get_estimates_naive {CJAMP} | R Documentation |
Naive estimates of the copula and marginal parameters.
Description
Function to compute naive estimates of the copula parameter(s)
and maximum likelihood (ML) estimates of the marginal parameters in a joint
copula model of Y1
and Y2
given the predictors of Y1
and Y2
. The main use of the function is to provide parameter
starting values for the optimization of the log-likelihood function of the
joint copula model in cjamp
in order to obtain maximum
likelihood estimates in the copula model.
Usage
get_estimates_naive(Y1 = NULL, Y2 = NULL, predictors_Y1 = NULL,
predictors_Y2 = NULL, copula_param = "both")
Arguments
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 the predictors of |
copula_param |
String indicating whether estimates should be computed
for |
Details
The estimates of the copula parameter(s) include estimates of \phi
(if copula_param == "phi"
), \theta
(if
copula_param == "theta"
) or both (if copula_param == "both"
).
They are obtained by computing Kendall's tau between Y1
and Y2
and using the relationship \tau = \phi/(\phi+2)
of the Clayton
copula to obtain an estimate of \phi
and \tau = (\theta-1)/\theta
of the Gumbel copula to obtain an estimate of \theta
.
The ML estimates of the marginal parameters include estimates of the log standard
deviations of Y1
, Y2
given their predictors (log(\sigma1), log(\sigma2)
)
and of the effects of predictors_Y1
on Y1
and
predictors_Y2
on Y2
. The estimates of the marginal effects are
obtained from linear regression models of Y1
given predictors_Y1
and Y2
given predictors_Y2
, respectively. If single nucleotide
variants (SNVs) are included as predictors, the genetic effect estimates
are obtained from an underlying additive genetic model if SNVs are provided
as 0-1-2 genotypes and from an underlying dominant model if SNVs are provided
as 0-1 genotypes.
Value
Vector of the numeric estimates of the copula parameters
log(\phi)
and/or log(\theta-1)
, of the marginal
parameters (log(\sigma1), log(\sigma2)
, and estimates
of the effects of the predictors predictors_Y1
on Y1
and predictors_Y2
on Y2
).
Examples
# 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)
predictors <- data.frame(X1 = phenodata$X1, X2 = phenodata$X2,
SNV = genodata$SNV1)
get_estimates_naive(Y1 = phenodata$Y1, Y2 = phenodata$Y2,
predictors_Y1 = predictors, predictors_Y2 = predictors,
copula_param = "both")