2 + ε1, ε1 ~ N(0,σ1^2),
Y1 = β0 + β1*X1 + ε2, ε2 ~ N(0,σ2^2),
the parameter vector has be
(log(φ), log(θ-1), log(σ1), log(σ2), α0, α2, α1, β0, β1).
log(φ) and log(θ-1) have to be provided instead of
φ, θ and log(σ1), log(σ2) instead of
σ1, σ2 for computational reasons when the log-likelihood
function is optimized in cjamp. As further necessary format,
the vector has to be named and the names of the copula parameter(s) has/have
to be log_phi and/or log_theta_minus1.
Value
Minus log-likelihood value (integer).
Examples
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# Generate genetic data:
set.seed(10)
genodata <- generate_genodata(n_SNV = 20, n_ind = 1000)
# Generate phenotype data:
phenodata <- generate_phenodata_2_copula(genodata = genodata, MAF_cutoff = 1,
prop_causal = 0.5, tau = 0.2,
b1 = 0.3, b2 = 0.3)
# Example 1: Log-likelihood of null model without covariates & genetic effects
estimates <- get_estimates_naive(Y1 = phenodata$Y1, Y2 = phenodata$Y2,
predictors_Y1 = NULL, predictors_Y2 = NULL,
copula_param = "both")
minusloglik(Y1 = phenodata$Y1, Y2 = phenodata$Y2, predictors_Y1 = NULL,
predictors_Y2 = NULL, parameters = estimates, copula = "2param")
# Example 2: Log-likelihood of null model with covariates, without genetic effects
predictors <- data.frame(X1 = phenodata$X1, X2 = phenodata$X2)
estimates <- get_estimates_naive(Y1 = phenodata$Y1, Y2 = phenodata$Y2,
predictors_Y1 = predictors,
predictors_Y2 = predictors,
copula_param = "both")
minusloglik(Y1 = phenodata$Y1, Y2 = phenodata$Y2, predictors_Y1 = predictors,
predictors_Y2 = predictors, parameters = estimates, copula = "2param")
# Example 3: Log-likelihood of model with covariates & genetic effect on Y1 only
predictors_Y1 <- data.frame(X1 = phenodata$X1, X2 = phenodata$X2,
SNV = genodata$SNV1)
predictors_Y2 <- data.frame(X1 = phenodata$X1, X2 = phenodata$X2)
estimates <- get_estimates_naive(Y1 = phenodata$Y1, Y2 = phenodata$Y2,
predictors_Y1 = predictors_Y1,
predictors_Y2 = predictors_Y2,
copula_param = "both")
minusloglik(Y1 = phenodata$Y1, Y2 = phenodata$Y2, predictors_Y1 = predictors_Y1,
predictors_Y2 = predictors_Y2, parameters = estimates,
copula = "2param")
# Example 4: Log-likelihood of model with covariates & genetic effect on Y2 only
predictors_Y1 <- data.frame(X1 = phenodata$X1, X2 = phenodata$X2)
predictors_Y2 <- data.frame(X1 = phenodata$X1, X2 = phenodata$X2,
SNV = genodata$SNV1)
estimates <- get_estimates_naive(Y1 = phenodata$Y1, Y2 = phenodata$Y2,
predictors_Y1 = predictors_Y1,
predictors_Y2 = predictors_Y2,
copula_param = "both")
minusloglik(Y1 = phenodata$Y1, Y2 = phenodata$Y2, predictors_Y1 = predictors_Y1,
predictors_Y2 = predictors_Y2, parameters = estimates,
copula = "2param")
# Example 5: Log-likelihood of model without covariates, with genetic effects
predictors <- data.frame(SNV = genodata$SNV1)
estimates <- get_estimates_naive(Y1 = phenodata$Y1, Y2 = phenodata$Y2,
predictors_Y1 = predictors,
predictors_Y2 = predictors,
copula_param = "both")
minusloglik(Y1 = phenodata$Y1, Y2 = phenodata$Y2, predictors_Y1 = predictors,
predictors_Y2 = predictors, parameters = estimates, copula = "2param")
# Example 6: Log-likelihood of model with covariates & genetic effects
predictors <- data.frame(X1 = phenodata$X1, X2 = phenodata$X2, SNV = genodata$SNV1)
estimates <- get_estimates_naive(Y1 = phenodata$Y1, Y2 = phenodata$Y2,
predictors_Y1 = predictors,
predictors_Y2 = predictors,
copula_param = "both")
minusloglik(Y1 = phenodata$Y1, Y2 = phenodata$Y2, predictors_Y1 = predictors,
predictors_Y2 = predictors, parameters = estimates, copula = "2param")
# Example 7: Log-likelihood of model with covariates & multiple genetic effects
predictors <- data.frame(X1 = phenodata$X1, X2 = phenodata$X2, genodata[, 1:5])
estimates <- get_estimates_naive(Y1 = phenodata$Y1, Y2 = phenodata$Y2,
predictors_Y1 = predictors,
predictors_Y2 = predictors,
copula_param = "both")
minusloglik(Y1 = phenodata$Y1, Y2 = phenodata$Y2, predictors_Y1 = predictors,
predictors_Y2 = predictors, parameters = estimates, copula = "2param")
CJAMP documentation built on May 1, 2019, 9:15 p.m.
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Description Usage Arguments Details Value Examples
Description
Function to compute the minus log-likelihood of the joint distribution
of Y1 and Y2 given the predictors predictors_Y1
of Y1 and predictors_Y2 of Y2 in a copula model
for given parameter values parameters. Implemented are the
Clayton and 2-parameter copula. The function assumes quantitative
predictors and uses an additive model, i.e. for categorical predictors
with more than 2 levels, dummy variables have to be created beforehand.
Accordingly, if single nucleotide variants (SNVs) are included as
predictors, the computation is based on an additive genetic model if
SNVs are provided as 0-1-2 genotypes and on a dominant model if SNVs
are provided as 0-1 genotypes.
Usage
1 2 |
Arguments
copula |
String indicating whether the likelihood should be computed
under the Clayton ( |
Y1 |
Numeric vector containing the first phenotype. |
Y2 |
Numeric vector containing the second phenotype. |
predictors_Y1 |
Dataframe containing the predictors of |
predictors_Y2 |
Dataframe containing predictors of |
parameters |
Named integer vector containing the parameter estimates of the marginal and copula parameters, for which the log-likelihood will be computed. For details and the necessary format of the vector, see the details below. |
Details
The number of predictors is not fixed and also different predictors
can be supplied for Y1 and Y2. However, for the functioning
of the log-likelihood function, the parameters vector has to be
supplied in a pre-specified form and formatting:
The vector has to include the copula parameter(s), marginal parameters
for Y1, and marginal parameters for Y2 in this order.
For example, for the 2-parameter copula with parameters φ, θ
and marginal models
Y1 = α0 + α1*X1 + α2*X2 + ε1, ε1 ~ N(0,σ1^2),
Y1 = β0 + β1*X1 + ε2, ε2 ~ N(0,σ2^2),
the parameter vector has be
(log(φ), log(θ-1), log(σ1), log(σ2), α0, α2, α1, β0, β1).
log(φ) and log(θ-1) have to be provided instead of
φ, θ and log(σ1), log(σ2) instead of
σ1, σ2 for computational reasons when the log-likelihood
function is optimized in cjamp. As further necessary format,
the vector has to be named and the names of the copula parameter(s) has/have
to be log_phi and/or log_theta_minus1.
Value
Minus log-likelihood value (integer).
Examples
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 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 | # Generate genetic data:
set.seed(10)
genodata <- generate_genodata(n_SNV = 20, n_ind = 1000)
# Generate phenotype data:
phenodata <- generate_phenodata_2_copula(genodata = genodata, MAF_cutoff = 1,
prop_causal = 0.5, tau = 0.2,
b1 = 0.3, b2 = 0.3)
# Example 1: Log-likelihood of null model without covariates & genetic effects
estimates <- get_estimates_naive(Y1 = phenodata$Y1, Y2 = phenodata$Y2,
predictors_Y1 = NULL, predictors_Y2 = NULL,
copula_param = "both")
minusloglik(Y1 = phenodata$Y1, Y2 = phenodata$Y2, predictors_Y1 = NULL,
predictors_Y2 = NULL, parameters = estimates, copula = "2param")
# Example 2: Log-likelihood of null model with covariates, without genetic effects
predictors <- data.frame(X1 = phenodata$X1, X2 = phenodata$X2)
estimates <- get_estimates_naive(Y1 = phenodata$Y1, Y2 = phenodata$Y2,
predictors_Y1 = predictors,
predictors_Y2 = predictors,
copula_param = "both")
minusloglik(Y1 = phenodata$Y1, Y2 = phenodata$Y2, predictors_Y1 = predictors,
predictors_Y2 = predictors, parameters = estimates, copula = "2param")
# Example 3: Log-likelihood of model with covariates & genetic effect on Y1 only
predictors_Y1 <- data.frame(X1 = phenodata$X1, X2 = phenodata$X2,
SNV = genodata$SNV1)
predictors_Y2 <- data.frame(X1 = phenodata$X1, X2 = phenodata$X2)
estimates <- get_estimates_naive(Y1 = phenodata$Y1, Y2 = phenodata$Y2,
predictors_Y1 = predictors_Y1,
predictors_Y2 = predictors_Y2,
copula_param = "both")
minusloglik(Y1 = phenodata$Y1, Y2 = phenodata$Y2, predictors_Y1 = predictors_Y1,
predictors_Y2 = predictors_Y2, parameters = estimates,
copula = "2param")
# Example 4: Log-likelihood of model with covariates & genetic effect on Y2 only
predictors_Y1 <- data.frame(X1 = phenodata$X1, X2 = phenodata$X2)
predictors_Y2 <- data.frame(X1 = phenodata$X1, X2 = phenodata$X2,
SNV = genodata$SNV1)
estimates <- get_estimates_naive(Y1 = phenodata$Y1, Y2 = phenodata$Y2,
predictors_Y1 = predictors_Y1,
predictors_Y2 = predictors_Y2,
copula_param = "both")
minusloglik(Y1 = phenodata$Y1, Y2 = phenodata$Y2, predictors_Y1 = predictors_Y1,
predictors_Y2 = predictors_Y2, parameters = estimates,
copula = "2param")
# Example 5: Log-likelihood of model without covariates, with genetic effects
predictors <- data.frame(SNV = genodata$SNV1)
estimates <- get_estimates_naive(Y1 = phenodata$Y1, Y2 = phenodata$Y2,
predictors_Y1 = predictors,
predictors_Y2 = predictors,
copula_param = "both")
minusloglik(Y1 = phenodata$Y1, Y2 = phenodata$Y2, predictors_Y1 = predictors,
predictors_Y2 = predictors, parameters = estimates, copula = "2param")
# Example 6: Log-likelihood of model with covariates & genetic effects
predictors <- data.frame(X1 = phenodata$X1, X2 = phenodata$X2, SNV = genodata$SNV1)
estimates <- get_estimates_naive(Y1 = phenodata$Y1, Y2 = phenodata$Y2,
predictors_Y1 = predictors,
predictors_Y2 = predictors,
copula_param = "both")
minusloglik(Y1 = phenodata$Y1, Y2 = phenodata$Y2, predictors_Y1 = predictors,
predictors_Y2 = predictors, parameters = estimates, copula = "2param")
# Example 7: Log-likelihood of model with covariates & multiple genetic effects
predictors <- data.frame(X1 = phenodata$X1, X2 = phenodata$X2, genodata[, 1:5])
estimates <- get_estimates_naive(Y1 = phenodata$Y1, Y2 = phenodata$Y2,
predictors_Y1 = predictors,
predictors_Y2 = predictors,
copula_param = "both")
minusloglik(Y1 = phenodata$Y1, Y2 = phenodata$Y2, predictors_Y1 = predictors,
predictors_Y2 = predictors, parameters = estimates, copula = "2param")
|
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